Patent Publication Number: US-9842757-B2

Title: Robot and adaptive placement system and method

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority under 35 USC 119(e) on Provisional Patent Application No. 61/831,320 filed Jun. 5, 2013 and Provisional Patent Application No. 61/868,131 filed Aug. 21, 2013 and Provisional Patent Application No. 61/945,306 filed Feb. 27, 2014, which are hereby incorporated by reference in their entireties. 
    
    
     BACKGROUND 
     Technical Field 
     The exemplary and non-limiting embodiments relate generally to a robot and an adaptive placement system and method and more particularly to a substrate transport robot and an adaptive substrate placement system and method. 
     Brief Description of Prior Developments 
     Substrate processing systems for semiconductor, LED or other suitable applications often require very accurate transfer and placement of substrates within the system to facilitate low process variability. Variables which affect the placement precision may include vibration, movement of the substrates on the transport system or within process modules of the processing system, thermal effects or otherwise. To overcome such variability, systems have added sensors and algorithms that attempt to detect and correct for such variables which affect the placement precision. In practice, the amount of error and variability is very sensitive to factors such as calibration accuracy, sensor variability or otherwise. Accordingly, there is a desire for a substrate transport robot and substrate placement system that is repeatable, precise and insensitive. 
     SUMMARY 
     The following summary is merely intended to be exemplary. The summary is not intended to limit the scope of the claims. 
     An example method may comprise moving a substrate, located on a first end effector of a robot, from a first location towards a second location by the robot; determining location of a fiducial on the substrate while the substrate is being moved from the first location towards the second location; and comparing the determined location of the fiducial with a reference fiducial location while the robot is moving the substrate from the first location towards the second location. 
     An example apparatus may comprise at least one processor; and at least one non-transitory memory including computer program code, the at least one memory and the computer program code configured to, with the at least one processor, cause the apparatus to: determine location of a fiducial on a substrate while the substrate is being moved from a first location towards a second location, where the substrate is located on a first end effector of the apparatus; and compare the determined location of the fiducial with a reference fiducial location while the apparatus is moving the substrate from the first location towards the second location. 
     An example apparatus may comprise a non-transitory program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine for performing operations, the operations comprising: determining location of a fiducial on a substrate while the substrate is being moved from a first location towards a second location, where the substrate is located on an end effector of a robot; and comparing the determined location of the fiducial with a reference fiducial location while the robot is moving the substrate from the first location towards the second location. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing aspects and other features are explained in the following description, taken in connection with the accompanying drawings, wherein: 
         FIG. 1  is a top view of an example substrate transport robot; 
         FIG. 2  is a top view of an example substrate transport robot; 
         FIG. 3  is a section schematic view of an example substrate transport robot; 
         FIG. 4  is a section schematic view of an example substrate transport robot; 
         FIG. 5  is a diagram illustrating an example apparatus; 
         FIG. 6  is a diagram illustrating an example apparatus; 
         FIG. 7  is a diagram illustrating an example apparatus; 
         FIG. 8  is a diagram illustrating an example apparatus; 
         FIG. 9  is a diagram illustrating an example apparatus; 
         FIG. 10A  is a diagram illustrating an image sensor in an example apparatus; 
         FIG. 10B  is a diagram illustrating an image sensor in an example apparatus; 
         FIG. 10C  is a diagram illustrating an image sensor in an example apparatus; 
         FIG. 11A  is a diagram illustrating an example apparatus; 
         FIG. 11B  is a diagram illustrating an example apparatus; 
         FIG. 12  is a pattern of vectors; 
         FIG. 13  is a substrate; 
         FIG. 14A  is a process flow diagram; 
         FIG. 14B  is a process flow diagram; 
         FIG. 14C  is a process flow diagram; 
         FIG. 15  is a top view of an example substrate transport robot; 
         FIG. 16  is a top view of an example substrate transport robot; 
         FIG. 17  is a section schematic view of an example substrate transport robot; 
         FIG. 18  is a section schematic view of an example substrate transport robot; 
         FIG. 19  is a top view of an example substrate transport robot; 
         FIG. 20  is a top view of an example substrate transport robot; 
         FIG. 21  is a section schematic view of an example substrate transport robot; 
         FIG. 22  is a top schematic view of an exemplary link apparatus; 
         FIG. 23  is a side schematic view of an exemplary linkage apparatus; 
         FIG. 24  is a top schematic view of an exemplary wrist apparatus; 
         FIG. 25  is a side section schematic view of an exemplary wrist apparatus; 
         FIG. 26  is a top section schematic view of an exemplary wrist apparatus; 
         FIG. 27  is a top schematic view illustrating an example end effector apparatus; 
         FIG. 28  is a top schematic view illustrating an example end effector apparatus; 
         FIG. 29  is a top schematic view illustrating an example end effector apparatus; 
         FIG. 30  is a top schematic view illustrating an example end effector apparatus; 
         FIG. 31  is a top schematic view illustrating an example end effector apparatus; 
         FIG. 32  is a top schematic view illustrating an example end effector apparatus; 
         FIG. 33  shows a top view of a robot; 
         FIG. 34  shows a side view of a robot; 
         FIG. 35A  shows a top view of a robot in a retracted position; 
         FIG. 35B  shows a top view of a robot with a first arm extended; 
         FIG. 35C  shows a top view of a robot with a second arm extended; 
         FIG. 36A  shows a top view of a robot in a retracted position; 
         FIG. 36B  shows a top view of a robot with first and second arms extending; 
         FIG. 36C  shows a top view of a robot with first and second arms extended; 
         FIG. 37A  shows a section schematic view of a robot; 
         FIG. 37B  shows a section schematic view of a robot; 
         FIG. 38A  shows a section schematic view of a robot; 
         FIG. 38B  shows a section schematic view of a robot; 
         FIG. 39A  shows a section schematic view of a robot; and 
         FIG. 39B  shows a section schematic view of a robot. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     Referring to  FIG. 1 , there is shown a schematic top plan view of an example substrate transport robot  100 . Although the present embodiment will be described with reference to the embodiments shown in the drawings, it should be understood that the present invention may be embodied in many forms of alternative embodiments. In addition, any suitable size, shape or type of materials or elements could be used. 
     Robot  100  may be a vacuum compatible or any suitable robot having drive portion  110  and arm portion  112  coupled to drive portion  110  as will be described in greater detail below. Arm  112  is shown having a common upper arm  114  and two independently operable forearms  116 ,  118  coupled by elbow joints  120 ,  122  respectively to upper arm  114 . Forearm  116  has independently operable end effector set  124 ,  126  coupled to forearm  116  at wrist  128 . Similarly, forearm  118  has independently operable end effector set  130 ,  132  coupled to forearm  118  at wrist  134 . In the embodiment shown, substrates  136 ,  138  may simultaneously be transported to and from stations within a piece of equipment where picking or placement of substrates  136 ,  138  may be done independently and simultaneously where each may be positioned at a location independent of the other. The plurality (one or more) of sets of end effectors have the end effectors connected to the drive by the movable arm assembly. Here, a first one of the sets of end effectors has at least two of the end effectors, where the drive and the movable arm assembly are configured to move the at least two end effectors substantially in unison from a retracted position towards an extended position towards two different respective target locations. The at least two end effectors are at least partially independently movable relative to each other on the moveable arm assembly. Referring also to  FIG. 2 , there is shown a schematic top plan view of an example substrate transport robot  150 . Robot  150  may be a vacuum compatible or any suitable robot having drive portion  110  and arm portion  160  coupled to drive portion  110  as will be described in greater detail below. Arm  160  is shown having two independently driven upper arms  162 ,  164  and two independently operable forearms  166 ,  168  coupled by elbow joints  170 ,  172  respectively to upper arms  162 ,  164 . Forearm  166  has independently operable end effectors  174 ,  176  coupled to forearm  166  at wrist  178 . Similarly, forearm  168  has independently operable end effectors  180 ,  182  coupled to forearm  168  at wrist  184 . In the embodiment shown, substrates  136 ,  138  may simultaneously be transported to and from stations within a piece of equipment where picking or placement of substrates  136 ,  138  may be done independently and simultaneously where each may be positioned at a location independent of the other. In the embodiment shown, the upper arm link lengths and forearm link lengths may be different and driven by circular or non circular pulleys. An example of arms having unequal link lengths and driven by non circular pulleys is given in U.S. patent application Ser. No. 13/833,732 entitled “Robot having Arm with Unequal Link Lengths” filed Mar. 15, 2013 which is incorporated by reference herein in its entirety. In alternate aspects, arms with the same link lengths or arms with unequal link lengths and having circular pulleys may be provided.  FIGS. 1 and 2  each show two arms having two end effectors. In alternate aspects, a single arm having a single or multiple end effectors may be provided. 
     Referring to  FIG. 3 , there is shown a schematic cross section of robot  100 . Drive  110  is shown having 5 coaxial shafts coupled to coaxial motor encoder arrangements  210 ,  212 ,  214 ,  216 ,  218  designated as inner shafts to the outer. Each motor arrangement may be located within vacuum tight housing  110 . Alternately, only the rotors of motors of drives  210 ,  212 ,  214 ,  216 ,  218  may be in vacuum in the drive housing  220  where a sleeve may be provided between the rotors and stators. A vertical drive  222 , such as a lead screw or other suitable drive may lift and lower housing  220  where slides  224  may constrain housing  220  in a vertical direction and bellows  226  may be coupled to housing  220  and flange  228  to maintain a vacuum environment where arm  112  and the inner portion of housing  220  may be exposed to vacuum. The shaft of drive  218  is directly coupled to the common upper arm  114 . The shaft of drive  216  is directly coupled to pulley  230  which is in turn coupled by bands to pulley  232  in elbow  122  where pulley  232  is directly coupled to forearm  118 . Here rotation of motor  216  rotates forearm  118  about the elbow  122 . The shaft of drive  214  is directly coupled to pulley  234  which is in turn coupled by bands to pulley  236  in elbow  120  where pulley  236  is directly coupled to forearm  116 . Here rotation of motor  214  rotates forearm  116  about the elbow  120 . The shaft of drive  212  is directly coupled to pulley  238  which is in turn coupled by bands to pulley  240  in elbow  122  where pulley  240  is directly coupled to pulley  242  in elbow  122 . Pulley  242  is then coupled by bands to pulley  244  in wrist  134  where pulley  244  is directly coupled to lower end effector  132 . Here, rotation of motor  212  rotates lower end effector  132  about the wrist  134 . Similarly, pulley  238  is also coupled by bands to pulley  246  in elbow  120  where pulley  246  is directly coupled to pulley  248  in elbow  120 . Pulley  248  is then coupled by bands to pulley  250  in wrist  128  where pulley  250  is directly coupled to lower end effector  126 . Here, rotation of motor  212  rotates lower end effector  126  about the wrist  128 . Further, rotation of motor  212  simultaneously rotates both lower end effectors  126 ,  132  about their respective wrists  128 ,  134 . The shaft of drive  210  is directly coupled to pulley  252  which is in turn coupled by bands to pulley  254  in elbow  122  where pulley  254  is directly coupled to pulley  256  in elbow  122 . Pulley  256  is then coupled by bands to pulley  258  in wrist  134  where pulley  258  is directly coupled to upper end effector  130 . Here, rotation of motor  210  rotates upper end effector  130  about the wrist  134 . Similarly, pulley  252  is also coupled by bands to pulley  260  in elbow  120  where pulley  260  is directly coupled to pulley  262  in elbow  120 . Pulley  262  is then coupled by bands to pulley  264  in wrist  128  where pulley  250  is directly coupled to upper end effector  124 . Here, rotation of motor  210  rotates upper end effector  124  about the wrist  128 . Further, rotation of motor  210  simultaneously rotates both upper end effectors  124 ,  130  about their respective wrists  128 ,  134 . The shafts associated with drives  210 ,  212 ,  214 ,  216 ,  218  are each independently and coaxially rotatable and may be supported by any suitable bearing or other arrangement with respect to housing  220  as shown or otherwise. The three pulleys in each of elbows  120 ,  122  and the two pulleys in each of wrists  128 ,  134  are each independently and coaxially rotatable with respect to a common axis in each joint and may be supported by any suitable bearing or other arrangement as shown or otherwise. The following description of respective pulley ratios is based on the premise that the link lengths of each link are the same. In alternate aspects, different ratios or driving arrangement may be provided, for example, where the link lengths are different. An example of arms having unequal link lengths and driven by non circular pulleys is given in U.S. patent application Ser. No. 13/833,732 entitled “Robot having Arm with Unequal Link Lengths” filed Mar. 15, 2013 which is incorporated by reference herein in its entirety. In the embodiment shown, pulleys and bands are provided. In alternate embodiments, any suitable power transmission arrangement may be provided, for example, belts, links, gears, cable or any suitable arrangement. In the embodiment shown, 5 coaxial direct driving shafts are provided. In alternate embodiments, any suitable driving arrangement may be provided, for example, motors in joints, links, speed reducers, belts, magnetic couplings, linear and/or rotational drives or any suitable drive may be provided. In the embodiment shown, the ratio between pulleys  230 ,  232  and  234 ,  236  may be any suitable ratio, for example, 1:1 or higher or lower than 1:1. In the embodiment shown, the ratio between pulleys  238 ,  240  and  238 ,  246  may be any suitable ratio, for example, 1:3 or higher or lower than 1:3. In the embodiment shown, the ratio between pulleys  252 ,  254  and  252 ,  250  may be any suitable ratio, for example, 1:3 or higher or lower than 1:3. In the embodiment shown, the ratio between pulleys  242 ,  244  and  248 ,  250  may be any suitable ratio, for example, 1:2. In the embodiment shown, the ratio between pulleys  256 ,  258  and  262 ,  264  may be any suitable ratio, for example, 1:2. In operation, simultaneous rotation of all of drives  210 ,  212 ,  214 ,  216 ,  218  rotates the entire arm assembly. Simultaneous rotation of common link  114 , pulleys  234 ,  238  and  252  with counter rotation of pulley  230  cause end effectors  130 ,  132  to extend or retract while end effectors  124 ,  126  rotate with common upper arm  114 . Similarly, simultaneous rotation of common link  114 , pulleys  230 ,  238  and  252  with counter rotation of pulley  234  cause end effectors  124 ,  126  to extend or retract while end effectors  130 ,  132  rotate with common upper arm  114 . Further, relative rotation of pulley  238  will cause a corresponding relative rotation of end effectors  132 ,  126 . Similarly, relative rotation of pulley  252  will cause a corresponding relative rotation of end effectors  130 ,  124 . With the 5 rotary axis drive and arm arrangement described, 2 substrates may be independently placed at different locations as will be described in greater detail below. For example, 2 substrates supported on end effectors  130 ,  132  may be independently placed at two locations. Similarly, 2 substrates supported on end effectors  124 ,  126  may be independently placed at two locations. In alternate aspects, more or less arms and axis&#39; may be provided. 
     Referring to  FIG. 4 , there is shown a schematic cross section of robot  150 . Drive  110  is shown having 5 coaxial shafts coupled to coaxial motor encoder arrangements  210 ,  212 ,  214 ,  216 ,  218  designated as inner shafts to the outer and as described above. The shaft of drive  218  is directly coupled to upper arm  164 . The shaft of drive  210  is directly coupled to upper arm  162 . Here, arms  162 ,  164  are independently rotatable. The shaft of drive  216  is directly coupled to pulley  310  which is in turn coupled by bands to pulley  312  in elbow  172  where pulley  312  is directly coupled to forearm  168 . Here rotation of motor  216  rotates forearm  168  about the elbow  172 . Pulley  310  which is then coupled by bands to pulley  314  in elbow  170  where pulley  314  is directly coupled to forearm  166 . Here rotation of motor  216  rotates forearm  166  about the elbow  170 . Further, rotation of motor  216  simultaneously rotates both forearms  168 ,  166  about their respective elbows  172 ,  170 . The shaft of drive  214  is directly coupled to pulley  316  which is in turn coupled by bands to pulley  318  in elbow  172  where pulley  318  is directly coupled to pulley  320  in elbow  172 . Pulley  320  is then coupled by bands to pulley  322  in wrist  184  where pulley  322  is directly coupled to lower end effector  182 . Here, rotation of motor  214  rotates lower end effector  182  about the wrist  184 . Similarly, pulley  310  is also coupled by bands to pulley  324  in elbow  170  where pulley  324  is directly coupled to pulley  326  in elbow  170 . Pulley  326  is then coupled by bands to pulley  328  in wrist  178  where pulley  328  is directly coupled to lower end effector  176 . Here, rotation of motor  214  rotates lower end effector  176  about the wrist  178 . Further, rotation of motor  214  simultaneously rotates both lower end effectors  176 ,  182  about their respective wrists  178 ,  184 . The shaft of drive  212  is directly coupled to pulley  330  which is in turn coupled by bands to pulley  332  in elbow  172  where pulley  332  is directly coupled to pulley  334  in elbow  172 . Pulley  334  is then coupled by bands to pulley  336  in wrist  184  where pulley  336  is directly coupled to upper end effector  180 . Here, rotation of motor  212  rotates upper end effector  180  about the wrist  184 . Similarly, pulley  330  is also coupled by bands to pulley  338  in elbow  170  where pulley  338  is directly coupled to pulley  340  in elbow  170 . Pulley  340  is then coupled by bands to pulley  342  in wrist  178  where pulley  242  is directly coupled to upper end effector  174 . Here, rotation of motor  212  rotates upper end effector  174  about the wrist  178 . Further, rotation of motor  212  simultaneously rotates both upper end effectors  174 ,  180  about their respective wrists  178 ,  184 . The shafts associated with drives  210 ,  212 ,  214 ,  216 ,  218  are each independently and coaxially rotatable and may be supported by any suitable bearing or other arrangement with respect to housing  220  as shown or otherwise. The three pulleys in each of elbows  170 ,  172  and the two pulleys in each of wrists  178 ,  184  are each independently and coaxially rotatable with respect to a common axis in each joint and may be supported by any suitable bearing or other arrangement as shown or otherwise. The following description of respective pulley ratios is based on the premise that the link lengths of each link are the same. In alternate aspects, different ratios or driving arrangement may be provided, for example, where the link lengths are different. An example of arms having unequal link lengths and driven by non circular pulleys is given in U.S. patent application Ser. No. 13/833,732 entitled “Robot having Arm with Unequal Link Lengths” filed Mar. 15, 2013 which is incorporated by reference herein in its entirety. In the embodiment shown, pulleys and bands are provided. In alternate embodiments, any suitable power transmission arrangement may be provided, for example, belts, links, gears, cable or any suitable arrangement. In the embodiment shown, 5 coaxial direct driving shafts are provided. In alternate embodiments, any suitable driving arrangement may be provided, for example, motors in joints, links, speed reducers, belts, magnetic couplings, linear and/or rotational drives or any suitable drive may be provided. In the embodiment shown, the ratio between pulleys  310 ,  312  and  310 ,  314  may be any suitable ratio, for example, 2:1. In the embodiment shown, the ratio between pulleys  238 ,  240  and  238 ,  246  may be any suitable ratio, for example, 1:3 or higher or lower than 1:3. In the embodiment shown, the ratio between pulleys  316 ,  318  and  316 ,  324  may be any suitable ratio, for example, 1:1. In the embodiment shown, the ratio between pulleys  320 ,  322  and  326 ,  328  may be any suitable ratio, for example, 1:1. In the embodiment shown, the ratio between pulleys  334 ,  336  and  340 ,  342  may be any suitable ratio, for example, 1:1. In operation, simultaneous rotation of all of drives  210 ,  212 ,  214 ,  216 ,  218  rotates the entire arm assembly. Rotation of upper arm  164  while holding pulleys  310 ,  316 ,  330  and upper arm  162  stationary cause end effectors  180 ,  182  to extend or retract while end effectors  174 ,  176  remain stationary. Similarly, rotation of upper arm  162  while holding pulleys  310 ,  316 ,  330  and upper arm  164  stationary cause end effectors  174 ,  176  to extend or retract while end effectors  180 ,  182  remain stationary. Further, relative rotation of pulley  316  will cause a corresponding relative rotation of end effectors  182 ,  176 . Similarly, relative rotation of pulley  330  will cause a corresponding relative rotation of end effectors  180 ,  174 . With the 5 rotary axis drive and arm arrangement described, 2 substrates may be independently placed at different locations as will be described in greater detail below. For example, 2 substrates supported on end effectors  180 ,  182  may be independently placed at two locations. Similarly, 2 substrates supported on end effectors  174 ,  176  may be independently placed at two locations. In alternate aspects, more or less arms and axis&#39; may be provided. 
     Referring to  FIG. 5 , there is shown a schematic top plan view of an example substrate processing apparatus  500  having a substrate transport apparatus or robot system  510 . Although the present embodiment will be described with reference to the embodiments shown in the drawings, it should be understood that the present invention may be embodied in many forms of alternative embodiments. In addition, any suitable size, shape or type of materials or elements could be used. System  500  is shown in a “quad” configuration where pairs of substrates are transported and processed. In alternate aspects, system  500  may be a conventional single substrate transport and processing system. Substrate transport apparatus  510  may have features as disclosed with respect to robots  100  and  150  disclosed above. In alternate aspects, system  500  may utilize any suitable robot. For example, were system  500  to be a single substrate transport and processing system, robot  500  may have features as disclosed with respect to robots  100  and  150  but with an arm that transports a single wafer as opposed to two as disclosed with respect to robots  100  and  150 . Here, by way of example, a robot drive having three coaxial drives may be used with respect to a single arm arrangement and a robot drive having four coaxial drives may be used with respect to a dual arm arrangement. In alternate aspects, any suitable robot capable of carrying out the disclosed methods may be used. In addition to the substrate transport apparatus  510  in this example embodiment, the substrate processing apparatus  500  may include multiple dual substrate processing chambers  512 ,  514 ,  516  and stacked dual substrate load locks  518 ,  520  connected to a vacuum chamber  122 . The transport apparatus  510  is located, at least partially, in the chamber  522  and is adapted to transport one or more planar substrate  530 ,  532  such as semiconductor wafers or flat panel displays or other suitable substrates, between and/or among the chambers  512 ,  514 ,  516  and elevators or locks  518 ,  520 . In alternate embodiments, the transport apparatus  510  could be used in any suitable type of substrate processing apparatus. Sensors  534 ,  536 ,  538 ,  540 ,  542 ,  544  are shown connected to chamber  522  and are provided to detect an edge crossing of substrates  130 ,  132  while being transported by robot  510  into corresponding process areas  546 ,  550  of module  514  where sensors  534 ,  536 ,  538  may correspond to process area  546  and sensors  540 ,  542 ,  544  may correspond to process area  550 . Similarly, modules  512 ,  516   518 ,  520  may have such sensor arrangements. In an alternate aspect, more or less sensors may be provided. In an alternate aspect, cameras may be provided at a suitable location for example, locations  536 ,  542  to detect a fiducial, such as a laser inscribed mark or otherwise of wafers  530 ,  532  instead of an edge as will be described in greater detail below. Here, the sensors may be optical through beam, reflective, inductive, capacitive or any suitable sensor or detector. Although three sensors are shown, more or less sensors may be provided. Although the sensors are shown in line and equidistant, any suitable sensor locations may be provided. Robot  510  may further be controlled by controller  552 . Here, controller  552  may be connected to a robot drive of robot  510  to controllably position upper arm  554 , forearm  556 , left or first end effector  558  and right or second end effector  560 . Here (and as with an arm of robots  100 ,  150 ), first and second end effectors  558 ,  560  may be independently positionable and independently rotatable about wrist joint  562 . Further, forearm  556  is connected to upper arm  554  at elbow  564  and independently positionable and rotatable. Controller  552  is shown connected to the drive, where the controller is configured to detect an offset of respective substrates on the at least two end effectors and adjust movement of the at least two end effectors relative to each other prior to placement of the substrates at the respective target locations. Arm  510  is rotatable about its origin or main drive axis  566 . Thus, in the embodiment shown, a four axis device (five if a vertical or Z axis is included) is shown. In alternate embodiments, any suitable arm, combination of arms or mechanism capable of carrying out the disclosed methods may be provided. Controller  552  may be connected to the transport apparatus  510  and the sensors and may control robot  510  and/or various devices. The controller  552  may comprise at least one processor, at least one memory, and software for performing operations, including at least partially controlling movement of the robot, as described herein. Any combination of one or more computer readable medium(s) may be utilized as the memory. The computer readable medium may be a computer readable signal medium or a non-transitory computer readable storage medium. A non-transitory computer readable storage medium does not include propagating signals and may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. 
     Referring also to  FIG. 6 , there is also shown a top view of system  500 . A given station or process module  514  may have target locations or station locations  600 ,  602  denoted by first and second vectors  604 ,  606  that are designated “T1” (left) and “T2” (right) in the view shown. In the embodiment shown, the target location may be located vertically above the place location for the substrate, for example, where the robot places the substrates to fixed teach locations with a z axis vertical movement. In alternate aspects, the target locations may be at the place location, for example, where no Z axis is provided or where the station picks the wafers from the end effectors with pins or otherwise. Vectors  604 ,  606  may be referenced from the robot origin  566  (for example, origin (0,0) of coordinate system  608  grounded to tool  500 ) and may be expressed in polar coordinates, Cartesian coordinates or otherwise. Target locations  600 ,  602  may also have respective coordinate systems  610 ,  612  that may be oriented in any suitable orientation. For example, coordinate systems  610 ,  612  may have axis&#39; that are parallel to the robot coordinate system  608 . Alternately, coordinate systems  610 ,  612  may have x axis&#39; that are parallel to each other. Alternately, coordinate systems  610 ,  612  may have any suitable axis&#39; that is aligned with or otherwise referenced relative to a wafer characteristic, for example, notch or feature location, crystallographic orientation, fiducial orientation or any suitable reference. Alternately, coordinate systems  610 ,  612  may have any suitable orientation, similar or different or otherwise. Target locations  600 ,  602  may be for example, a destination location in station  514  for substrates  530 ,  532  respectively. Similarly, robot  510  may have first and second (or left and right) robot end effector location vectors  620 ,  622 , for example, located at a reference portion of first or left end effector  558  that is designated “R1”  620  and located at a reference portion of second or right end effector  560  that is designated “R2”  622  in the view shown. First and second end effectors  558 ,  560  also have reference frames  624 ,  626  fixed thereto, for example, located at the end of vectors  620 ,  622  respectively and on center of a properly located substrate on each end effector. Reference frames  624 ,  626  fixed to first and second end effectors  558 ,  560  may have any suitable orientation, for example, where the y axis of the respective reference frames points in a direction nominally parallel to a radial line extending from robot axis  608  when end effectors  558 ,  560  are separated by a distance being the nominal distance between stations  600 ,  602  or otherwise. Alternately, reference frames  624 ,  626  fixed to first and second end effectors  558 ,  560  may have any suitable orientation, similar, different or otherwise. Vectors  620 ,  622  may be referenced from the robot origin  566  and move with their respective end effectors  558 ,  560  designating the location of the end effectors  558 ,  560  at any point in time as end effectors  558 ,  560  move and may be expressed in polar coordinates, Cartesian coordinates or otherwise. In one example, when substrates  530  and  532  are properly located on end effectors  558 ,  560  respectively and the robot  510  directs end effector  558  to target or station  600  and end effector  560  to target or station  602 , the location of wafers  530 ,  532  may be properly placed within station  514  where the robot location or position vector  620  may be the same as and align with the station or target vector  604  and where the robot location or position vector  622  may be the same as and align with the station or target vector  606 . In one aspect, a line  630  between station origins  610 ,  612  may be provided and another line  632  perpendicular thereto and intersecting robot origin  566  may be provided to define a nominal path wrist  562  may travel through during operation or prior to or at setup. Where the station locations are offset from the nominal wrist path, the end effectors may nominally travel with their origins at such offset along first and second offset paths  634 ,  636  and nominally parallel to line  632  where the respective offsets may be the same different or otherwise. After station locations have been established, a combination of or different path(s) may be provided, for example, paths defined with respect to coordinate systems  610 ,  612 , alone or in combination with  608  or otherwise. In alternate aspects, the disclosed embodiment may be used with any suitable coordinate system or vectors with any suitable reference locations, for example, with respect to a different portion of end effectors  558 ,  560 , station  514 , system  500  or otherwise. Sensors  534 ,  536 ,  538  are shown nominally positioned along a sensor axis  638  substantially perpendicular to path  632  and the transport path  634  with sensor  536  located in line with the transport path and sensors  534 ,  536  equidistant and offset from the nominal transport path  634 . In alternate aspects, the sensors need not be equidistant or located on the transport path and need not be located along sensor axis  638 . Similarly, sensors  540 ,  542 ,  546  are shown nominally positioned along a sensor axis  640  substantially perpendicular to path  632  and the transport path  636  with sensor  542  located in line with the transport path and sensors  540 ,  544  equidistant and offset from the nominal transport path  636 . In alternate aspects, the sensors need not be equidistant or located on the transport path and need not be located along sensor axis  640 . 
     Referring also to  FIG. 7 , the disclosed embodiment outlines the function and algorithms for the calibration and operation of an exemplary adaptive placement system (APS) system. The disclosed embodiment may be used the hardware of the APS system may consist of two triplets  534 ,  536 ,  538  and  540 ,  542 ,  544  of substantially equi-spaced through beam sensors placed between the robot  510  and substrate station  514  or target location  600 ,  602 . Sets of triplets may operate with respect to end effectors  558 ,  560  and as such, the left or first station  600  operation will be described in greater detail. The center sensor  536  may be nominally on a straight line  634  as described with respect to robot origin  566  and the concerned station  600 . During a substrate pick or place operation the moving substrate  530  interrupts the continuity of the sensor  534 ,  536 ,  1538  light beams. The location  620  and orientation  624  of the end effector  558  at the instant of interruption is the input processed by the APS algorithm. At the highest level, the APS performs in two modes. The first mode is calibration, wherein the APS executes test moves with the robot and uses feedback from the robot and sensors to determine the operational and tuning parameters for the APS setup. In the second mode, referred to as the operational mode, the APS adapts the end effectors place locations for optimal substrate placement at the target or station locations  600 ,  602 . These two modes are described in more detail. 
     Referring also to  FIGS. 8 and 9 , in the calibration mode, the spatial positioning of the sensors and their performance are measured. With respect to sensor positions, each substrate station may have three APS sensors associated with it. Alternately, more or less APS sensors may be provided at any suitable location. In order to maximize the accuracy of the APS algorithm the coordinates of these APS sensors may be known very precisely with respect to the robot coordinate system. To achieve this, the position information may be measured after the APS sensors have been mechanically fixtured, for example, to chamber  5   22  or otherwise. The sensor positions are measured by moving a test substrate or fixture as part of or placed on the robot end effector through the sensor beams and capturing the substrate position at the instant a beam is interrupted. The corresponding sensor location is calculated from the captured substrate location as will be described in greater detail below. 
     During calibration, sensor locations, for example vectors  700 ,  702 ,  704  as seen in  FIG. 7  corresponding to sensor #1,  534 , sensor #2,  536  and sensor #3,  538  associated with station  600  are precisely determined. For calibration, a calibration fixture, for example, a circular test substrates  530 ′ and  532 ′ are placed on the robot end effectors  558 ,  560 , for example, such that the center or reference location of the test substrates coincide with the end effector origins  624 ,  626 , for example at the ends of vectors  620 ,  622  typically referred as the center or origins (0,0) of the end effector and where end effector reference frames  624 ,  626  may be fixed to and move with end effectors  558 ,  560  respectively and location vectors  620 ,  622 . Here, location vector  620  may be the sum of robot origin to wrist location vector  704  and wrist to first end effector location vector  706 . Similarly, location vector  622  may be the sum of robot origin to wrist location vector  704  and wrist to second end effector location vector  708 . Here, wrist location vector  705  may be the sum of robot origin to elbow vector  710  and elbow to wrist vector  712 . Here, the location vectors  620 ,  622  and orientation of end effector reference frames  624 ,  626  may be determined at any point in the robot&#39;s work space based on the robots kinematics and the relationship between the arm linkages and bands and the drive encoders positions. Based on the known radius&#39;  720  of substrates  530 ′ and  532 ′ and the captured joint positions, the locations of the sensors, for example, location vector  704  may be determined as well as that associated with the other sensors. The calibration procedure may be repeated, in entirety, for all the stations equipped with APS sensors. All of the calibration procedures may be repeated as several times as required and the measurements may be averaged by averaging, least squares averaging or otherwise. By way of example, the number of times the measurement process is repeated for a station may be a configurable parameter. 
     As seen, the first step in calibration is determining the approximate position of the APS sensors by executing a move. This is achieved as follows:
         1. Extend the robot  510  with the test substrates  530 ′,  532 ′ on it from a retracted position to a extended position, for example, a nominal station position. Here, there will be six sensor events for each station location as the leading and trailing edge of substrates  530 ′,  532 ′ cross the sets of three APS sensors  534 ,  536 ,  538  and  540 ,  542 ,  544 .   2. At each sensor event the end effector locations  620 ,  622  and orientations of end effector reference frames  624 ,  626  are captured as well as the type of transition i.e. leading edge vs. trailing edge. It is noted that a leading edge is defined as a light to dark (l2d) transition for the sensor while a trailing edge is a dark to light (d2l) transition.   3. Retract the robot, for example, to R home position or other suitable retract position.       

