Patent Publication Number: US-8539854-B2

Title: Microrobots with large actuation volumes, and controllers, systems, and methods

Description:
RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Application No. 61/103,014, filed Oct. 6, 2008, which is incorporated by reference in its entirety. 
    
    
     GOVERNMENT SUPPORT 
     This invention was made with government support under research grant #N00014-06-1-1150 awarded by the Office of Naval Research. The government has certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to microrobots, and, more particularly, but not by way of limitation, to microrobots that are configured for micro- or nano-manipulation within a large actuation volume, and to methods, devices, and systems for such microrobots. 
     2. Description of Related Art 
     Robots have empowered manufacturing since the early 1960&#39;s when Unimation™ implemented a 1.5 m tall hydraulic manipulator to supply parts to die casting machines. Since then, robots have evolved with ever growing application areas such as industrial, medical, human-assistance, recreation, defense, etc. [1]. Over the past two decades, with the advent of microsystems and nanotechnology, precision requirements for robot manipulators have increased considerably, while robot sizes have generally decreased. Precision robots can be valuable tools for micro- and nano-manipulation [2], and for automated and teleoperated assembly [3-5]. More recently, micro- and nano-robots with sub-mm dimensions have been pursued [6-8]. 
     Typical top-down micro- and nano-assembly hardware may use precision robots and end-effectors that are still many orders of magnitude larger than the size of the parts they manipulate [9]. With advances in Micro Electro Mechanical Systems (MEMS), new types of positioning stages have been proposed to aid nanoscale manipulation, probing and force measurement, optical microsystems, and high density data storage devices [10-11]. The design of such positioners often must balance key performance parameters such as range of motion, force output/payload capacity, and dexterity (degrees of freedom). A popular example of monolithically fabricated micropositioners is actuated using electrostatic comb-drives [11]. As a result, they have limited out-of-plane displacement outputs (e.g. mostly planar dexterity) [11]. Other examples include atomic force microscope (AFM) tips, which generally operate along a single vertical direction [12]. On the other hand, positioners with more than 3 degrees of freedom have been fabricated using thin-film deposition and etching, but they have limited force outputs, payload capacities, and reliability to operate as independent micromanipulators [13]. To overcome these inherent trade-offs, micro-positioners have been used as grippers or force probes in conjunction with larger conventional positioning stages, and therefore the overall dimensions of such manipulators typically spans several inches [14-15]. This is a severe limitation in applications requiring multiple such positioners within confined volumes, such as, for example, inside a scanning electron microscope (SEM) chamber. 
     SUMMARY 
     The present disclosure presents an articulated four-axis microrobot (AFAM) that can be operated without a macro-positioner. 
     Applications of the present robot embodiments include manipulation of micro or nanoscale objects such as MEMS components, nanoscale objects (like carbon nanotubes or nanospheres), or biological objects (such as cells, tissue samples, etc), in a confined, small environment such as inside a scanning electron microscope. Such embodiments of the present robots can be used to carry micro- and nano-tools, such as probes, grippers, proximity sensors, and the like, to investigate properties of micro/nano objects and/or manipulate them. Arrays of such probe-carrying manipulators can also be used in high density data storage applications. 
     Embodiments of the present robots comprise: a first actuator drive having a first shuttle and one or more in-plane actuators coupled to the first shuttle, the first actuator drive configured such that the one or more actuators are actuatable to move the first shuttle along a first plane; an arm having a base portion and a cantilever portion movably coupled to and extending from the base portion, the base portion coupled in fixed relation to the first shuttle of the first actuator drive; a second actuator drive having a second shuttle and one or more in-plane actuators coupled to the second shuttle, the second actuator drive configured such that the one or more actuators are actuatable to move the second shuttle along a second plane; a cable having a first end coupled to the second shuttle of the second actuator drive and a second end coupled to the cantilever portion of the arm. 