     The data captured above is the location and orientation of the end effector centers when the test wafers interrupt each set of the three APS sensors on the l2d and d2l transitions. The index j refer to quantities related to the six edge detection events and the index i refers to the sensors as summarized in the table below: 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Events associated with index j associated 
               
               
                 with a given end effector 
               
            
           
           
               
               
               
            
               
                 Index (j) 
                 Sensor (i) 
                 Event 
               
               
                   
               
               
                 1 
                 Left 1 
                 Light to dark/Leading edge 
               
               
                 3 
                 Center 2 
                 Light to dark/Leading edge 
               
               
                 5 
                 Right 3 
                 Light to dark/Leading edge 
               
               
                 2 
                 Left 1 
                 Dark to light/Trailing edge 
               
               
                 4 
                 Center 2 
                 Dark to light/Trailing edge 
               
               
                 6 
                 Right 3 
                 Dark to light/Trailing edge 
               
               
                   
               
            
           
         
       
     
     Here, for each end effector, the six events correspond to locations where the edge of the test substrate cross the sensors for example, extending or retracting. The steps in the determination of the sensor locations may be as follows. The procedure below may be performed multiple times. Alternately, the procedure below may be performed once, for example, during an extend or retract. Alternately, any suitable combination or number of moves may be utilized and the results averaged or utilized as will be described. For example, the sensor location results from the one, two or more moves may be averaged. Here, the sensor locations may be determined as follows.
         1. Move the robot to the T position corresponding to the station location in context and robot R to retracted position, for example, as seen in  FIG. 5 .   2. Extend the arm.   3. Record the Polar position of the end effectors at the single light to dark sensor events at sensors  536 ,  542 .   4. Record the Polar positions end effectors at the two light to dark sensor events at sensors  534 ,  538  and  540 ,  542 .   5. Record the Polar positions of the end effectors at the two dark to light sensor events at sensors  534 ,  538  and  540 ,  542 .   6. Record the Polar positions of the end effectors at the single dark to light sensor events at sensors  536 ,  542 .   7. Retract the robot.       

     In alternate aspects, the above procedure may be done with a retract move or other suitable move. 
     The positions of the sensors respectively in polar coordinates may then be calculated as follows. The example below calculates the position of the left side sensor  534  (Rsen1, Tsen1). Similarly, the other sensor positions may be calculated. In the following equations Rwaf is the radius of the test fixture or substrate. 
     First the captured end effector positions  620  for i=1 and j=1 &amp;  2  for end effector  558  are converted to Cartesian coordinates Eq. 1:
 
 x   1   ee   ×R   rbt1 ×cos( T   rbt1 )
 
 y   1   ee   ×R   rbt1 ×sin( T   rbt1 )
 
 x   2   ee   ×R   rbt2 ×cos( T   rbt2 )
 
 y   2   ee   ×R   rbt2 ×sin( T   rbt2 )  (Eq. 1)
 
     Following intermediate variables are calculated Eq. 2:
 
 dx =( x   2   ee   −x   1   ee )/2
 
 dy =( y   2   ee   −y   1   ee )/2
 
 z= √{square root over ( dx   2   +dy   2 )}
 
 v= √{square root over (Rwaf 2   −z   2 )}   (Eq. 2)
 
     The position of the sensor is calculated in Cartesian coordinates as Eq. 3:
 
 x   1   sen   =x   1   ee   dx−dy v/z  
 
 y   1   sen   =y   1   ee   dy−dx v/z    (Eq. 3)
 
     Finally the position  700  of the sensor  534  is converted to Polar coordinates as Eq. 4:
 
 R   sen1 =√{square root over ( x   1   sen     2     +y   1   sen     2   )}
 
 T   sen1   =a  tan 2( y   1   sen   ,x   1   sen )   (Eq. 4)
 
     Similarly, the center  2  and right  3  positions  702 ,  704  may be calculated. Similarly, the positions associated with sensors  540 ,  542 ,  544  may be calculated using the captured positions  622  of end effector  560  at the transitions. The procedure above may be repeated for the same move and the results for each sensor averaged. Alternately, the procedure above may be repeated for different moves and the results of each sensor averaged. 
     Referring now to  FIGS. 10A-10C , there are shown various views of a camera field of view  536 ′. In an alternate aspect of the disclosed embodiment, instead of multiple through beam sensors, one or more cameras may be placed per station, for example, located at positions  536 ,  542  for stations  600 ,  602  of module  514 . Referring also to  FIG. 13 , there is shown an exemplary substrate  530 ″. Substrate  530 ″ may have markings etched or otherwise placed on a side of the substrate, for example, the back side of the substrate such that camera  536 ′ may take one or more images of the markings where the markings may comprise one or more fiducials, identification mark or marks, or any suitable marking. Camera  536 ′ may have a processor configured to identify the associated mark and provide the robot controller with one or more time stamp associated with the point in time the mark was captured, a location of the mark with respect to a reference and an orientation of the mark. The mark may comprise cross hair and bulls eye arrangement  800  with identification indicia, such as a wafer id number, bar code or 2 dimensional bar code or other suitable identification indicia therein. The fiducial  800  may have cross hairs oriented with respect to a reference, for example, the center of the substrate and a crystalline orientation. Alternately, the fiducial may be offset and a reference vector to the center of the substrate and orientation may be provided. Further additional fiducials  802 ,  804  may be provided, for example to more accurately determine the location of the substrate and orientation. Further, a line  806  may be etched that is in line with or referenced with respect to the crystalline orientation of substrate  530 ″. Further, a line  808  with an identification indicia that may be etched that is in line with or referenced with respect to the crystalline orientation and the center of substrate  530 ″. Further, notch  812  may be provided. In alternate aspects, any suitable mark, indicia, feature or otherwise may be provided. In  FIG. 10A , there is shown a field of view of camera or array  536 ′. Here array  536 ′ may be a CCD or other suitable array having m×n pixels with orientation  822  and location vector  816  with respect to robot origin  566  and orientation reference frame  608 . Initially, an accurate location vector  816  and reference frame  822  are unknown and need to be calibrated. One approach is to provide a test substrate with the center fiducial located at the end effector center or at the end effector reference frame. Here, camera  536 ′ may take an image  824  and identify location vector  818  based upon the pixel location of the fiducial center. Further, with the position  620  and orientation of the end effector  624 , the location  816  and orientation  822  of array  536 ′ may be determined. Another approach may be to take two or more images, for example,  824 ,  826  and based on the robot locations associated with positions  824  and  826  in combination with pixel locations or vectors  818 ,  820  the distance between locations  824 ,  826  may be determined (i.e. calibrate effective pixel size) and the location  816  and orientation  822  determined. Further approaches to calibration of array location  816 , orientation  822  and effective pixel size  828  may be provided involving averaging, least squares averaging or otherwise converging on a calibrated location and orientation of the array  536 ′ based on the robot locations and orientations in any suitable calibration method. Referring also to  FIG. 10B , with the location  816  and orientation  822  of array being known, an image of the substrate may be taken as it passes over the field of view of array  536 ′ and the image processed resulting on a location  832  and orientation  834  of the fiducial on the substrate. The time associated with the image may be time stamped and correlated with a location  830  being vector  620  and orientation  624  of robot  510  at the same time of the image event. Robot array location vector  816  and fiducial location vector  832  may be subtracted from location vector  620  resulting in an apparent eccentricity vector  836  of the substrate which may be provided in any suitable reference frame, for example, the end effector reference frame  830 . Similarly, the orientation of reference frame  834  may be determined relative to end effector reference frame  624  or otherwise such that the orientation of the substrate may be corrected if so desired. Similarly, as seen in  FIG. 10C , multiple samples  838  . . .  840  of the location and orientation of the fiducial may be taken, associated eccentricity vectors and orientations determined and averaged to converge on a substrate eccentricity  836 ′ and orientation  834 ′, for example, least squares averaged to converge on a substrate eccentricity vector  836 ′ and orientation  834 ′ relative to some reference frame, for example, end effector reference frame  624 . The disclosed methods associated with an image array may be utilized by a substrate handler that may transport one or more substrates where the controller of the handler may correct substrate placement or picking for eccentricity, angular orientation, individually or in combination with each other in any suitable method. Described are suitable methods of providing an adaptive placement system for wafers or substrates with an inscribed fiducial mark. 
     Referring also to  FIGS. 11A, 11B and 12 , there is shown a view of system  500  where placement location determination may be described. During a pick or place or other suitable operation, vectors  620  representing the polar position (Rrbtj, Trbtj); j=1-6 of the end effector may be collected at each sensor event. The measurements may be used to directly calculate an eccentricity to achieve optimum station or target placement as will be described Eq. 5:
 
 {right arrow over (r)}   rbtj =[ R   rbtj , T   rbtj ]   (Eq. 5)
 
     As described, a vector  604  to the station or target location in a main coordinate system is defined Eq. 6:
 
 {right arrow over (r)}   tgt =[ R   tgt , T   tgt ]   (Eq. 6)
 
     As described, vector  700 ,  702 ,  704  to location of sensor i, i=1, 2, 3, in main coordinate system is defined Eq. 7:
 
 {right arrow over (r)}   seni =[ R   seni , T   seni ],i=1,2,3   (Eq. 7)
 
     Next, vectors  850  rsns ( FIG. 12 ) representing the location vector to each point j on the wafer edge which was detected by sensor i in the coordinate system  624  attached to the robot end effector are calculated from the end effector positions (Rrbtj, Trbtj) corresponding to the six sensor events for j=1, 2, . . . , 6; i=1 for j=1, 2; i=2 for j=3, 4; i=3 for j=5, 6 Eq. 8:
 
[ R   j   sns , T   j   sns ]={right arrow over (r)} j   sns ={right arrow over (r)} seni −{right arrow over (r)} rbtj    (Eq. 8)
 
     Next, define a hypothetical vector  852  rjtgt to each of above defined points j from the wafer center using the coordinate system associated with the end effector Eq. 9:
 
[ R   j   tgt , T   j   tgt ]={right arrow over (r)} j   tgt ={right arrow over (r)} j   sns −{right arrow over (e)},j=1,2, . . . ,6   (Eq. 9)
 
     Here, e is an unknown eccentricity vector in the end effector coordinate system  624 . Next, minimize the distance of the above defined points j from the circumference of a fictitious circle located at the end of the eccentricity vector, using the following minimization function Eq. 10: 
     
       
         
           
             
               
                 
                   FN 
                   = 
                   
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         6 
                       
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                                
                               
                                 
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     Next, solve or use a numerical iterative technique to minimize above cost function by iterating through e, for example starting with the previously calculated e for the target or station location or target location or starting from an arbitrary value, for example 0. Here, a final eccentricity vector of the substrate in the end effector reference frame  624  may be determined as a solution by minimization of the above FN. 
     Upon solving for separate eccentricity vectors  870 ,  872  in the end effector reference frames  624 ,  626  respectively, utilizing station locations  604 ,  606  in combination with eccentricity vectors  870 ,  872  the common wrist location vector  704  place, first end effector location vector  706  place and second end effector location vector  708  place may be determined using inverse kinematics solving for a common  705  place such that the center of the substrates  530 ,  532  are placed on center of their respective station frames  610 ,  612 . Here the coordinates of placement location; i.e. the end point of robot extension move may be adjusted to achieve target wafer location are obtained. The robot may track the nominal transport path to the target location. The robot may then be directed to the place location as seen in  FIGS. 11A and 11B . Alternately, the robot may track the nominal transport path to an intermediate location and the robot may then alternately be directed to the place locations. As above or in the event one or more images are used to compute the eccentricity vectors, any suitable algorithm may be used to further correct for velocity, latency or otherwise, as applied to edge data, image data or otherwise, for example, as disclosed in US Publication No. 2004/0167743 Dated Aug. 26, 2004 and U.S. Pat. No. 4,819,167 Dated Apr. 4, 1989, both of which are incorporated by reference herein in their entirety. 
     During setup, teaching and operation of robot  510 , various modes of operation may be provided. A first mode preloads default station locations in the robot. Another mode allows the user to move or jog the robot in a radial direction with the end effectors at a fixed programmable offset from the nominal radial path of the wrist and where the programmable offsets may be the same or different or otherwise. A third mode blends radial moves such that the wrist tracks with respect to path  623  which is perpendicular to a line between actual teach locations  610 ,  612  and where the wrist is constrained to pass over the center  566  of robot  510  where the link lengths of the upper arm and forearm are the same or passes over offset as constrained by unequal length forearms and upper arms. In another mode, the user may jog either the left or right end effector with respect to the left or right end effectors reference frame or with respect to default or taught station reference frames. In another mode, for example, when either the left or right station is taught, the user may switch to the adjacent station or end effector reference frame for jogging where the taught end effector is locked in position while teaching and jogging the other. By way of example, the taught fixed location end effector may rotate during the teaching or jogging of the adjacent end effector where the position of the end effector location (ex: vector  620  or  622 ) may be fixed. 
     In accordance with one example, a non-transitory program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine for performing operations may be provided, such as the memory for example, where the operations comprise any of the operations performed by the controller as described herein. The methods described above may be at least partially performed or controlled with the processor, memory and software. 
     Referring now to  FIG. 14A , there is shown a process flow diagram  900 . The process  900  determines a camera location  910 , determines a substrate location  912  and corrects the substrate location as will be described below with an adaptive placement system for a wafer with an inscribed fiducial mark. Referring also to  FIG. 14C , there is shown a process flow diagram  940 . The example method  940  may comprise moving  942  a substrate, located on a first end effector of a robot, from a first location towards a second location by the robot; determining  944  location of a fiducial on the substrate while the substrate is being moved from the first location towards the second location; comparing  946  the determined location of the fiducial with a reference fiducial location while the robot is moving the substrate from the first location towards the second location. The nomenclature follows.
         CF Cost function (unitless or m 2 )   N Number of snapshots taken by camera   k d  Cost function weight coefficient (1/m 2 )   k θ  Cost function weight coefficient (1/rad 2 )   x i   cam  x-coordinate of point i measured in camera coordinate system (m)   x waf   rbt  x-coordinate of wafer center in robot end-effector coordinate system (m)   x adj  x-coordinate of adjusted placement location in main coordinate system (m)   x tgt  x-coordinate of target placement location in main coordinate system (m)   x i  x-coordinate of point i measured in main coordinate system (m)   x cam  x-coordinate of origin of camera coordinate system measured in main coordinate system (m)   x cam * Estimated x-coordinate of origin of camera coordinate system in main coordinate system (m)   y i   cam  y-coordinate of point i measured in camera coordinate system (m)   y waf   rbt  y-coordinate of wafer center in robot end-effector coordinate system (m)   Y adj  y-coordinate of adjusted placement location in main coordinate system (m)   Y tgt  y-coordinate of target placement location in main coordinate system (m)   y i  x-coordinate of point i measured in main coordinate system (m)   y cam  x-coordinate of origin of camera coordinate system measured in robot coordinate system (m)   y RBT0 * Estimated y-coordinate of origin of camera coordinate system in main coordinate system (m)   θ waf   rbt  Orientation of wafer in robot end-effector coordinate system (rad)   θ i   cam  Orientation associated with point i measured in camera coordinate system (rad)   θ adj  Orientation of adjusted placement location in main coordinate system (rad)   θ tgt  Orientation of target placement location in robot coordinate system (rad)   θ i  Orientation associated with point i measured in main coordinate system (rad)   θ cam  Orientation of camera coordinate system measured in main coordinate system (rad)   θ cam * Estimated orientation of camera coordinate system in main coordinate system (rad)   θ rbti  Orientation of robot end-effector coordinate system in main coordinate system when snapshot i taken (rad)       

     Transformation from Camera to Robot Coordinates may be as follows. Transformation from x i   cam , y i   cam  and θ i   cam  to x i , y i  and θ i :
 
 x   i   =x   cam   +x   i   cam  cos θ cam   −y   i   cam  sin θ cam   (Eq. 11)
 
 y   i   =y   cam   +x   i   cam  sin θ cam   +y   i   cam  cos θ cam   (Eq. 12)
 
θ i =θ cam +θ i   cam   (Eq. 13)
 
     Calibration Based on Single Camera Snapshot may be as follows. 
     Input information: measurements extracted from camera snapshot x i   cam , y i   cam  and θ i   cam , where i=1, and measurements determined based on robot encoders x i , y i  and θ i , where i=1. Objective: calculate location of camera, x cam , y cam  and θ cam , in main coordinate system:
 
θ cam =θ i −θ i   cam   ,i= 1  (Eq. 14)
 
 x   cam   =x   i   −x   i   cam  cos θ cam   +y   i   cam  sin θ cam   ,i= 1  (Eq. 15)
 
 y   cam   =y   i   −x   i   cam  sin θ cam   −y   i   cam  cos θ cam   ,i= 1  (Eq. 16)
 
     Alternatively, the location of the camera in the main coordinate system may be expressed in terms of polar or cylindrical coordinates or in any other suitable coordinates. 
     Calibration Based on Multiple Snapshots Utilizing Orientation Info may be as follows. 
     Input information: measurements extracted from camera snapshots x i   cam , y i   cam  and θ i   cam , where i=1, 2, . . . , N, and measurements determined based on robot encoders x i , y i  and θ i , where i=1, 2, . . . , N. Objective: estimate location of camera, x cam , y cam  and θ cam , in main coordinate system: 
     
       
         
           
             
               
                 
                   
                       
                   
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                                   x 
                                   i 
                                   ′ 
                                 
                                 - 
                                 
                                   x 
                                   i 
                                 
                               
                               ) 
                             
                             2 
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   y 
                                   i 
                                   ′ 
                                 
                                 - 
                                 
                                   y 
                                   i 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       i 
                       = 
                       1 
                     
                     , 
                     2 
                     , 
                     … 
                     ⁢ 
                     
                         
                     
                     , 
                     N 
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     20 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         e 
                         
                           θ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           i 
                         
                       
                       = 
                       
                         
                           θ 
                           i 
                           ′ 
                         
                         - 
                         
                           θ 
                           i 
                         
                       
                     