     In some embodiments, the second plane is substantially parallel to the first plane. In some embodiments, the second plane is substantially coplanar with the first plane. In some embodiments, the arm is substantially perpendicular to the first plane, and the arm is coupled to the first shuttle with a micro-snap fastener. 
     In some embodiments, the robot is configured such that first and second actuator drives are actuatable to: (i) translate the base portion of the arm along the first plane; and (ii) pivot the cantilever portion of the arm relative to the base portion of the arm. In some embodiments, the robot is configured such that the first and second actuator drives are actuatable to: (i) translate the base portion of the arm in at least two directions along the first plane; and (ii) pivot the cantilever portion of the arm relative to the base portion of the arm around at least two axes of rotation. 
     In some embodiments, the maximum dimensions of the robot do not exceed 3.2 millimeters (mm)×2.2 mm×1.2 mm, the cantilever portion of the arm comprises an end effector, and the robot is configured such that the actuator drives are actuatable to move the end effector laterally by at least 40 micrometers (μm), longitudinally by at least 40 μm, and vertically by at least 50 μm. In some embodiments, the maximum dimensions of the robot do not exceed 3 mm×2 mm×1 mm. In some embodiments, the robot is configured such that the actuator drives can be actuated to cause the end effector to apply at least 40 milliNewtons (mN) of force to an object in a direction substantially parallel to the first plane. In some embodiments, the robot is configured such that the actuator drives can be actuated to cause the end effector to apply at least 20 mN of force to an object in a direction substantially perpendicular to the first plane. 
     In some embodiments, the one or more in-plane actuators of the first actuator drive comprise: a first actuator configured to be actuated along a first axis; a second actuator configured to be actuated along a second axis that is substantially perpendicular to the first axis. In some embodiments, the one or more in-plane actuators of the second actuator drive comprise: a third actuator configured to be actuated along a third axis that is substantially parallel to the first axis; a second actuator configured to be actuated along a fourth axis that is substantially parallel to the second axis. In some embodiments, the actuators of the first and second actuator drives comprise electrothermal chevron actuators. 
     In some embodiments, the cantilever portion of the arm is coupled to the base portion of the arm with a two-axis flexure. In some embodiments, the cantilever portion, base portion, and flexure of the arm are of unitary construction. In some embodiments, the cable has a diameter between 20 μm and 40 μm. In some embodiments, the cable has a diameter between 25 μm and 35 μm. 
     Some embodiments of the present robots comprise: a first actuator drive having a first shuttle and two in-plane actuators coupled to the first shuttle, the first actuator drive configured such that the actuators are actuatable to move the first shuttle along a first plane; an arm having a base portion and a cantilever portion movably coupled to and extending from the base portion, the base portion coupled in fixed relation to the first shuttle of the first actuator drive; a second actuator drive having a second shuttle and two in-plane actuators coupled to the second shuttle, the second actuator drive configured such that the actuators are actuatable to move the second shuttle along the first plane; a cable having a first end coupled to the second shuttle of the second actuator drive and a second end coupled to the cantilever portion of the arm; where the maximum dimensions of the robot do not exceed 3.2 mm×2.2 mm×1.2 mm, the cantilever portion of the arm comprises an end effector, and the robot is configured such that the actuator drives are actuatable along the first plane to move the move the end effector laterally by at least 40 μm, longitudinally by at least 40 μm, and vertically by at least 50 μm. 
     Some embodiments of the present atomic force microscopes (AFMs) comprise: a robot (the robot comprising: a first actuator drive having a first shuttle and one or more in-plane actuators coupled to the first shuttle, the first actuator drive configured such that the one or more actuators are actuatable to move the first shuttle along a first plane; an arm having a base portion and a cantilever portion movably coupled to and extending from the base portion, the base portion coupled in fixed relation to the first shuttle of the first actuator drive, the cantilever portion having a distal end with a probe tip; a second actuator drive having a second shuttle and one or more in-plane actuators coupled to the second shuttle, the second actuator drive configured such that the one or more actuators are actuatable to move the second shuttle along a second plane; a cable having a first end coupled to the second shuttle of the second actuator drive and a second end coupled to the cantilever portion of the arm) and a detector module coupled to the robot for sensing the position of the probe tip. 