                     , 
                     
                       i 
                       = 
                       1 
                     
                     , 
                     2 
                     , 
                     … 
                     ⁢ 
                     
                         
                     
                     , 
                     N 
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     21 
                   
                   ) 
                 
               
             
             
               
                 
                   CF 
                   = 
                   
                     
                       
                         
                           k 
                           d 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             e 
                             di 
                             2 
                           
                         
                       
                       + 
                       
                         
                           k 
                           θ 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             e 
                             θi 
                             2 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           k 
                           d 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             [ 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       x 
                                       i 
                                       ′ 
                                     
                                     - 
                                     
                                       x 
                                       i 
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       y 
                                       i 
                                       ′ 
                                     
                                     - 
                                     
                                       y 
                                       i 
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                             
                             ] 
                           
                         
                       
                       + 
                       
                         
                           k 
                           θ 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             
                               [ 
                               
                                 
                                   θ 
                                   i 
                                   ′ 
                                 
                                 - 
                                 
                                   θ 
                                   i 
                                 
                               
                               ] 
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     22 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       CF 
                       ⁡ 
                       
                         ( 
                         
                           
                             x 
                             cam 
                             * 
                           
                           , 
                           
                             y 
                             cam 
                             * 
                           
                           , 
                           
                             θ 
                             cam 
                             * 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       min 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         CF 
                         ⁡ 
                         
                           ( 
                           
                             
                               x 
                               cam 
                             
                             , 
                             
                               y 
                               cam 
                             
                             , 
                             
                               θ 
                               cam 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     23 
                   
                   ) 
                 
               
             
           
         
       
     
     A numerical iterative technique may be used to minimize the above cost function by iterating through x cam , y cam  and θ cam . The starting point may be selected based on one of the snapshots according to Equations (14) to (16). 
     Alternatively, the location of the camera in the main coordinate system may be expressed in terms of polar or cylindrical coordinates or in any other suitable coordinates. 
     Calibration Based on Multiple Snapshots Excluding Orientation Info may be as follows. 
     Input information: measurements extracted from camera snapshots x i   cam  and y i   cam , where i=1, 2, . . . , N, and measurements determined based on robot encoders x i  and y i , where i=1, 2, . . . , N. Objective: estimate location of camera, x cam , y cam  and θ cam , in main coordinate system: 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       i 
                       ′ 
                     
                     = 
                     
                       
                         x 
                         cam 
                       
                       + 
                       
                         
                           x 
                           i 
                           cam 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           cam 
                         
                       
                       - 
                       
                         
                           y 
                           i 
                           cam 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           cam 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     i 
                     = 
                     1 
                   
                   , 
                   2 
                   , 
                   … 
                   ⁢ 
                   
                       
                   
                   , 
                   N 
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     24 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       y 
                       i 
                       ′ 
                     
                     = 
                     
                       
                         y 
                         cam 
                       
                       + 
                       
                         
                           x 
                           i 
                           cam 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           cam 
                         
                       
                       + 
                       
                         
                           y 
                           i 
                           cam 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           cam 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     i 
                     = 
                     1 
                   
                   , 
                   2 
                   , 
                   … 
                   ⁢ 
                   
                       
                   
                   , 
                   N 
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     25 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       e 
                       di 
                     
                     = 
                     
                       
                         
                           
                             ( 
                             
                               
                                 x 
                                 i 
                                 ′ 
                               
                               - 
                               
                                 x 
                                 i 
                               
                             
                             ) 
                           
                           2 
                         
                         + 
                         
                           
                             ( 
                             
                               
                                 y 
                                 i 
                                 ′ 
                               
                               - 
                               
                                 y 
                                 i 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     i 
                     = 
                     1 
                   
                   , 
                   2 
                   , 
                   … 
                   ⁢ 
                   
                       
                   
                   , 
                   N 
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     26 
                   
                   ) 
                 
               
             
             
               
                 
                   CF 
                   = 
                   
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         N 
                       
                       ⁢ 
                       
                         e 
                         di 
                         2 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         N 
                       
                       ⁢ 
                       
                         [ 
                         
                           
                             
                               ( 
                               
                                 
                                   x 
                                   i 
                                   ′ 
                                 
                                 - 
                                 
                                   x 
                                   i 
                                 
                               
                               ) 
                             
                             2 
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   y 
                                   i 
                                   ′ 
                                 
                                 - 
                                 
                                   y 
                                   i 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     27 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     CF 
                     ⁡ 
                     
                       ( 
                       
                         
                           x 
                           cam 
                           * 
                         
                         , 
                         
                           y 
                           cam 
                           * 
                         
                         , 
                         
                           θ 
                           cam 
                           * 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     min 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       CF 
                       ⁡ 
                       
                         ( 
                         
                           
                             x 
                             cam 
                           
                           , 
                           
                             y 
                             cam 
                           
                           , 
                           
                             θ 
                             cam 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     28 
                   
                   ) 
                 
               
             
           
         
       
     
     A numerical iterative technique may be used to minimize the above cost function by iterating through x cam , y cam  and θ cam . The starting point may be selected based on one of the snapshots according to Equations (14) to (16). 
     Alternatively, the location of the camera in the robot coordinate system may be expressed in terms of polar or cylindrical coordinates or in any other suitable coordinates. 
     Correction of Wafer Location Based on Single Camera Snapshot may be as follows. 
     Input information: measurements extracted from camera snapshot x i   cam  and y i   cam , where i=1, and measurements determined based on robot encoders x i , y i  and θ i  (θ i  is function of x i  and y i  if end-effector not independently actuated), where i=1. Objective: calculate location of wafer on robot end-effector x waf   rbt  and y waf   rbt , and determine adjusted placement location x adj  and y adj  (if robot has independently articulated end-effector, θ adj  may be selected arbitrarily; if it does not, θ adj  is function of x adj  and y adj ):
 
 x   cam   +x   i   cam  cos θ cam   −y   i   cam  sin θ cam   =x   i   +x   waf   rbt  cos θ rbti   −y   waf   rbt  sin θ rbti   ,i= 1  (Eq. 29)
 
 y   cam   +x   i   cam  sin θ cam   +y   i   cam  cos θ cam   =y   i   +x   waf   rbt  sin θ rbti   +y   waf   rbt  cos θ rbti   ,i= 1  (Eq. 30)
 
(30) and (31)   x   waf   rbt   ,y   waf   rbt   (Eq. 31)
 
     Once the location of the wafer on the robot end-effector, x waf   rbt  and y waf   rbt , is calculated, the adjusted placement location x adj  and y adj  (i.e., placement location adjusted to achieve target wafer location, defined in main coordinate system) may be determined:
 
 x   adj   =x   tgt   −x   waf   rbt  cos θ adj   +y   waf   rbt  sin θ adj   (Eq. 32)
 
 y   adj   =y   tgt   −x   waf   rbt  sin θ adj   −y   waf   rbt  cos θ adj   (Eq. 33)
 
     where θ adj  may be selected arbitrarily if the robot has an independently articulated end-effector or an orienter, or θ adj  is a function of x adj  and y adj  if the robot does not have an independently articulated end-effector or an orienter. In the latter case, x adj , y adj  and θ adj . may be calculated together based on Equations (21), (22) and the relationship between θ adj  and x adj , y adj . 
     Alternatively, the placement location may be calculated directly, without calculating the location of the wafer in the end-effector coordinate system, as described in [12]. A polar, cylindrical or any other suitable coordinate system may be used. 
     Correction of Wafer Location Based on Multiple Camera Snapshots may be as follows. 
     Input information: measurements extracted from camera snapshots x i   cam  and y i   cam , where i=1, 2, . . . , N, and measurements determined based on robot encoders x i , y i  and θ i (θ i  is function of x i  and y 1  if end-effector not independently actuated), where i=1, 2, . . . , N. Objective: estimate location of wafer on robot end-effector x waf   rbt  and y waf   rbt , and determine adjusted placement location x adj  and y adj  (if robot has independently articulated end-effector, θ adj  may be selected arbitrarily): 
     
       
         
           
             
               
                 
                   
                     Conversion 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       x 
                       i 
                     
                   
                   , 
                   
                     y 
                     i 
                   
                   , 
                   
                     
                       x 
                       i 
                       cam 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       y 
                       i 
                       cam 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     to 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       x 
                       i 
                       rbt 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       y 
                       i 
                       rbt 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     34 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       e 
                       di 
                     
                     = 
                     
                       
                         
                           
                             ( 
                             
                               
                                 x 
                                 i 
                                 rbt 
                               
                               - 
                               
                                 x 
                                 waf 
                                 rbt 
                               
                             
                             ) 
                           
                           2 
                         
                         + 
                         
                           
                             ( 
                             
                               
                                 y 
                                 i 
                                 rbt 
                               
                               - 
                               
                                 y 
                                 waf 
                                 rbt 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     i 
                     = 
                     1 
                   
                   , 
                   2 
                   , 
                   … 
                   ⁢ 
                   
                       
                   
                   , 
                   N 
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     35 
                   
                   ) 
                 
               
             
             
               
                 
                   CF 
                   = 
                   
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         N 
                       
                       ⁢ 
                       
                         e 
                         di 
                         2 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         N 
                       
                       ⁢ 
                       
                         [ 
                         
                           
                             
                               ( 
                               
                                 
                                   x 
                                   i 
                                   rbt 
                                 
                                 - 
                                 
                                   x 
                                   waf 
                                   rbt 
                                 
                               
                               ) 
                             
                             2 
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   y 
                                   i 
                                   rbt 
                                 
                                 - 
                                 
                                   y 
                                   waf 
                                   rbt 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     36 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     CF 
                     ⁡ 
                     
                       ( 
                       
                         
                           x 
                           waf 
                           
                             rbt 
                             * 
                           
                         
                         , 
                         
                           y 
                           waf 
                           
                             rbt 
                             * 
                           
                         
                       
                       ) 
                     
                   
                   = 
                   
                     min 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       CF 
                       ⁡ 
                       
                         ( 
                         
                           
                             x 
                             waf 
                             rbt 
                           
                           , 
                           
                             y 
                             waf 
                             rbt 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     37 
                   
                   ) 
                 
               
             
           
         
       
     
     A numerical iterative technique may be used to minimize the above cost function by iterating through x waf   rbt  and y waf   rbt . The starting point may be selected based on one of the snapshots according to Equations (29) to (31). 
     Once the location of the wafer on the robot end-effector, x waf   rbt  and y waf   rbt , is estimated, the adjusted placement location x adj  and y adj  (i.e., placement location adjusted to achieve target wafer location, defined in main coordinate system) may be determined:
 
 x   adj   =x   tgt   −x   waf   rbt  cos θ adj   +y   waf   rbt  sin θ adj   (Eq. 38)
 
 y   adj   =y   tgt   −x   waf   rbt  sin θ adj   −y   waf   rbt  cos θ adj   (Eq. 39)
 
     where θ adj  may be selected arbitrarily if the robot has an independently articulated end-effector or an orienter, or θ adj  is a function of x adj  and y adj  if the robot does not have an independently articulated end-effector or an orienter. In the latter case, x adj , y adj  and θ adj . may be calculated together based on Equations (38), (39) and the relationship between θ adj  and x adj , y adj . 
     Alternatively, the placement location may be calculated directly, without calculating the location of the wafer in the end-effector coordinate system, as described in [12]. A polar, cylindrical or any other suitable coordinate system may be used. 
     Correction of Wafer Location and Orientation Based on Single Snapshot may be as follows. 
     Robot with articulated end-effector or rotary feature (orienter) on end-effector required. Input information: measurements extracted from camera snapshot x i   cam , y i   cam  and θ i   cam , where i=1, and measurements determined based on robot encoders x i , y i  and θ i , where i=1. Objective: estimate location and orientation of wafer on robot end-effector x waf   rbt , y waf   rbt  and θ waf   rbt , and determine adjusted placement location x adj , y adj  and θ adj :
 
 x   cam   +x   i   cam  cos θ cam   −y   i   cam  sin θ cam   =x   i   +x   waf   rbt  cos θ rbti   −y   waf   rbt  sin θ rbti   ,i= 1  (Eq. 40)
 
 y   cam   +x   i   cam  sin θ cam   +y   i   cam  cos θ cam   =y   i   +x   waf   rbt  sin θ rbti   +y   waf   rbt  cos θ rbti   ,i= 1  (Eq. 41)
 
(30) and (31)   x   waf   rbt   ,y   waf   rbt   (Eq. 42)
 
θ waf   rbt =θ cam +θ i   cam −θ i   ,i= 1  (Eq. 43)
 
     Once the location of the wafer on the robot end-effector, x waf   rbt , y waf   rbt  and θ waf   rbt , is calculated, the adjusted placement location x adj , y adj  and θ adj  (i.e., placement location adjusted to achieve target wafer location and orientation, defined in main coordinate system) may be determined:
 
θ adj =θ tgt −θ waf   rbt   (Eq. 44)
 
 x   adj   =x   tgt   −x   waf   rbt  cos θ adj   +y   waf   rbt  sin θ adj   (Eq. 45)
 
 y   adj   =y   tgt   −x   waf   rbt  sin θ adj   −y   waf   rbt  cos θ adj   (Eq. 46)
 
     Alternatively, the placement location may be calculated directly, without calculating the location of the wafer in the end-effector coordinate system, as described in [12]. A polar, cylindrical or any other suitable coordinate system may be used. 
     Correction of Wafer Location and Orientation Based on Multiple Snapshots may be as follows. 
     Robot with articulated end-effector or rotary feature (orienter) on end-effector required. Input information: measurements extracted from camera snapshots x i   ca , y i   cam  and θ i   cam , where i=1, 2, . . . , N, and measurements determined based on robot encoders x i , y i  and θ i , where i=1, 2, . . . , N. Objective: estimate location and orientation of wafer on robot end-effector x waf   rbt , y waf   rbt  and θ waf   rbt , and determine adjusted placement location x adj , y adj  and θ adj : 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         Conversion 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         of 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           x 
                           i 
                         
                       
                       , 
                       
                         y 
                         i 
                       
                       , 
                       
                         θ 
                         i 
                       
                       , 
                       
                         x 
                         i 
                         cam 
                       
                       ⁢ 
                       
                           
                       
                       , 
                       
                         
                           y 
                           i 
                           cam 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         and 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           θ 
                           i 
                           cam 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         to 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           x 
                           i 
                           rbt 
                         
                       
                       , 
                       
                         
                           y 
                           i 
                           rbt 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         and 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           i 
                           rbt 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     47 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         e 
                         di 
                       
                       = 
                       
                         
                           
                             
                               ( 
                               
                                 
                                   x 
                                   i 
                                   rbt 
                                 
                                 - 
                                 
                                   x 
                                   waf 
                                   rbt 
                                 
                               
                               ) 
                             
                             2 
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   y 
                                   i 
                                   rbt 
                                 
                                 - 
                                 
                                   y 
                                   waf 
                                   rbt 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       i 
                       = 
                       1 
                     
                     , 
                     2 
                     , 
                     … 
                     ⁢ 
                     
                         
                     
                     , 
                     N 
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     48 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         e 
                         
                           θ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           i 
                         
                       
                       = 
                       
                         
                           θ 
                           i 
                           rbt 
                         
                         - 
                         
                           θ 
                           waf 
                           rbt 
                         
                       
                     
                     , 
                     
                       i 
                       = 
                       1 
                     
                     , 
                     2 
                     , 
                     … 
                     ⁢ 
                     
                         
                     
                     , 
                     N 
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     49 
                   
                   ) 
                 
               
             
             
               
                 
                   CF 
                   = 
                   
                     
                       
                         
                           k 
                           d 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             e 
                             di 
                             2 
                           
                         
                       
                       + 
                       
                         
                           k 
                           θ 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             e 
                             θi 
                             2 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           k 
                           d 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             [ 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       x 
                                       i 
                                       rbt 
                                     
                                     - 
                                     
                                       x 
                                       waf 
                                       rbt 
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       y 
                                       i 
                                       rbt 
                                     
                                     - 
                                     
                                       y 
                                       waf 
                                       rbt 
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                             
                             ] 
                           
                         
                       
                       + 
                       
                         
                           k 
                           θ 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             
                               [ 
                               
                                 
                                   θ 
                                   i 
                                   rbt 
                                 
                                 - 
                                 
                                   θ 
                                   waf 
                                   rbt 
                                 
                               
                               ] 
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     50 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
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                               x 
                               waf 
                               rbt 
                             
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     A numerical iterative technique may be used to minimize the above cost function by iterating through x waf   rbt , y waf   rbt  and θ waf   rbt . The starting point may be selected based on one of the snapshots according to Equations (40) to (43). 
     Since the two sums in the cost function of Equation (50) are independent, they can be minimized independently. 
     Once the location of the wafer on the robot end-effector, x waf   rbt , y waf   rbt  and θ waf   rbt , is estimated, the adjusted placement location x adj , y adj  and θ adj  (i.e., placement location adjusted to achieve target wafer location and orientation, defined in main coordinate system) may be determined:
 
θ adj =θ tgt −θ waf   rbt   (Eq. 52)
 
 x   adj   =x   tgt   −x   waf   rbt  cos θ adj   +y   waf   rbt  sin θ adj   (Eq. 53)
 
 y   adj   =y   tgt   −x   waf   rbt  sin θ adj   −y   waf   rbt  cos θ adj   (Eq. 54)
 
     Alternatively, the placement location may be calculated directly, without calculating the location of the wafer in the end-effector coordinate system. A polar, cylindrical or any other suitable coordinate system may be used. 
     An adaptive placement system with Multiple Calibration Paths may be as follows. 
     The adaptive placement system may utilize multiple camera calibrations (locations) to calculate the location of the wafer on the robot end-effector and/or the adjusted placement location, the camera locations being identified for different motion paths in the initial calibration process. This is expected to improve the accuracy of the APS because it takes into account various inaccuracies in the robot system, particularly when the wafer is misaligned on the robot end-effector (this scenario is emulated by the different motion paths in the initial calibration process). 
     In the calibration process, the robot performs multiple moves to find the camera location. These moves include the nominal motion path as well as additional calibration motion paths on each side of the nominal motion path, the additional calibration paths being, for example, substantially parallel to the nominal motion path. Typically, the additional calibration motion paths are defined so that the wafer follows a similar path that it would follow if it were misalignment on the robot end-effector up to the point of the maximum expected misalignment of the wafer on the robot end-effector. As an example, assuming that the maximum expected misalignment of the wafer on the robot end-effector is 5 mm, five additional calibration motion paths on each side of the nominal motion path may be used, the five additional calibration motion paths being equally spaced with an increment of 1 mm. Alternatively, any suitable shape and spacing of the calibration motion paths may be used. 
     When the robot performs an APS place operation, the location of the wafer on the robot end-effector and/or the adjusted placement location is first calculated using the camera location identified based on the nominal calibration motion path. The resulting lateral difference is then used to determine the calibration motion path that is closest to the actual path of the wafer, and the location of the wafer on the robot end-effector and/or the adjusted placement location is recalculated using the sensor locations identified based on this calibration motion path. Alternatively, the location of the wafer on the robot end-effector and/or the adjusted placement location may be recalculated as an average of results determined using the camera locations identified based on the two closest calibration motion paths, each on one side of the actual path of the wafer. The average may be weighted to reflect the distance of the actual path of the wafer from the two closest calibration motion paths. Alternatively, any suitable algorithm may be employed to recalculate the location of the wafer on the robot end-effector and/or the adjusted placement location using the camera locations identified based on the additional calibration motion paths. 
     Referring to  FIG. 14B , there is shown a flow diagram of an exemplary method  920 . The example method  920  may comprise providing  922  a robot having a drive, a movable arm assembly connected to the drive, and a plurality of sets of end effectors, where the end effectors are connected to the drive by the movable arm assembly, where a first one of the sets of end effectors comprises at least two of the end effectors, where the drive and the movable arm assembly are configured to move the at least two end effectors substantially in unison from a retracted position towards an extended position towards two different respective target locations, and where the at least two end effectors are independently movable relative to each other on the moveable arm assembly. The example method  920  may comprise partially independently moving  924  the end effectors in the first set relative to each other by the robot, where a controller connected to the drive detects  926  an offset of respective substrates on the at least two end effectors and adjusts  928  movement of the at least two end effectors relative to each other prior to placement of the substrates at the respective target locations. 
     Referring to  FIG. 15 , there is shown a schematic top plan view of an example substrate transport robot  1100 . Robot  1100  may be a vacuum compatible or any suitable robot having drive portion  1110  and arm portion  1112  coupled to drive portion  1110  as will be described in greater detail below. Arm  1112  is shown having a common upper arm  1114  and two independently operable forearms  1116 ,  1118  coupled by elbow joints  1120 ,  1122  respectively to upper arm  1114 . Forearm  1116  has independently operable end effectors  1124 ,  1126  coupled to forearm  1116  at wrist  1128 . Similarly, forearm  1118  has independently operable end effectors  1130 ,  1132  coupled to forearm  1118  at wrist  1134 . In the embodiment shown, substrates  1136 ,  1138  may simultaneously be transported to and from stations within a piece of equipment where picking or placement of substrates  1136 ,  1138  may be done independently and simultaneously where each may be positioned at a location independent of the other. Referring also to  FIG. 16 , there is shown a schematic top plan view of an example substrate transport robot  1150 . Robot  1150  may be a vacuum compatible or any suitable robot having drive portion  1110  and arm portion  1160  coupled to drive portion  1110  as will be described in greater detail below. Arm  1160  is shown having two independently driven upper arms  1162 ,  1164  and two independently operable forearms  1166 ,  1168  coupled by elbow joints  1170 ,  1172  respectively to upper arms  1162 ,  1164 . Forearm  1166  has independently operable end effectors  1174 ,  1176  coupled to forearm  1166  at wrist  1178 . Similarly, forearm  1168  has independently operable end effectors  1180 ,  1182  coupled to forearm  1168  at wrist  1184 . In the embodiment shown, substrates  1136 ,  1138  may simultaneously be transported to and from stations within a piece of equipment where picking or placement of substrates  1136 ,  1138  may be done independently and simultaneously where each may be positioned at a location independent of the other. In the embodiment shown, the upper arm link lengths and forearm link lengths may be different and driven by circular or non circular pulleys. An example of arms having unequal link lengths and driven by non circular pulleys is given in U.S. patent application Ser. No. 13/833,732 entitled “Robot having Arm with Unequal Link Lengths” filed Mar. 15, 2013 which is incorporated by reference herein in its entirety. In alternate aspects, arms with the same link lengths or arms with unequal link lengths and having circular pulleys may be provided.  FIGS. 15 and 16  each show two arms having two end effectors. In alternate aspects, a single arm having a single or multiple end effectors may be provided. 
     Referring to  FIG. 17 , there is shown a schematic cross section of robot  1100 . Drive  1110  is shown having 5 coaxial shafts coupled to coaxial motor encoder arrangements  1210 ,  1212 ,  1214 ,  1216 ,  1218  designated as inner shafts to the outer. Each motor arrangement may be located within vacuum tight housing  1110 . Alternately, only the rotors of motors of drives  1210 ,  1212 ,  1214 ,  1216 ,  1218  may be in vacuum in the drive housing  1220  where a sleeve may be provided between the rotors and stators. A vertical drive  1222 , such as a lead screw or other suitable drive may lift and lower housing  1220  where slides  1224  may constrain housing  1220  in a vertical direction and bellows  1226  may be coupled to housing  1220  and flange  1228  to maintain a vacuum environment where arm  1112  and the inner portion of housing  1220  may be exposed to vacuum. The shaft of drive  1218  is directly coupled to the common upper arm  1114 . The shaft of drive  1216  is directly coupled to pulley  1230  which is in turn coupled by bands to pulley  1232  in elbow  1122  where pulley  1232  is directly coupled to forearm  1118 . Here rotation of motor  1216  rotates forearm  1118  about the elbow  1122 . The shaft of drive  1214  is directly coupled to pulley  1234  which is in turn coupled by bands to pulley  1236  in elbow  1120  where pulley  1236  is directly coupled to forearm  1116 . Here rotation of motor  1214  rotates forearm  1116  about the elbow  1120 . The shaft of drive  1212  is directly coupled to pulley  1238  which is in turn coupled by bands to pulley  1240  in elbow  1122  where pulley  1240  is directly coupled to pulley  1242  in elbow  1122 . Pulley  1242  is then coupled by bands to pulley  1244  in wrist  1134  where pulley  1244  is directly coupled to lower end effector  1132 . Here, rotation of motor  1212  rotates lower end effector  1132  about the wrist  1134 . Similarly, pulley  1238  is also coupled by bands to pulley  1246  in elbow  1120  where pulley  1246  is directly coupled to pulley  1248  in elbow  1120 . Pulley  1248  is then coupled by bands to pulley  1250  in wrist  1128  where pulley  1250  is directly coupled to lower end effector  1126 . Here, rotation of motor  1212  rotates lower end effector  1126  about the wrist  1128 . Further, rotation of motor  1212  simultaneously rotates both lower end effectors  1126 ,  1132  about their respective wrists  1128 ,  1134 . The shaft of drive  1210  is directly coupled to pulley  1252  which is in turn coupled by bands to pulley  1254  in elbow  1122  where pulley  1254  is directly coupled to pulley  1256  in elbow  1122 . Pulley  1256  is then coupled by bands to pulley  1258  in wrist  1134  where pulley  1258  is directly coupled to upper end effector  1130 . Here, rotation of motor  210  rotates upper end effector  1130  about the wrist  1134 . Similarly, pulley  1252  is also coupled by bands to pulley  1260  in elbow  120  where pulley  1260  is directly coupled to pulley  1262  in elbow  1120 . Pulley  1262  is then coupled by bands to pulley  1264  in wrist  1128  where pulley  1250  is directly coupled to upper end effector  1124 . Here, rotation of motor  210  rotates upper end effector  124  about the wrist  1128 . Further, rotation of motor  1210  simultaneously rotates both upper end effectors  1124 ,  1130  about their respective wrists  1128 ,  1134 . The shafts associated with drives  1210 ,  1212 ,  1214 ,  1216 ,  2118  are each independently and coaxially rotatable and may be supported by any suitable bearing or other arrangement with respect to housing  1220  as shown or otherwise. The three pulleys in each of elbows  1120 ,  1122  and the two pulleys in each of wrists  1128 ,  1134  are each independently and coaxially rotatable with respect to a common axis in each joint and may be supported by any suitable bearing or other arrangement as shown or otherwise. The following description of respective pulley ratios is based on the premise that the link lengths of each link are the same. In alternate aspects, different ratios or driving arrangement may be provided, for example, where the link lengths are different. An example of arms having unequal link lengths and driven by non circular pulleys is given in U.S. patent application Ser. No. 13/833,732 entitled “Robot having Arm with Unequal Link Lengths” filed Mar. 15, 2013 which is incorporated by reference herein in its entirety. In the embodiment shown, pulleys and bands are provided. In alternate embodiments, any suitable power transmission arrangement may be provided, for example, belts, links, gears, cable or any suitable arrangement. In the embodiment shown, 5 coaxial direct driving shafts are provided. In alternate embodiments, any suitable driving arrangement may be provided, for example, motors in joints, links, speed reducers, belts, magnetic couplings, linear and/or rotational drives or any suitable drive may be provided. In the embodiment shown, the ratio between pulleys  1230 ,  1232  and  1234 ,  1236  may be any suitable ratio, for example, 1:1 or higher or lower than 1:1. In the embodiment shown, the ratio between pulleys  1238 ,  1240  and  1238 ,  1246  may be any suitable ratio, for example, 1:3 or higher or lower than 1:3. In the embodiment shown, the ratio between pulleys  1252 ,  1254  and  1252 ,  1250  may be any suitable ratio, for example, 1:3 or higher or lower than 1:3. In the embodiment shown, the ratio between pulleys  1242 ,  1244  and  1248 ,  2150  may be any suitable ratio, for example, 1:2. In the embodiment shown, the ratio between pulleys  1256 ,  1258  and  1262 ,  1264  may be any suitable ratio, for example, 1:2. In operation, simultaneous rotation of all of drives  1210 ,  1212 ,  1214 ,  1216 ,  1218  rotates the entire arm assembly. Simultaneous rotation of common link  1114 , pulleys  1234 ,  1238  and  1252  with counter rotation of pulley  1230  cause end effectors  1130 ,  1132  to extend or retract while end effectors  1124 ,  1126  rotate with common upper arm  1114 . Similarly, simultaneous rotation of common link  1114 , pulleys  1230 ,  1238  and  1252  with counter rotation of pulley  1234  cause end effectors  1124 ,  1126  to extend or retract while end effectors  1130 ,  1132  rotate with common upper arm  1114 . Further, relative rotation of pulley  1238  will cause a corresponding relative rotation of end effectors  1132 ,  1126 . Similarly, relative rotation of pulley  1252  will cause a corresponding relative rotation of end effectors  1130 ,  1124 . With the 5 rotary axis drive and arm arrangement described, 2 substrates may be independently placed at different locations as will be described in greater detail below. For example, 2 substrates supported on end effectors  1130 ,  1132  may be independently placed at two locations. Similarly, 2 substrates supported on end effectors  1124 ,  1126  may be independently placed at two locations. In alternate aspects, more or less arms and axis&#39; may be provided. 
     Referring to  FIG. 18 , there is shown a schematic cross section of robot  1150 . Drive  1110  is shown having 5 coaxial shafts coupled to coaxial motor encoder arrangements  1210 ,  1212 ,  1214 ,  1216 ,  1218  designated as inner shafts to the outer and as described above. The shaft of drive  1218  is directly coupled to upper arm  1164 . The shaft of drive  1210  is directly coupled to upper arm  1162 . Here, arms  1162 ,  1164  are independently rotatable. The shaft of drive  1216  is directly coupled to pulley  1310  which is in turn coupled by bands to pulley  1312  in elbow  1172  where pulley  1312  is directly coupled to forearm  1168 . Here rotation of motor  1216  rotates forearm  1168  about the elbow  1172 . Pulley  1310  which is then coupled by bands to pulley  1314  in elbow  1170  where pulley  1314  is directly coupled to forearm  1166 . Here rotation of motor  1216  rotates forearm  1166  about the elbow  1170 . Further, rotation of motor  1216  simultaneously rotates both forearms  1168 ,  1166  about their respective elbows  1172 ,  1170 . The shaft of drive  1214  is directly coupled to pulley  1316  which is in turn coupled by bands to pulley  1318  in elbow  1172  where pulley  1318  is directly coupled to pulley  1320  in elbow  1172 . Pulley  1320  is then coupled by bands to pulley  1322  in wrist  1184  where pulley  1322  is directly coupled to lower end effector  1182 . Here, rotation of motor  1214  rotates lower end effector  1182  about the wrist  1184 . Similarly, pulley  1310  is also coupled by bands to pulley  1324  in elbow  1170  where pulley  1324  is directly coupled to pulley  1326  in elbow  1170 . Pulley  1326  is then coupled by bands to pulley  1328  in wrist  1178  where pulley  1328  is directly coupled to lower end effector  1176 . Here, rotation of motor  1214  rotates lower end effector  1176  about the wrist  1178 . Further, rotation of motor  1214  simultaneously rotates both lower end effectors  1176 ,  1182  about their respective wrists  1178 ,  1184 . The shaft of drive  1212  is directly coupled to pulley  1330  which is in turn coupled by bands to pulley  1332  in elbow  1172  where pulley  1332  is directly coupled to pulley  1334  in elbow  1172 . Pulley  1334  is then coupled by bands to pulley  1336  in wrist  1184  where pulley  1336  is directly coupled to upper end effector  1180 . Here, rotation of motor  1212  rotates upper end effector  1180  about the wrist  1184 . Similarly, pulley  1330  is also coupled by bands to pulley  1338  in elbow  1170  where pulley  1338  is directly coupled to pulley  1340  in elbow  1170 . Pulley  1340  is then coupled by bands to pulley  1342  in wrist  1178  where pulley  1242  is directly coupled to upper end effector  1174 . Here, rotation of motor  1212  rotates upper end effector  1174  about the wrist  1178 . Further, rotation of motor  1212  simultaneously rotates both upper end effectors  1174 ,  1180  about their respective wrists  1178 ,  1184 . The shafts associated with drives  1210 ,  1212 ,  1214 ,  1216 ,  1218  are each independently and coaxially rotatable and may be supported by any suitable bearing or other arrangement with respect to housing  1220  as shown or otherwise. The three pulleys in each of elbows  1170 ,  1172  and the two pulleys in each of wrists  1178 ,  1184  are each independently and coaxially rotatable with respect to a common axis in each joint and may be supported by any suitable bearing or other arrangement as shown or otherwise. The following description of respective pulley ratios is based on the premise that the link lengths of each link are the same. In alternate aspects, different ratios or driving arrangement may be provided, for example, where the link lengths are different. An example of arms having unequal link lengths and driven by non circular pulleys is given in U.S. patent application Ser. No. 13/833,732 entitled “Robot having Arm with Unequal Link Lengths” filed Mar. 15, 2013 which is incorporated by reference herein in its entirety. In the embodiment shown, pulleys and bands are provided. In alternate embodiments, any suitable power transmission arrangement may be provided, for example, belts, links, gears, cable or any suitable arrangement. In the embodiment shown, 5 coaxial direct driving shafts are provided. In alternate embodiments, any suitable driving arrangement may be provided, for example, motors in joints, links, speed reducers, belts, magnetic couplings, linear and/or rotational drives or any suitable drive may be provided. In the embodiment shown, the ratio between pulleys  1310 ,  1312  and  1310 ,  1314  may be any suitable ratio, for example, 2:1. In the embodiment shown, the ratio between pulleys  1238 ,  1240  and  1238 ,  1246  may be any suitable ratio, for example, 1:3 or higher or lower than 1:3. In the embodiment shown, the ratio between pulleys  1316 ,  1318  and  1316 ,  1324  may be any suitable ratio, for example, 1:1. In the embodiment shown, the ratio between pulleys  1320 ,  1322  and  1326 ,  1328  may be any suitable ratio, for example, 1:1. In the embodiment shown, the ratio between pulleys  1334 ,  1336  and  1340 ,  1342  may be any suitable ratio, for example, 1:1. In operation, simultaneous rotation of all of drives  1210 ,  1212 ,  1214 ,  1216 ,  1218  rotates the entire arm assembly. Rotation of upper arm  1164  while holding pulleys  1310 ,  1316 ,  1330  and upper arm  1162  stationary cause end effectors  1180 ,  1182  to extend or retract while end effectors  1174 ,  1176  remain stationary. Similarly, rotation of upper arm  1162  while holding pulleys  1310 ,  1316 ,  1330  and upper arm  1164  stationary cause end effectors  1174 ,  1176  to extend or retract while end effectors  1180 ,  1182  remain stationary. Further, relative rotation of pulley  1316  will cause a corresponding relative rotation of end effectors  1182 ,  1176 . Similarly, relative rotation of pulley  1330  will cause a corresponding relative rotation of end effectors  1180 ,  1174 . With the 5 rotary axis drive and arm arrangement described, 2 substrates may be independently placed at different locations as will be described in greater detail below. For example, 2 substrates supported on end effectors  1180 ,  1182  may be independently placed at two locations. Similarly, 2 substrates supported on end effectors  1174 ,  1176  may be independently placed at two locations. In alternate aspects, more or less arms and axis&#39; may be provided. 
     Vacuum robots disclosed herein may be provided within the vacuum chamber of transport platform and may have features as disclosed in U.S. patent application having Ser. No. 13/618,067 entitled “Robot Drive with Passive Rotor” and filed Sep. 14, 2012. Further, vacuum robots may be provided within the vacuum chamber of a platform and may have features as disclosed in U.S. patent application having Ser. No. 13/618,117 entitled “Low Variability Robot” and filed Sep. 14, 2012. Further, vacuum robots may be provided within the a vacuum chamber of a platform and may have features as disclosed in U.S. patent application having Ser. No. 13/833,732 entitled “Robot Having Arm With Unequal Link Lengths” and filed Mar. 15, 2013. Further, vacuum robots may be provided within the vacuum chamber of a platform and may have features as disclosed in U.S. Patent applications having Ser. No. 61/831,320 entitled “Robot and Adaptive Placement System and Method” and filed Jun. 5, 2013. All of the above referenced applications are hereby incorporated by reference here in in their entirety. 