     Any embodiment of any of the present methods can consist of or consist essentially of—rather than comprise/include/contain/have—any of the described steps, elements, and/or features. Thus, in any of the claims, the term “consisting of” or “consisting essentially of” can be substituted for any of the open-ended linking verbs recited above, in order to change the scope of a given claim from what it would otherwise be using the open-ended linking verb. 
     Details associated with the embodiments described above and others are presented below. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The following drawings illustrate by way of example and not limitation. For the sake of brevity and clarity, every feature of a given structure is not always labeled in every figure in which that structure appears. Identical reference numbers do not necessarily indicate an identical structure. Rather, the same reference number may be used to indicate a similar feature or a feature with similar functionality, as may non-identical reference numbers. The structures that appears in photographs (e.g., those in  FIGS. 1A ,  4 ,  6 A,  7 B,  9 B,  9 C,  12 ,  14 ,  15 ( a )- 15 ( e ), and  16 ) as well as those in  FIGS. 1B ,  1 C,  2 ,  3 , and  19  are drawn to scale, meaning the sizes of the depicted elements are accurate relative to each other for at least the set of embodiments depicted in these figures. 
         FIG. 1A  depicts a picture of one of the present microrobots. 
         FIG. 1B  depicts an isolated perspective view of the microrobot of  FIG. 1 . 
         FIG. 1C  depicts a top view of the microrobot of  FIG. 1 . 
         FIG. 2  depicts a top view of an alternate embodiment of one of the present microrobots. 
         FIG. 3  depicts an isolated perspective view of an alternate embodiment of the present microrobots. 
         FIG. 4  depicts a picture of the vertical arm of the microrobot of  FIG. 1 . 
         FIG. 5  depicts a flowchart of one of the present methods of selecting design parameters for embodiments of the present microrobots. 
         FIG. 6A  depicts a picture of a chevron actuator suitable for use in embodiments of the present microrobots. 
         FIG. 6B  depicts a top view of a chevron actuator suitable for use in embodiments of the present microrobots. 
         FIG. 7A  depicts a micro-snap fastener joint of the microrobot of  FIG. 1 . 
         FIG. 7B  depicts another joint suitable for use in embodiments of the present microrobots. 
         FIGS. 8A-8D  depicts depict charts of finite-element analysis (FEA) simulations of displacement of a chevron actuator suitable for use in embodiments of the present microrobots relative to actuation voltage. 
         FIG. 9A  depicts a side view of a vertical arm suitable for use in embodiments of the present microrobots. 
         FIG. 9B  depicts a picture of the vertical arm of the microrobot of  FIG. 1 . 
         FIG. 9C  depicts a picture of a vertical arm manufactured for use in embodiments of the present microrobots. 
         FIG. 10  depicts a diagram of a vertical arm of the present microrobots and a cable. 
         FIG. 11  depicts a chart of force transmission along a Y axis on a cantilever of the vertical arm for various angles of cable connection to the cantilever arm. 
         FIG. 12  depicts a picture of the connection of a cable to the cantilever of the vertical arm of the present microrobots of  FIG. 1 . 
         FIG. 13  depicts the volumetric sweep of the cantilever of the vertical arm of the microrobot of  FIG. 1 . 
         FIGS. 14A-14D  depict pictures of a portion of the cantilever of the vertical arm of the microrobot of  FIG. 1  during various stages of actuation. 
         FIGS. 15A-15E  depict pictures of various views of a prototype robot, and components of the prototype robot, configured for use in the present atomic force microscopes (AFMs). 
         FIGS. 16A-16B  depict an image and chart, respectively, of indents generated with a prototype robot. 
         FIGS. 17A-17B  depict repeatability data obtained for the prototype robot. 
         FIGS. 18A-18C  conceptually illustrate a laser interferometer configuration and resolution charts of pitch generated with the laser interferometer configuration. 
         FIG. 19  depicts one of the present microfactories. 
         FIG. 20  conceptually illustrates the work volume of one of the present microfactories. 
     
    
    
     DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
     The term “coupled” is defined as connected, although not necessarily directly, and not necessarily mechanically; two items that are “coupled” may be integral with each other. The terms “a” and “an” are defined as one or more unless this disclosure explicitly requires otherwise. The terms “substantially,” “approximately,” and “about” are defined as largely but not necessarily wholly what is specified, as understood by a person of ordinary skill in the art. 
     The terms “comprise” (and any form of comprise, such as “comprises” and “comprising”), “have” (and any form of have, such as “has” and “having”), “include” (and any form of include, such as “includes” and “including”) and “contain” (and any form of contain, such as “contains” and “containing”) are open-ended linking verbs. As a result, a robot that “comprises,” “has,” “includes” or “contains” one or more elements possesses those one or more elements, but is not limited to possessing only those elements. For example, a robot that comprises two actuator drives, an arm, and a cable, can also include an AFM probe (e.g., coupled to the arm). Likewise, an AFM that “comprises,” “has,” “includes,” or “contains” one or more elements possesses those one or more elements, but is not limited to possessing only those one or more elements. For example, a AFM that comprises one of the present robots, can also include more than one of the present robots. 
     Further, a device or structure that is configured in a certain way is configured in at least that way, but it can also be configured in other ways than those specifically described. 
     The present disclosure presents a unique four-axis articulated MEMS robot (e.g., constructed by microassembly techniques) for micro- and nano-scale manipulation and probing applications. 
     A prototype robot was assembled at UT Arlington&#39;s Texas Microfactory using μ 3 , a precision microassembly system [16]. The prototype covers a relatively large work volume, or approximately 50 μm×50 μm in the substrate plane, and 75 μm out of plane, has a total footprint of 3 mm×3 mm×1 mm (including actuators, transmission system and end-effector), and has four degrees of freedom (prismatic X/Y in plane, ‘pitch’ φ and ‘yaw’ ψ both out of plane). The prototype robot can apply up to 50 mN of in-plane force in X and Y directions, and/or 25 mN in à Z direction, through an end-effector arm with a jammer tip. The microrobot joints are driven by four (4) electrothermal actuators, all of which are located in-plane on a die substrate (e.g., a silicon on insulator (SOI) die). Micro snap-fasteners and a cable-driven transmission drive the in-plane and out-of-plane flexure joints. 
     Remote actuation via cables can been used to transmit motion to joints which cannot be powered with a direct drive due to constraints such as speed/torque stepping and space. Since generating large out-of-plane motion with MEMS involves complex fabrication, the inventors employed a cable driven transmission as an alternative to out-of-plane flexure joints. Relatively simple fabrication processes were used to create 2½D, high aspect ratio microrobot links and in-plane actuators, hybrid 3D microassembly was used to construct strong joints and transmission systems. The resulting microrobot prototype has a workspace closer in shape to a cube than to a plane, and can address important requirements inside SEMs or microfactories by combining increased dexterity, a long range of motion, high resolution and repeatability in a modest self-volume. 
     The prototype, which represents one embodiment of the present microrobots, has what may be referred to in this disclosure as a 2P2R (Prismatic Prismatic Revolute Revolute) kinematic configuration, occupies a total volume of 3 mm×3 mm×1 mm, and operates within a workspace envelope of 50 μm×50 μm×75 μm. This is believed to be, by far, the largest operating envelope of any other independent micropositioner with non-planar dexterity. As a result, embodiments of the present microrobots can be classified as a new type of 3-dimensional microrobot that enables miniaturization of top-down assembly systems to dimensions under 1 cm. Embodiments of the present microrobots incorporate a combination of miniature flexures and cables to drive its joints from high force MEMS actuators. Actuation can be accomplished via two banks of in-plane electrothermal actuators, one coupled through an out-of-plane compliant socket, and the other one coupled remotely via a 30 μm-diameter cable. The present disclosure includes details for decoupling the motion of the robot joints with an identified robot Jacobian, and offers experimental characterization of the repeatability a prototype of the present microrobots. Results show that the prototype robot is repeatable to under 0.5 μm along X and Y axes, and to 0.015 degrees along pitch and yaw degrees of freedom. 
     I. Overview and General Description 
     Referring now to the drawings, and more particularly to  FIGS. 1A-1C , shown there and designated by the numeral  10  is one of the present microrobots.  FIG. 1  depicts a photograph of a prototype the microrobot  10 ;  FIG. 1B  depicts an isolated (shown without substrate/die) perspective view of the microrobot  10 ; and  FIG. 1C  depicts a top view of the microrobot  10 . Microrobot  10  may be interchangeably referred to in this disclosure as robot  10 . 