     Referring now to  FIG. 19 , there is shown a top view of an example substrate transport robot  1400  in an extended position. Referring also to  FIG. 20 , there is shown a top view of an example substrate transport robot  1400  in a retracted position. Robot  1400  has arm  1412  having independently operable arms  1420 ,  1418  such that substrates  1416 ,  1414  may be independently position detected and placed at two stations independently. Arms  1420  and  1418  are coupled to drive  1410  as will be described in greater detail below. Arm  1420  has upper arm  1428  coupled to forearm  1430  by an elbow axis. Forearm  1430  is coupled to end effector  1432  by a wrist axis. End effector  1432  supports substrate  1416 . Similarly, arm  1418  has upper arm  1422  coupled to forearm  1424  by an elbow axis. Forearm  1424  is coupled to end effector  1426  by a wrist axis. End effector  1426  supports substrate  1414 . Arms  1420 ,  1418  are independently driven, each by a two axis drive such that substrates  1414 ,  1416  may be independently picked and/or placed. 
     Referring now to  FIG. 21 , there is shown a section schematic view of an example substrate transport robot  1400 . Arm  1420  is coupled to drive  1410  via shafts  1444 ,  1446 . Arm  1418  is coupled to drive  1410  via shafts  1440 ,  1442 . The shafts may be directly driven by motors or any suitable method and may have position encoders to feed position to a controller. Arm  1420  has shaft  1446  coupled to upper arm  1428 . Upper arm  1428  is coupled to forearm  1430  by an elbow axis  1470 . Forearm  1430  is coupled to end effector  1432  by a wrist axis  1472 . End effector  1432  supports substrate  1416 . Shaft  1444  is coupled to shoulder pulley  1474  where shoulder pulley  1474  is coupled to elbow pulley  1478  via band  1476  and where elbow pulley  1478  is coupled to forearm  1430 . Elbow pulley  1480  is coupled to upper arm  1428  where elbow pulley  1480  is further coupled to wrist pulley  1484  via band  1486 . Wrist pulley  1484  is further coupled to end effector  1432 . Here, the combination of links, pulleys and bands cooperates with driving shafts  1444 ,  1446  such that via rotation of driving shafts  1444 ,  1446  the end effector  1432  of arm  1420  may be independently positioned. Arm  1418  has shaft  1440  coupled to upper arm  1422 . Upper arm  1422  is coupled to forearm  1424  by an elbow axis  1448 . Forearm  1424  is coupled to end effector  1426  by a wrist axis  1450 . End effector  1426  supports substrate  1414 . Shaft  1442  is coupled to shoulder pulley  1452  where shoulder pulley  1452  is coupled to elbow pulley  1456  via band  1454  and where elbow pulley  1456  is coupled to forearm  1424 . Elbow pulley  1458  is coupled to upper arm  1424  where elbow pulley  1458  is further coupled to wrist pulley  1462  via band  1460 . Wrist pulley  1462  is further coupled to end effector  1426 . Here, the combination of links, pulleys and bands cooperates with driving shafts  1440 ,  1442  such that via rotation of driving shafts  1440 ,  1442  the end effector  1426  of arm  1418  may be independently positioned. 
     Referring now to  FIG. 22 , there is shown a top schematic view of an exemplary link apparatus  1510 . Exemplary link apparatus  1510  is shown where two pulley pairs may be provided within a link with small relative rotation between them. Here, the two pulley pairs may have bands that share a common elevation such that link depths may be made similar to that where a single pulley pair is located within a given link. Here, respective pulleys have surfaces that engage their respective bands over a length or range of operation and further are relieved such that a corresponding coaxial pulley of the other pulley pair may occupy substantially the same elevation. Here, axis  1512  may have coaxial  1516  pulleys  1520 ,  1530  that substantially occupy the same elevation as being relieved as shown. Similarly, axis  1514  may have coaxial  1518  pulleys  1522 ,  1532  that substantially occupy the same elevation as being relieved as shown. Here, pulley  1520  is coupled to pulley  1522  with bands  1524  and  1526 . Similarly, pulley  1530  is coupled to pulley  1532  with bands  1534  and  1536 . In the embodiment shown, any suitable pulleys may be used, for example, circular, non circular or otherwise. In the embodiment shown, any suitable ratio between the pulleys may be used, fixed, variable or otherwise. In alternate aspects, any suitable linkage may be utilized in substantially similar elevations to drive concentric or non concentric axis, for example, solid links and bearings, flexures or any suitable linkage. 
     Referring now to  FIG. 23 , there is shown a side schematic view of an exemplary linkage apparatus  1610 . Here, apparatus  1610  has drive unit  1612  coupled to arms  1614 ,  1616  respectively. Here, arms  1614 ,  1616  may be any suitable arm or linkage. Arm  1614  may have shafts of drive  1612  coupled to upper arm  1618  with upper arm  1618  coupled to forearm  1620  and with forearm  1620  coupled to end effector  1622 . A secondary driving device  1630  may be positioned coupled to or within any link, axis or end effector, for example, coupled to end effector  1622  and positioned in the unused space as shown. Drive  1630  may control any suitable axis within arm  1614  or alternately may control one or more end effector(s) independently or one or more wafer support(s) independently. Similarly, arm  1616  may have shafts of drive  1612  coupled to upper arm 1   624  with upper arm  1624  coupled to forearm  1626  and with forearm  1626  coupled to end effector  1628 . A secondary driving device  1632  may be positioned coupled to or within any link, axis or end effector, for example, coupled to end effector  1628  and positioned in the unused space as shown. Drive  1632  may control any suitable axis within arm  1616  or alternately may control one or more end effector(s) independently or one or more wafer support(s) independently. By way of example, in one aspect, a single or multiple secondary drive unit(s) may be positioned within one or more links, for example, in a linkage as shown in  FIG. 15  or  FIG. 16  or otherwise to drive rotation or relative rotation of one or more end effector(s). Accordingly, these and all such variations may be provided. 
     Referring now to  FIG. 24 , there is shown a top schematic view of an exemplary wrist apparatus  1652 . Referring also to  FIG. 25 , there is shown a side section schematic view of an exemplary wrist apparatus  1652 . Referring also to  FIG. 26 , there is shown a top section schematic view of an exemplary wrist apparatus  1652 . Wrist apparatus  1652  is provided with link  1654  coupled to end effector apparatus  1656  via wrist axis  1658 . Here, by way of example only, band  1666  may drive pulley  1664  where pulley  1664  is coupled to end effector  1656  by bearing  1662  on post  1660  of wrist axis  1658 . Exemplary secondary actuator  1668  is further shown coupled to end effector  1656 . Secondary actuator  1668  may be coupled to end effector  1656  by coupling members  1672 ,  1674  where coupling members  1672 ,  1674  may be any suitable coupling member, solid or compliant or otherwise. Coupling members  1672 ,  1674  may further be provided to thermally isolate actuator  1668  from end effector  1656 . In alternate embodiments the secondary actuator may be coupled to any member, link or otherwise. In the embodiment shown, secondary actuator  1668  is a single axis device. In alternate aspects, any suitable number of axis may be provided. In the embodiment shown, secondary actuator  1668  is a linear single axis device. In alternate aspects, any suitable type of axis may be provided, for example, linear, rotary or otherwise. Here the axis may have any suitable driver such as brushless, stepping or any suitable motor. Further, the axis may have any suitable power transmission, for example, lead screw, harmonic drive, brake or any suitable power transmission. Further, the axis may have any suitable feedback device such as a position encoder, homing flag or other suitable position detection device. Secondary actuator  1668  may have housing  1670 , actuator  1676  and control portion  1682 . Secondary actuator  6168  may be supplied power from a harness to the robot drive or may harvest power from relative motion, for example, relative motion of end effector  1656  and link  1654  or relative motion of any suitable components within the arm robot drive or otherwise. Here, magnets  1686  may be coupled to link  1654  and winding  1684  may be coupled to housing  1670 . Relative motion may generate current within the winding  1684  where control portion  1682  may have power circuitry to harvest the energy, for example, rectifier, power conditioning circuitry, DC-DC converter, battery or capacitive power storage and charge and discharge circuitry. Control portion  1682  may further have a processor, memory servo or stepper amplification and feedback circuitry, communication interface circuitry, for example, optical, wireless or wire based communication interface circuitry. Control portion  1682  may further have any suitable circuitry, for example analog or digital I/O, temperature and over temperature detection circuitry, vibration detection circuitry or any suitable circuitry. Control portion  682  may drive a servo or stepper motor  1676  having a lead screw  1680  driving pin  1662  in slot  1660  of end effector  1656 . The pin may drive any suitable member, for example, an end effector, flexure or otherwise. Here, the actuator  1676  may be locking such that power may be removed when not in operation to minimize the need for heat dissipation. The components of actuator  1668  may be sealed within housing  1670  and interface with end effector  1656  with bellows  1678  allowing for linear motion translation. Alternately, the components may be potted within or thermally coupled to housing  1670 . Housing  1670  may be provided with a high emissivity material or coating such that maximum heat may be radiated from housing  1670  to dissipate heat from the components within housing  1670 . 
     Referring now to  FIG. 27 , there is shown a top schematic view illustrating an example end effector apparatus  1710  coupled to wrist W. End effector  1710  supports substrates  1712 ,  1714  relative to the end effector frame  1716 . Mounted to the frame by flexures  1726  are moveable substrate supports  1718 ,  1720  that are relatively moveable in orthogonal directions  1730 ,  1728 . In alternate aspects, the supports may be relatively moveable in any direction, orthogonal or otherwise. Secondary actuators  1722 ,  1724  are coupled to frame  1716  and selectively move supports  1718 ,  1720  respectively. Secondary actuators  1722 ,  1724  may be as described or any suitable actuator. 
     Referring now to  FIG. 28 , there is shown a top schematic view illustrating an example end effector apparatus  1710 A. End effector  1710 A supports substrates  1712 ,  1714  relative to the end effector frame  1716 A. Mounted to the frame by flexures  1726 A are moveable substrate supports  1718 A,  1720 A that are relatively moveable in orthogonal directions  1730 A,  1728 A. In alternate aspects, the supports may be relatively moveable in any direction, orthogonal or otherwise. Secondary actuators  1722 A,  1724 A are coupled to frame  1716 A and selectively move supports  1718 A,  1720 A respectively. Secondary actuators  1722 A,  1724 A may be as described or any suitable actuator. 
     Referring now to  FIG. 29 , there is shown a top schematic view illustrating an example end effector apparatus  1760 . End effector  1760  has a stationary link coupled to wrist W with two rotary driven axis  1776 ,  1778  coupled to the wrist, arm or otherwise. Rotationally moveable wafer supports  1762 ,  1764  are rotationally coupled to the stationary link at pivot axis  1760 ,  1770  respectively. Bands  1776 ,  1778  (with pulleys) couple rotational drives  1776 ,  1778  to links  1762 ,  1764  such that links  1762 ,  1764  may be selectively rotated. In alternate aspects, any suitable arrangement may be provided, for example, rotational drives  1776 ,  1778  may directly drive supports  1760 ,  1770  where no stationary link need be provided. 
     Referring now to  FIG. 30 , there is shown a top schematic view illustrating an example end effector apparatus  1780 . End effector  1780  has a stationary link coupled to wrist W with two rotary driven axis  1796 ,  1798  coupled to the wrist, arm or otherwise. Rotationally moveable wafer supports  1782 ,  1784  are rotationally coupled to the stationary link at pivot axis  1788 ,  1790  respectively. Links  1792 ,  1794  couple rotational drives  1796 ,  1798  to supports  1782 ,  1784  such that supports  1782 ,  1784  may be selectively rotated. In alternate aspects, any suitable arrangement may be provided, for example, rotational drives  1796 ,  1798  may directly drive supports  1782 ,  1784  where no stationary link need be provided. 
     Referring now to  FIG. 31 , there is shown a top schematic view illustrating an example end effector apparatus  1810 . End effector  1810  has a stationary link  1812  coupled to wrist W with one or two driven axis  1826  coupled to the wrist, arm or otherwise. Rotationally moveable wafer supports  1814 ,  1816  are rotationally coupled to the stationary link  1812  pivot axis  1818 ,  1820  respectively. Bands  1822 ,  1824  couple rotational drives  1828 ,  1830  to supports  1814 ,  1816  such that supports  1814 ,  1816  may be selectively rotated  1842 ,  1844 . Here, translation  1840  of drive  1826  selectively rotates links  1814 ,  1816  in opposite directions. Rotation of drive  1826  selectively rotates links  1814 ,  1816  in same directions. In alternate aspects, any suitable arrangement may be provided, for example, rotational drives  1828 ,  1830  may directly drive supports  1814 ,  1816  where no stationary link need be provided. 
     Referring now to  FIG. 32 , there is shown a top schematic view illustrating an example end effector apparatus  1850 . End effector  1850  has a stationary link  1852  coupled to wrist W with one or two driven axis  1866  coupled to the wrist, arm or otherwise. Rotationally moveable wafer supports  1854 ,  1856  are rotationally coupled to the stationary link  1852  by pivot axis  1858 ,  1860  respectively. Bands  1862 ,  1864  couple rotational drives  1868 ,  1870  to supports  1854 ,  1856  such that supports  854 ,  856  may be selectively rotated  882 ,  884 . Here, translation  1880  of drive  1866  selectively rotates links  1854 ,  1856  in opposite directions. Rotation of drive  1866  selectively rotates links  1854 ,  1856  in same directions. In alternate aspects, any suitable arrangement may be provided, for example, rotational drives  868 ,  870  may directly drive supports  1854 ,  1856  where no stationary link need be provided. 
     Referring to  FIG. 33 , there is shown a schematic top plan view of an example substrate transport robot  2010 . Although the present embodiment will be described with reference to the embodiments shown in the drawings, it should be understood that the present invention may be embodied in many forms of alternative embodiments. In addition, any suitable size, shape or type of materials or elements could be used. Referring also to  FIG. 34 , there is shown a side view of robot  2010 . Exemplary robot  2010  is shown having drive portion  2012 , first driven arm  2012 , second driven arm  2014 , third driven arm  2016  and fourth driven arm  2018 . Robot  2010  having drive and driven arms may have features as disclosed in PCT/US2014/011416 having an international filing date of Jan. 14, 2014 and entitled “Robot having Arm With Unequal Link Lengths” which is hereby incorporated by reference herein in its entirety. Further, Robot  2010  having drive and driven arms may have features and may take advantage of features as disclosed. In the embodiment shown, each of the driven arms has upper arms coupled to the drive at a shoulder joint, forearms coupled to the upper arms at an elbow joint and an end effector coupled to the forearm at a wrist joint. The embodiment shown in  FIG. 34  has the fore arms of arms  2014 ,  2016  located below their respective upper arms. In alternate aspects, one or both of the fore arms of arms  2014 ,  2016  may be located above their respective upper arms. The embodiment shown in  FIG. 34  has the fore arms of arms  2018 ,  2020  located above their respective upper arms. In alternate aspects, one or both of the fore arms of arms  2018 ,  2020  may be located below their respective upper arms. 
     Referring now to  FIG. 35 a   , there is shown a top view of robot  2010  in a retracted position. Referring also to  FIG. 35 b   , there is shown a top view of robot  2010  with first arm  2014  extended. Referring also to  FIG. 35 c   , there is shown a top view of robot  2010  with second arm  2016  extended. Referring also to  FIG. 36 a   , there is shown a top view of robot  2010  in a retracted position. Referring also to  FIG. 36 b   , there is shown a top view of robot  2010  with first and second arms  2014 ,  2016  extending simultaneously. Referring also to  FIG. 36 c   , there is shown a top view of robot  2010  with first and second arms  2014 ,  2016  extended. With respect to  FIGS. 37A and 37B , each of the four driven arms are moveable independently in a radial direction while each of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction as will be described. With respect to  FIGS. 38A and 38B , each of the four driven arms are moveable independently in a radial direction while first and second of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction and while third and fourth of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction with first and second driven arms rotatable independent of the third and fourth driven arms as will be described. With respect to  FIGS. 39A and 39B , each of the four driven arms are moveable independently in a radial direction while first and third of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction and while second and fourth of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction with first and third driven arms rotatable independent of the second and fourth driven arms as will be described. In alternate aspects, any suitable axis dependency may be provided. 
     Referring now to  FIG. 37A , there is shown a section schematic view of robot  2200 . Referring also to  FIG. 37B , there is shown a section schematic view of robot  2200 ′. In the embodiment shown, each of the driven arms  2214 ,  2216 ,  2218 ,  2220  has upper arms coupled to the drive  2212  at a shoulder joint, forearms coupled to the upper arms at an elbow joint and an end effector coupled to the forearm at a wrist joint. The embodiment shown in  FIG. 37A  has the fore arms of arms  2214 ,  2216  located below their respective upper arms. In alternate aspects, one or both of the fore arms of arms  2214 ,  2216  may be located above their respective upper arms. For example,  FIG. 37B  shows both of the fore arms of arms  2214 ′,  2216 ′ located above their respective upper arms. The embodiment shown in  FIG. 37A  has the fore arms of arms  2218 ,  2220  located above their respective upper arms. In alternate aspects, one or both of the fore arms of arms  2218 ,  2220  may be located below their respective upper arms. For example,  FIG. 37B  shows both of the fore arms of arms  2218 ′,  2220 ′ located below their respective upper arms.  FIG. 37A  shows drive  2212  having 25 concentric rotary drive axis  2222 ,  2224 ,  2226 ,  2228 ,  2230 . Each rotary drive axis may have a motor and encoder with a drive shaft extending from housing  2234  through bellows  2236  into vacuum or other environment  2238 . In the embodiment shown, rotary drive  2230  is coupled to the upper arm of driven arm  2218 ; rotary drive  2228  is coupled to pulley  2250 ; rotary drive  2226  is coupled to the upper arm of driven arm  2220 ; rotary drive  2224  is coupled to the upper arm of driven arm  2214  and rotary drive  2222  is coupled to the upper arm of driven arm  2216 . Pulley  2250  has 4 pulley portions that interface with corresponding forearm driving pulleys in each arm. Bridge  2254  couples the upper portion of pulley  2250  to the lower portion of pulley  2250 . Bridge  2254  may have any configuration, for example, bridge  2254  may be one or more posts that passes through kidney slots in the upper arms of arms  2214  and  2220 . With respect to  FIGS. 37A and 37B , each of the four driven arms are moveable independently in a radial direction while each of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction. Here, the four driven arms are moveable independently in a radial direction due to independent rotation of axis  2230 ,  2226 ,  2224 ,  2222  while holding pulley axis  2228  stationary. Here, each of the four driven arms are moveable dependently in a rotary or theta direction by simultaneous rotation of axis  2222 ,  2224 ,  2226 ,  2228 ,  2230 . 