     Robot  10  comprises two in-plane XY actuator drives  14   a  and  14   b  ( 14 , collectively) (actuatable, or powerable/powered to move, in X and Y directions) that cooperate to control the robot&#39;s four degrees of freedom (DOFs); an arm  18 ; and a cable  22 . As shown in  FIG. 1 , actuator drives  14  are supported by substrates  26   a  and  26   b , as is described in more detail below. Actuator drives  14  are substantially similar, with the exception of differences noted below, and actuator drive  14   a  is described as representative of both actuator drives  14 . Actuator drive  14   a  can be described as a first actuator drive, and has a first shuttle  30   a  and one or more (e.g., two, as shown) in-plane actuators  34   a - 1  and  34   a - 2  ( 34   a , collectively) coupled to first shuttle  30   a . In particular, actuators  34   a  are coupled to shuttle  30   a  by way of shuttle arms  38  that extend between shuttle  30   a  and a respective actuator  34   a - 1  or  34   a - 2 , and, in the embodiment shown, shuttle arms  38 , shuttle  30   a , and actuators  34   a , are of unitary construction (manufactured as a single piece). First actuator drive  14   a  is configured such that the one or more actuators  34  are actuatable (can be powered to drive, or are drivable) to move first shuttle  30   a  along a first plane (e.g., along the plane of substrate  26   a ). Second actuator drive  14   b  is substantially similar to first actuator drive  14   a  in that second actuator drive  14   b  has a second shuttle  30   b  and one or more (e.g., two, as shown) in-plane actuators  34   c  and  34   d  coupled to second shuttle  30   b , and is configured such that actuators  34   b - 1  and  34   b - 2  ( 34   b , collectively) are actuatable to move second shuttle  30   b  along a second plane (e.g., along the plane of substrate  26   b ). In some embodiments, one or both actuator drives  14   a  and/or  14   b  are configured such that their respective shuttles are physically constrained from moving other than along their respective planes of actuation by their respectively coupled actuators  34   a  or  34   b . The primary difference between first actuator drive  14   a  and second actuator drive  14   b  is that first shuttle  30   a  is configured to be coupled to arm  18  (e.g., via a micro-snap fastener, as described in more detail below), and second shuttle  30   b  is configured to be coupled to cable  22 . 
     In the embodiment shown, the one or more in-plane actuators  34   a  of first actuator drive  14   a  comprise: a first actuator  34   a - 1  configured to be actuated along a first axis (e.g., either or both directions along an actuation axis that, here, is the longitudinal axis of shuttle arm  38  that couples actuator  34   a - 1  to shuttle  30   a ); and a second actuator  34   a - 2  configured to be actuated along a second axis (e.g., either or both directions along an actuation axis that, here, is the longitudinal axis of shuttle arm  38  that couples actuator  34   a - 2  to shuttle  30   a ) that is substantially perpendicular to the first axis. In other embodiments, the actuation axis of actuator  34   a - 1  need not be substantially perpendicular to the actuation axis of actuator  34   a - 2 . In the embodiment shown, the one or more in-plane actuators  34   b  of second actuator drive  14   b  comprise: a third actuator  34   b - 1  configured to be actuated along a third axis (e.g., either or both directions along an actuation axis that, here, is the longitudinal axis of shuttle arm  38  that couples actuator  34   b - 1  to shuttle  30   b ) that, in the embodiment shown, is also substantially parallel to the first axis (actuation axis of actuator  34   a - 1 ); and a fourth actuator  34   b - 2  configured to be actuated along a fourth axis (e.g., either or both directions along an actuation axis that, here, is the longitudinal axis of shuttle arm  38  that couples actuator  34   b - 2  to shuttle  30   b ) that, in the embodiment shown, is also substantially parallel to the second axis (actuation axis of actuator  34   a - 1 ). As described below, in the embodiment shown, actuators  34   a ,  34   b  comprise electrothermal chevron actuators. 
     Arm  18  has a base portion  42  and a cantilever portion  46 . Cantilever portion  46  is movably coupled to (e.g., by way of a flexure) and extending from base portion  42 . Base portion  42  is coupled (e.g., in fixed relation) to first shuttle  30   a  of first actuator drive  14   a . Cable  22  has a first end  50  coupled to second shuttle  30   b  of second actuator drive  14   b  and a second end  54  coupled to cantilever portion  46  of the arm. In the embodiment shown, cable  22  comprises a copper wire having a diameter between 20 μm and 40 μm, more particularly between 25 μm and more particularly substantially equal to 30 μm. 
     Robot  10  is configured such that first and second actuator drives  14   a  and  14   b  are actuatable (can be powered or driven) to: (i) translate base portion  42  of the arm along the first plane (e.g., in directions parallel to the first plane of first actuator drive  14   a ); and (ii) pivot cantilever portion  46  of the arm relative to base portion  42  of the arm. For example, when first actuator drive  14   a  is actuated to move first shuttle  30   a , arm  18  is also moved. As another example, second actuator drive  14   b  can be actuated to pull cable in a direction away from arm  18 , such that cantilever portion  46  of the arm is raised (e.g., rotated relative to base portion  42  of the arm). Further, in the embodiment shown, robot  10  is configured such that first and second actuator drives  14   a  and  14   b  are actuatable (can be powered on or driven) to: (i) translate the base portion of the arm in at least two directions along the first plane (e.g., in the actuation directions of each of actuators  34   a ); and (ii) pivot cantilever portion  46  of the arm relative to the base portion of the arm around at least two axes of rotation (e.g., up/down rotation relative to base portion  42  of the arm, and left/right rotation relative to base portion  42  of the arm). 
     In the embodiment shown, the maximum dimensions of robot  10  do not exceed 3.2 mm×2.2 mm×1.2 mm, and more particularly, do not exceed 3 mm×2 mm×1 mm. Further, cantilever portion  46  of arm  18  comprises an end effector  58 , and the robot is configured such that actuator drives  14  are actuatable (can be powered on or driven) to move end effector  58  (e.g., via base portion  42 , cantilever portion  46 , cable  22 , etc.) laterally (side-to-side in a direction perpendicular to base portion  42 , perpendicular to cantilever portion  46 , and parallel to the plane of substrate  26   a ) by at least 40 micrometers (μm), longitudinally (parallel to the longitudinal axis of cantilever portion  46 ) by at least 40 μm, and vertically by at least 50 μm, as described in more detail below. Additionally, robot  10  is configured such that actuator drives  14  can be powered or driven to cause end effector  58  to apply at least 40 milliNewtons (mN) of force to an object in a direction substantially parallel to the first plane; and/or such that actuator drives  14  can be powered or driven to cause end effector  58  to apply at least 20 mN of force to an object in a direction substantially perpendicular to the first plane (e.g., in a downward direction toward the plane of substrate  26   a ). 
       FIG. 2  depicts a top view of an alternate embodiment of one of the present microrobots  10   a . Robot  10   a  is substantially similar in operation to robot  10 , with the primary exception that the actuator drives are condensed to reduce the overall dimensions of the robot. To this end, shuttle arms  38   a  are provided in place of two out of the four straight shuttle arms  38  of robot  10 . As shown, shuttle arms  38   a  have a Z-shaped or zig-zag configuration that permits actuators  34  to be configured in a smaller area to reduce the overall dimensions of the robot. 
       FIG. 3  depicts an alternate embodiment  10   b  of the present microrobots. Robot  10   b  is substantially similar in function to the prototyped robot  10  of  FIGS. 1A-1C , and, as such, the function of robots  10  and  10   b  are both described with reference to the coordinate system depicted in  FIG. 3  (which also describes the function of robot  10   a ). The only difference between robot  10   b  of  FIG. 3  and robot  10  of  FIGS. 1A-1C  is that the two XY stages (actuator drives) are moved closer together, as shown. 
       FIG. 4  depicts an enlarged picture of arm  18  and cable  22  of robot  10 . The tip of end effector  58  can be referenced as a tool coordinate point (TCP), and movement of the TCP can be obtained and/or described via two prismatic (X TIP , Y IP ) and two revolute (φ pitch . ψ yaw ) motions or degrees of freedom (DOFs). In the prototype evaluated in this disclosure (depicted in  FIG. 1 ), the robot comprises a first actuator drive  14   a  and a second actuator drive  14   b . In the prototype of this disclosure, the actuator drives  14   a  and  14   b  are substantially identical, with the exception of differences in their respective shuttles  30   a  and  30   b . More particularly, shuttle  30   a  couples to vertically assembled (extending vertically from the plane of substrate  26   a ) arm  22  (which, in the embodiment shown, is 800 μm tall). The second XY actuator drive  14   b  is coupled to cable  22  (which, in the embodiment shown, has a 30 μm diameter and a length of 3.2 mm) that is that is bonded to the cantilever portion (flexure arm) on the other end. The actuators  34   a  and  34   b  comprise electrothermal chevron prismatic actuators. Four independent pose (or position) parameters of the TCP can be achieved through a combination of planar motions by the actuators  34   a  and  34   b . The first actuator pair  34   a - 1  and  34   a - 2  drives the first shuttle  30   a  (and the base portion  42  of arm  18 ) along axes denoted by X D  and Y D , where the subscript ‘D’ represents direct coupling to the base portion  46  of arm  18 . The second actuator pair  34   b - 1  and  34   b - 2  drives or controls the cantilever portion  46  of arm  18  via second shuttle  30   b  and cable  22 , along axes denoted by X C  and Y C . A summary of a typical actuation sequence for the robot and the resulting motion at the TCP is outlined in Table 1. Pure translational motion along X TIP  and Y TIP  requires that both X C  and X D  or Y C  and Y D  be actuated by the same displacement. Vertical motion of the TCP is a result of the pitch motion of the arm through the cable when X C  and X D  are not actuated by the same displacement. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Actuator to joint relation 
               