     Referring now to  FIG. 38A , there is shown a section schematic view of robot  2400 . Referring also to  FIG. 38B , there is shown a section schematic view of robot  2400 ′. In the embodiment shown, each of the driven arms  2414 ,  2416 ,  2418 ,  2420  has upper arms coupled to the drive  2412  at a shoulder joint, forearms coupled to the upper arms at an elbow joint and an end effector coupled to the forearm at a wrist joint. The embodiment shown in  FIG. 38A  has the fore arms of arms  2414 ,  2416  located below their respective upper arms. In alternate aspects, one or both of the fore arms of arms  2414 ,  2416  may be located above their respective upper arms. For example,  FIG. 38B  shows both of the fore arms of arms  2414 ′,  2416 ′ located above their respective upper arms. The embodiment shown in  FIG. 38A  has the fore arms of arms  2418 ,  2420  located above their respective upper arms. In alternate aspects, one or both of the fore arms of arms  2418 ,  2420  may be located below their respective upper arms. For example,  FIG. 38B  shows both of the fore arms of arms  2418 ′,  2420 ′ located below their respective upper arms.  FIG. 38A  shows drive  2412  having 6 concentric rotary drive axis  2422 ,  2424 ,  2426 ,  2428 ,  2430 ,  2432 . Each rotary drive axis may have a motor and encoder with a drive shaft extending from housing  2434  through bellows  2436  into vacuum or other environment  2438 . In the embodiment shown, rotary drive  2432  is coupled to the upper arm of driven arm  2418 ; rotary drive  2430  is coupled to pulley  2450 ; rotary drive  2428  is coupled to the upper arm of driven arm  2420 ; rotary drive  2426  is coupled to the upper arm of driven arm  2414 ; rotary drive  424  is coupled to the pulley  2452  and rotary drive  2422  is coupled to the upper arm of driven arm  2416 . Pulley  2450  has 2 pulley portions that interface with corresponding forearm driving pulleys of driven arms  2418 ,  2420 . Pulley  2452  has 2 pulley portions that interface with corresponding forearm driving pulleys of driven arms  2414 ,  2416 . With respect to  FIGS. 38A and 38B , each of the four driven arms are moveable independently in a radial direction while first and second of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction and while third and fourth of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction with first and second driven arms rotatable independent of the third and fourth driven arms. Here, the four driven arms are moveable independently in a radial direction due to independent rotation of axis  2432 ,  2428 ,  2426 ,  2422  while holding both pulley axis  2430 ,  2424  stationary. Here, each of the four driven arms are moveable in a rotary or theta direction by simultaneous rotation of axis  2422 ,  2424 ,  2426 ,  2428 ,  2430 ,  2432 . Here, first and second driven arms are rotatable independent of the third and fourth driven arms by simultaneously rotation of axis  2422 ,  2424 ,  2426 . Here, third and fourth driven arms are rotatable independent of the first and second driven arms by simultaneously rotation of axis  2428 ,  2430 ,  2432 . 
     Referring now to  FIG. 39A , there is shown a section schematic view of robot  2600 . Referring also to  FIG. 39B , there is shown a section schematic view of robot  2600 ′. In the embodiment shown, each of the driven arms  2614 ,  2616 ,  2618 ,  2620  has upper arms coupled to the drive  2612  at a shoulder joint, forearms coupled to the upper arms at an elbow joint and an end effector coupled to the forearm at a wrist joint. The embodiment shown in  FIG. 39A  has the fore arms of arms  2614 ,  2616  located below their respective upper arms. In alternate aspects, one or both of the fore arms of arms  2614 ,  2616  may be located above their respective upper arms. For example,  FIG. 39B  shows both of the fore arms of arms  2614 ′,  2616 ′ located above their respective upper arms. The embodiment shown in  FIG. 39A  has the fore arms of arms  2618 ,  2620  located above their respective upper arms. In alternate aspects, one or both of the fore arms of arms  2618 ,  2620  may be located below their respective upper arms. For example,  FIG. 39B  shows both of the fore arms of arms  2618 ′,  2620 ′ located below their respective upper arms.  FIG. 39A  shows drive  2612  having 6 concentric rotary drive axis  2622 ,  2624 ,  2626 ,  2628 ,  2630 ,  2632 . Each rotary drive axis may have a motor and encoder with a drive shaft extending from housing  2634  through bellows  2636  into vacuum or other environment  638 . In the embodiment shown, rotary drive  2632  is coupled to the upper arm of driven arm  2618 ; rotary drive  2630  is coupled to pulley  2650 ; rotary drive  2628  is coupled to the upper arm of driven arm  2620 ; rotary drive  2626  is coupled to pulley  2652 ; rotary drive  2624  is coupled to the upper arm of driven arm  2616  and rotary drive  2622  is coupled to the upper arm of driven arm  2614 . Pulley  2650  has 2 pulley portions that interface with corresponding forearm driving pulleys of driven arms  2614 ,  2618 . Bridge  6254  couples the upper portion of pulley  2650  to the lower portion of pulley  2650 . Bridge  2654  may have any configuration, for example, bridge  2654  may be one or more posts or semi circular structure that passes outside the upper arms of arms  2616  and  2620 . Pulley  2652  has pulley portions that interface with corresponding forearm driving pulleys of driven arms  2616 ,  2620 . With respect to  FIGS. 39A and 393 , each of the four driven arms are moveable independently in a radial direction while first and third of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction and while second and fourth of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction with first and third driven arms rotatable independent of the second and fourth driven arms as will be described. Here, the four driven arms are moveable independently in a radial direction with independent rotation of axis  2632 ,  2628 ,  2624 ,  2622  while holding pulleys  2650 ,  2652  stationary. In one aspect, substrates may be placed independently at different arbitrary Cartesian or polar locations with the arrangement of  FIGS. 39A and 39B . For example, arms  2614  and  2616  may extend simultaneously and substrates may be picked or placed independently at different arbitrary Cartesian or polar locations while keeping arms  2618 ,  2620  retracted. Similarly, for example, arms  2618  and  2620  may extend simultaneously and substrates may be picked or placed independently at different arbitrary Cartesian or polar locations while keeping arms  2614 ,  2616  retracted. Here, pulleys  2650  and  2652  couple to the left and right pairs of arms respectively allowing independent picking or placement with either the upper and lower pairs of arms where pulleys  2650 ,  2652  may be rotated to adjust the respective theta locations of their respective left or right arm. Here, first  2614  and third  2618  of the four driven arms are moveable dependently in a rotary or theta direction by simultaneous rotation of axis  2632 ,  2630 ,  2622  and a vertical or z direction and while second  2616  and fourth  2620  of the four driven arms are moveable dependently in a rotary or theta direction by simultaneous rotation of axis  2628 ,  2626 ,  2624  and a vertical or z direction with first  2614  and third  2618  driven arms rotatable independent of the second  2616  and fourth  2620  driven arms. 
     As used herein a “set” may comprise one or more than one end effector. 
     An example embodiment may be provided in an apparatus comprising a drive; a movable arm assembly connected to the drive; a plurality of sets of end effectors, where the end effectors are connected to the drive by the movable arm assembly, where a first one of the sets of end effectors comprises at least two of the end effectors, where the drive and the movable arm assembly are configured to move the at least two end effectors substantially in unison from a retracted position towards an extended position towards two different respective target locations, and where the at least two end effectors are at least partially independently movable relative to each other on the moveable arm assembly; and a controller connected to the drive, where the controller is configured to detect an offset of respective substrates on the at least two end effectors and adjust movement of the at least two end effectors relative to each other prior to placement of the substrates at the respective target locations. 
     An example embodiment may be provided in an apparatus where a second one of the sets of end effectors comprises at least two other ones of the end effectors, where the drive and the movable arm assembly are configured to move the at least two other end effectors substantially in unison from the retracted position towards the extended position towards the two respective target locations, and where the at least two other end effectors are at least partially independently movable relative to each other on the moveable arm assembly. 
     An example embodiment may be provided in an apparatus where the first and second sets of end effectors are connected by a common upper arm of the movable arm assembly to a common rotational axis of the drive. 
     An example embodiment may be provided in an apparatus where the first and second sets of end effectors are connected by respective independently driven upper arms of the movable arm assembly to a common rotational axis of the drive. 
     An example embodiment may be provided in an apparatus where the first and second sets of end effectors are connected by respective independently driven upper arms of the movable arm assembly to spaced parallel rotational axes of the drive. 
     An example embodiment may be provided in an apparatus where the at least two end effectors of the first set of end effectors are connected to the movable arm assembly by a common wrist, where the wrist is configured to at least partially independently rotate the at least two end effectors relative to each other. 
     An example embodiment may be provided in an apparatus further comprising sensors connected to the controller, where the sensors are configured to sense location of the respective substrates relative to each other as the apparatus moves the at least two end effectors towards the extended position prior to the substrates reaching the target locations. 
     An example embodiment may be provided in an apparatus further comprising at least one camera connected to the controller where, based upon images from the at least one camera, the controller is configured to sense location of the respective substrates relative to each other as the apparatus moves the at least two end effectors towards the extended position and prior to the substrates reaching the target locations. 
     An example embodiment may be provided in an apparatus where the controller is configured to detect the offset of the respective substrates relative to each other based, at least partially, upon detecting a fiducial on each of the substrates. 
     An example method may comprise providing a robot comprising a drive, a movable arm assembly connected to the drive, and a plurality of sets of end effectors, where the end effectors are connected to the drive by the movable arm assembly, where a first one of the sets of end effectors comprises at least two of the end effectors, where the drive and the movable arm assembly are configured to move the at least two end effectors substantially in unison from a retracted position towards an extended position towards two different respective target locations, and where the at least two end effectors are independently movable relative to each other on the moveable arm assembly; and at least partially independently moving the end effectors in the first set relative to each other by the robot, where a controller connected to the drive detects an offset of respective substrates on the at least two end effectors and adjusts movement of the at least two end effectors relative to each other prior to placement of the substrates at the respective target locations. 
     An example method may comprise where a second one of the sets of end effectors comprises at least two other ones of the end effectors, where the drive and the movable arm assembly move the at least two other end effectors substantially in unison from the retracted position towards the extended position towards the two respective target locations, and where the at least two other end effectors are partially independently moved relative to each other on the moveable arm assembly. 
     An example method may comprise where the first and second sets of end effectors are moved by a common upper arm of the movable arm assembly on a common rotational axis of the drive. 
     An example method may comprise where the first and second sets of end effectors are moved by respective independently driven upper arms of the movable arm assembly on a common rotational axis of the drive. 
     An example method may comprise where the first and second sets of end effectors are moved by respective independently driven upper arms of the movable arm assembly on spaced parallel rotational axes of the drive. 
     An example method may comprise where the at least two end effectors of the first set of end effectors are connected to the movable arm assembly by a common wrist, where the wrist is moved to at least partially independently rotate the at least two end effectors relative to each other. 
     An example method may further comprise sensors connected to the controller, where the sensors sense location of the respective substrates relative to each other as the robot moves the at least two end effectors towards the extended position and prior to placement of the substrates at the target locations. 
     An example method may further comprise at least one camera connected to the controller where, based upon images from the at least one camera, the controller senses location of the respective substrates relative to each other as the robot moves the at least two end effectors towards the extended position and prior to placement of the substrates at the target locations. 
     An example method may comprise where the controller determines the offset of the respective substrates relative to each other based, at least partially, upon detecting a fiducial on each of the substrates. 
     An example embodiment may be provided in a non-transitory program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine for performing operations, the operations comprising determining positions of a first set of at least two end effectors of a robot, where the robot comprises a drive, a movable arm assembly connected to the drive, and a plurality of sets of the end effectors, where the end effectors are connected to the drive by the movable arm assembly, where a first one of the sets of end effectors comprises at least two of the end effectors, where the drive and the movable arm assembly are configured to move the at least two end effectors substantially in unison from a retracted position towards an extended position towards two different respective target locations, and where the at least two end effectors are independently movable relative to each other on the moveable arm assembly; and at least partially independently moving the end effectors in the first set relative to each other by the robot, where an offset of respective substrates on the at least two end effectors is detected and movement of the at least two end effectors relative to each other is adjusted prior to placement of the substrates at the respective target locations. 
     An example method may comprise moving a substrate, located on a first end effector of a robot, from a first location towards a second location by the robot; determining location of a fiducial on the substrate while the substrate is being moved from the first location towards the second location; comparing the determined location of the fiducial with a reference fiducial location while the robot is moving the substrate from the first location towards the second location. 
     An example method may comprise where determining the location of the fiducial on the substrate comprises a sensor and/or a camera providing input to a controller to determine the location of the fiducial. 
     An example method may comprise where the controller compares the determined location of the fiducial with the reference fiducial location to determine an offset of the substrate relative to a desired location of the substrate along a path between the first and second locations. 
     An example method may further comprise comparing the determined location of the fiducial relative to a fiducial on a second end effector of the robot while the second end effector is being moved in substantial unison with the first end effector. 
     An example method may further comprise based at least partially upon the comparing, determining an offset of the substrate and adjusting movement of the first end effector prior to moving the substrate into the second location. 
     An example method may further comprise determining an offset of a second substrate of a second end effector of the robot, based at least partially upon a fiducial on the second substrate, and adjusting movement of the first and second end effectors relative to each other while the substrates are moving and prior to the substrates reaching their spaced respective second locations. 
     An example method may comprise where the fiducial is located at least partially along a bottom planar side of the substrate. 
     An example method may comprise where the robot comprises a plurality of sets of end effectors, where the end effectors are connected to a drive by the movable arm assembly of the robot, where a first one of the sets of end effectors comprises at least two of the end effectors including the first end effector, where the drive and the movable arm assembly move the at least two end effectors substantially in unison from a retracted position towards an extended position towards two different respective target locations, and where the at least two end effectors at least partially independently move relative to each other on the moveable arm assembly, where a second one of the sets of end effectors comprises at least two other of the end effectors, where the drive and the movable arm assembly move the at least two other end effectors substantially in unison from the retracted position towards the extended position towards the two different respective target locations, and where the at least two other end effectors at least partially independently move relative to each other on the moveable arm assembly based upon location of fiducials on the substrates as the robot moves the substrates and prior to reaching the target locations. 
     An example method may further comprise a controller, connected to the robot, adjusting movement of the end effector based, at least partially, upon the compared determined location versus the reference fiducial location. 
     An example apparatus may comprise at least one processor; and at least one non-transitory memory including computer program code, the at least one memory and the computer program code configured to, with the at least one processor, cause the apparatus to determine location of a fiducial on a substrate while the substrate is being moved from a first location towards a second location, where the substrate is located on a first end effector of the apparatus; and compare the determined location of the fiducial with a reference fiducial location while the apparatus is moving the substrate from the first location towards the second location. 
     An example embodiment apparatus may comprise where the processor, memory and program code are configured to use input from at least one sensor and/or a camera to determine the location of the fiducial. 
     An example embodiment apparatus may comprise where the processor, memory and program code are configured to compare the determined location of the fiducial with the reference fiducial location to determine an offset of the substrate relative to a desired location of the substrate. 
     An example embodiment apparatus may comprise where the processor, memory and program code are configured to compare the determined location of the fiducial relative to a fiducial on a second end effector of the apparatus while the second end effector is being moved in substantial unison with the first end effector. 
     An example embodiment apparatus may comprise where the processor, memory and program code are configured to, based at least partially upon the comparing, determine an offset of the substrate and adjusting movement of the end effector prior to moving the substrate into the second location. 
     An example embodiment apparatus may comprise where the processor, memory and program code are configured to determine an offset of a second substrate of a second end effector of the apparatus, based at least partially upon a fiducial on the second substrate, and adjust movement of the first and second end effectors relative to each other while the substrates are moving and prior to the substrates reaching their spaced respective second locations. 
     An example embodiment apparatus may comprise where the processor, memory and program code are configured to use information regarding the fiducial, being located at least partially along a bottom planar side of the substrate, for determining location of the substrate. 
     An example embodiment apparatus may comprise where the apparatus comprises a plurality of sets of end effectors, where the end effectors are connected to a drive by the movable arm assembly of the robot, where a first one of the sets of end effectors comprises at least two of the end effectors including the first end effector, where the drive and the movable arm assembly move the at least two end effectors substantially in unison from a retracted position towards an extended position towards two different respective target locations, and where the at least two end effectors at least partially independently move relative to each other on the moveable arm assembly, where a second one of the sets of end effectors comprises at least two other of the end effectors, where the drive and the movable arm assembly move the at least two other end effectors substantially in unison from the retracted position towards the extended position towards the two different respective target locations, and the processor, memory and program code are configured to at least partially independently move the at least two other end effectors relative to each other on the moveable arm assembly based upon location of fiducials on the substrates as the apparatus moves the substrates and prior to reaching the target locations. 
     An example embodiment apparatus may comprise where the processor, memory and program code are configured to adjust movement of the end effector based, at least partially, upon the compared determined location versus the reference fiducial location. 
     An example embodiment may be provided in a non-transitory program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine for performing operations, the operations comprising determining location of a fiducial on a substrate while the substrate is being moved from a first location towards a second location, where the substrate is located on an end effector of a robot; and comparing the determined location of the fiducial with a reference fiducial location while the robot is moving the substrate from the first location towards the second location. 
     An example embodiment may be provided in an apparatus comprising at least one processor; and at least one non-transitory memory including computer program code, the at least one memory and the computer program code configured to, with the at least one processor, cause the apparatus to: determine locations of at least two substrates on respective end effectors of the apparatus while the substrates are being moved by the end effectors in substantial unison towards respective target locations for the substrates; and while the end effectors are being moved towards the respective target locations, and based upon the determined locations of the substrates, adjust a position of at least a first one of the end effectors on the apparatus relative to a second one of the end effectors, where the position of the first end effector is adjusted relative to the second end effector while the apparatus is moving the substrates in substantial unison towards the respective target locations and prior to reaching the target locations. 
     An example embodiment may be provided in an apparatus where the processor, memory and program code are configured to determine locations of the substrates based upon input from one or more sensors and/or cameras. 
     An example embodiment may be provided in an apparatus where the processor, memory and program code are configured to adjust the position of the first and second end effectors relative to each other at a common wrist connecting the first and second end effectors to a forearm of a movable arm assembly of the apparatus. 
     An example embodiment may be provided in an apparatus where the processor, memory and program code are configured to rotate the first end effector at the wrist without rotating the second end effector at the wrist. 
     An example embodiment may be provided in an apparatus where the processor, memory and program code are configured to: determine locations of at least two other substrates on respective two other end effectors of the apparatus while the other substrates are being moved by the other end effectors in substantial unison from respective target locations for the other substrates; and while the other end effectors are being moved from the respective target locations, and based upon the determined locations of the other substrates, adjust a position of at least a first one of the other end effectors on the apparatus relative to a second one of the other end effectors, where the position of the first other end effector is adjusted relative to the second other end effector while the apparatus is moving the other substrates in substantial unison from the respective target locations and prior to reaching the retracted locations. 
     An example embodiment may be provided in an apparatus where the processor, memory and program code are configured to determine locations of the other substrates based upon input from one or more sensors and/or cameras. 
     An example embodiment may be provided in an apparatus where the processor, memory and program code are configured to adjust the position of the first and second other end effectors relative to each other at a common wrist connecting the first and second other end effectors to a forearm of a movable arm assembly of the apparatus. 
     An example embodiment may be provided in an apparatus where the processor, memory and program code are configured to rotate the first other end effector at the wrist without rotating the second other end effector at the wrist. 
     An example embodiment may be provided in an apparatus where the processor, memory and program code are configured to determine the locations of the substrates based, at least partially, upon fiducials on planar bottom sides of the substrates. 
     An example method may comprise determining locations of at least two substrates on respective end effectors of a robot while the substrates are being moved by the end effectors in substantial unison towards respective target locations for the substrates; and while the end effectors are being moved towards the respective target locations, and based upon the determined locations of the substrates, adjusting a position of at least a first one of the end effectors on the robot relative to a second one of the end effectors, where the position of the first end effector is adjusted relative to the second end effector while the robot is moving the substrates in substantial unison towards the respective target locations and prior to the substrates reaching the target locations. 
     An example method may comprise where the locations of the substrates are determined based upon input from one or more sensors and/or cameras. 
     An example method may comprise where adjusting the position of the first and second end effectors relative to each other occurs at a common wrist connecting the first and second end effectors to a forearm of a movable arm assembly of the robot. 
     An example method may further comprise rotating the first end effector at the wrist without rotating the second end effector at the wrist. 
     An example method may further comprise determining locations of at least two other substrates on respective two other end effectors of the robot while the other substrates are being moved by the other end effectors in substantial unison from respective target locations for the other substrates; and, while the other end effectors are being moved from the respective target locations, and based upon the determined locations of the other substrates, adjust a position of at least a first one of the other end effectors on the robot relative to a second one of the other end effectors, where the position of the first other end effector is adjusted relative to the second other end effector while the robot is moving the other substrates in substantial unison from the respective target locations and prior to reaching the retracted locations. 
     An example method may comprise where locations of the other substrates are determined based upon input from one or more sensors and/or cameras. 
     An example method may comprise where adjusting the position of the first and second other end effectors relative to each other occurs at a common wrist connecting the first and second other end effectors to a forearm of a movable arm assembly of the robot. 
     An example method may further comprise rotating the first other end effector at the wrist without rotating the second other end effector at the wrist. 
     An example method may comprise where the locations of the substrates are determined based, at least partially, upon fiducials on planar bottom sides of the substrates. 
     An example embodiment may be provided in a non-transitory program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine for performing operations, the operations comprising determining locations of at least two substrates on respective end effectors of a robot while the substrates are being moved by the end effectors in substantial unison towards respective target locations for the substrates; and while the end effectors are being moved towards the respective target locations, and based upon the determined locations of the substrates, adjusting a position of at least a first one of the end effectors on the robot relative to a second one of the end effectors, where the position of the first end effector is adjusted relative to the second end effector while the robot is moving the substrates in substantial unison towards the respective target locations and prior to the substrates reaching the target locations. 
     An example embodiment may be provided in an apparatus comprising a drive; a movable arm assembly connected to the drive; and a plurality of sets of end effectors, where the end effectors are connected to the drive by the movable arm assembly, where each of the sets of end effectors comprises at least two of the end effectors, where the drive and the movable arm assembly are configured to move the at least two end effectors of each set substantially in unison from a retracted position towards an extended position, and where the at least two end effectors in at least a first one of the sets are independently movable relative to each other on the moveable arm assembly. 
     An example method may comprise providing a robot comprising a drive, a movable arm assembly connected to the drive, and a plurality of sets of end effectors, where the end effectors are connected to the drive by the movable arm assembly, where each of the sets of end effectors comprises at least two of the end effectors, where the drive and the movable arm assembly are configured to move the at least two end effectors of each set substantially in unison from a retracted position towards an extended position, and where the at least two end effectors in at least a first one of the sets are independently movable relative to each other on the moveable arm assembly; and independently moving the end effectors in the first set relative to each other by the robot. 
     An example embodiment may be provided in a non-transitory program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine for performing operations, the operations comprising determining positions of a first set of at least two end effectors of a robot, where the robot comprises a drive, a movable arm assembly connected to the drive, and a plurality of sets of the end effectors, where the end effectors are connected to the drive by the movable arm assembly, where each of the sets of end effectors comprises at least two of the end effectors, where the drive and the movable arm assembly are configured to move the at least two end effectors of each set substantially in unison from a retracted position towards an extended position, and where the at least two end effectors in at least the first set are independently movable relative to each other on the moveable arm assembly; and independently moving the end effectors in the first set relative to each other by the robot. 
     An example method may comprise moving a substrate, located on an end effector of a robot, from a first location towards a second location; determining location of a fiducial on the substrate while the substrate is being moved from the first location towards the second location; comparing the determined location of the fiducial with a reference fiducial location while the robot is moving the substrate from the first location towards the second location. 
     An example embodiment may be provided in an apparatus comprising at least one processor; and at least one non-transitory memory including computer program code, the at least one memory and the computer program code configured to, with the at least one processor, cause the apparatus to determine location of a fiducial on a substrate while the substrate is being moved from a first location towards a second location, where the substrate is located on an end effector of a robot; and comparing the determined location of the fiducial with a reference fiducial location while the robot is moving the substrate from the first location towards the second location. 
     An example embodiment may be provided in a non-transitory program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine for performing operations, the operations comprising determining location of a fiducial on a substrate while the substrate is being moved from a first location towards a second location, where the substrate is located on an end effector of a robot; and comparing the determined location of the fiducial with a reference fiducial location while the robot is moving the substrate from the first location towards the second location. 
     An example embodiment may be provided in an apparatus comprising at least one processor; and at least one non-transitory memory including computer program code, the at least one memory and the computer program code configured to, with the at least one processor, cause the apparatus to determine location of an end effector of a robot and/or a substrate on the end effector, while the end effector is being moved by the robot from a first location towards a second location; and while the end effector is being moved from the first location towards the second location, and based upon the determined location of the end effector and/or substrate, adjust a position of the end effector on the robot to a new dynamically adjusted position on the robot, where the position of the end effector is adjusted based upon the determined location while the robot is moving the end effector from the first location towards the second location. 
     An example method may comprise determining a location of an end effector of a robot and/or a substrate on the end effector, while the end effector is being moved by the robot from a first location towards a second location; and while the end effector is being moved from the first location towards the second location, and based upon the determined location of the end effector and/or substrate, adjusting a position of the end effector on the robot to a new dynamically adjusted position on the robot, where the position of the end effector is adjusted based upon the determined location while the robot is moving the end effector from the first location towards the second location. 
     An example embodiment may be provided in a non-transitory program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine for performing operations, the operations comprising determining a location of an end effector of a robot and/or a substrate on the end effector, while the end effector is being moved by the robot from a first location towards a second location; and while the end effector is being moved from the first location towards the second location, and based upon the determined location of the end effector and/or substrate, adjusting a position of the end effector on the robot to a new dynamically adjusted position on the robot, where the position of the end effector is adjusted based upon the determined location while the robot is moving the end effector from the first location towards the second location. 
     In accordance with one aspect, an example method comprises determining a robot place location for a robot, the robot adapted to transport a substrate. The method comprises moving two calibration fixtures past corresponding one or more edge sensors or fiducial sensors along substantially parallel calibration paths; determining robot locations when an edge of the calibration fixture changes a state of the one or more edge sensors or when a fiducial sensor detects a fiducial of the substrates; determining one or more sensor locations of the one or more edge sensors or fiducial sensors based on the robot locations; transporting the two substrates along nominal transport paths past the one or more edge sensors or fiducial sensors to target locations; determining the robot place locations of the two substrates based on the sensor locations; and placing the two substrates at the target locations with the robot located at the robot place locations. 
     In accordance with one aspect, an example method comprises determining robot placement for a robot, the robot adapted to transport a substrate. The method comprises transporting the substrate along a nominal transport path one or more fiducial sensors to a target location; determining robot locations when a fiducial of the substrate changes a state of the one or more fiducial sensors; determining a robot place location; and placing the substrate at the target location with the robot located at the actual robot place location. 
     In accordance with another aspect, an example embodiment comprises an adaptive substrate placement system for placing two substrates at corresponding two target locations. The placement system has a substrate transport robot; two or more sensors configured to detect a feature of the two substrates as the substrate transport robot moves the substrates along a nominal transport path to the target location; a controller configured to detect robot locations when the features of the substrates changes a state of the two or more sensors; and the controller configured to determine place locations based on the robot locations and the target locations. The two substrates are simultaneously placed at the target locations with the robot located at the place locations and wherein the place locations are different than the target locations. 
     In accordance with another aspect of the exemplary embodiment, a substrate transport robot is provided to transport substrates. The substrate transport robot has a drive portion and an arm portion, the arm portion having first, second, third and fourth driven arms, each of the driven arms capable of supporting different substrates. Each of the driven arms has first and second links where the first and second links may have different lengths. The first link may be an upper arm and is coupled to the drive portion at a shoulder joint. The second link may be a forearm and is coupled to the first link at an elbow joint. Each of the driven arms has an end effector adapted to support a substrate with the end effector coupled to the forearm at a wrist joint. Each of the driven arms is independently moveable in one or more axis. In one aspect, each of the four driven arms are moveable independently in a radial direction while each of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction. In another aspect, each of the four driven arms are moveable independently in a radial direction while first and second of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction and while third and fourth of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction with first and second driven arms rotatable independent of the third and fourth driven arms. In another aspect, each of the four driven arms are moveable independently in a radial direction while first and third of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction and while second and fourth of the four driven arms are moveable dependently in a rotary or theta direction and a vertical or z direction with first and third driven arms rotatable independent of the second and fourth driven arms. 
     An example embodiment may comprise means for providing a robot comprising a drive, a movable arm assembly connected to the drive, and a plurality of sets of end effectors, where the end effectors are connected to the drive by the movable arm assembly, where a first one of the sets of end effectors comprises at least two of the end effectors, where the drive and the movable arm assembly are configured to move the at least two end effectors substantially in unison from a retracted position towards an extended position towards two different respective target locations, and where the at least two end effectors are independently movable relative to each other on the moveable arm assembly; and means for at least partially independently moving the end effectors in the first set relative to each other by the robot, where a controller connected to the drive detects an offset of respective substrates on the at least two end effectors and adjusts movement of the at least two end effectors relative to each other prior to placement of the substrates at the respective target locations. 
     An example embodiment may comprises means for moving a substrate, located on a first end effector of a robot, from a first location towards a second location by the robot; means for determining location of a fiducial on the substrate while the substrate is being moved from the first location towards the second location; and means for comparing the determined location of the fiducial with a reference fiducial location while the robot is moving the substrate from the first location towards the second location. 
     An example embodiment may comprises means for determining locations of at least two substrates on respective end effectors of a robot while the substrates are being moved by the end effectors in substantial unison towards respective target locations for the substrates; and while the end effectors are being moved towards the respective target locations, and based upon the determined locations of the substrates, means for adjusting a position of at least a first one of the end effectors on the robot relative to a second one of the end effectors, where the position of the first end effector is adjusted relative to the second end effector while the robot is moving the substrates in substantial unison towards the respective target locations and prior to the substrates reaching the target locations. 
     It should be understood that the foregoing description is only illustrative. Various alternatives and modifications can be devised by those skilled in the art. For example, features recited in the various dependent claims could be combined with each other in any suitable combination(s). In addition, features from different embodiments described above could be selectively combined into a new embodiment. Accordingly, the description is intended to embrace all such alternatives, modifications and variances.