            
           
           
               
               
               
            
               
                   
                   
                 Joints Actuated 
               
               
                   
                 Actuator powered 
                 (including coupling) 
               
               
                   
                   
               
               
                   
                 X D   
                 Mostly Pitch(φ), Some Yaw (ψ) 
               
               
                   
                 X C , X D   
                 Mostly X, Some Y 
               
               
                   
                 Y D   
                 Mostly Yaw (ψ), Some Pitch(φ), 
               
               
                   
                 Y C , Y D   
                 Mostly Y, Some X 
               
               
                   
                 X C , X D , Y C , Y D   
                 X, Y 
               
               
                   
                 X D , Y D   
                 Pitch(φ), Yaw (ψ) 
               
               
                   
                   
               
            
           
         
       
     
     Embodiments of the present robots (e.g.,  10 ,  10   a ,  10   b ) can have a number of characteristics and advantages not found in prior MEMS robots and devices. For example, all primary components except wire  22  (e.g., actuator drives  14 , arm  18 ) can be fabricated using deep-reactive-ion-etching (DRIE) on 50˜100 microns (device) SOI. After etching, arm  18  can be de-tethered and assembled out-of-plane (out of the plane of substrate  26   a ) using, for example, a passive jammer. Additionally, even smaller sizes can be achieved (e.g., size can be reduced by up to a factor of ten) using the same types of construction and technology, such that an array of microrobots  10  can be fabricated on a wafer in a scalable way. In this way, for example, robots  10  can be used in an array configurations inside a scanning electron microscope (SEM) for probing, handling an array of probes and nano-manipulation. As described in more detail, robot  10  is also configured for nanometer-scale resolution and repeatability, and is suitable for high-precision applications such as nano-probing, nano-positioning. 
     In one example, multiple (e.g., numerous, such as hundreds of) robots  10  can be packed in an array on the surface of the wafer to create a nanoprober array. The probers in the array can be controlled independently along all degrees of freedom (X, Y, and Z). Current technology for such arrays are used in the IBM Millipede as high density data storage tips, but they cannot be independently moved in X, Y, and Z. The present robots  10  can be configured as probers to replace the IBM Millipede cantilever tips, and/or the mechanism for moving/replacing the data storage surface when it gets permanently damaged after repeated use, to permit the flexibility of controlled X, Y, and Z motion. 
     II. Fabrication and Assembly 
     One feature of the present microrobots is that all actuators can be placed in-plane. This allows for adopting standard lithographic microfabrication processes, and the vertical interconnections can be accomplished by 3D microassembly. Deep reactive ion etching (DRIE) on silicon on insulator (SOI) substrates with a 100 μm thick device layer was used to fabricate links, joints and actuators of robot  10 , with the exception of cable  22 . The aspect ratio of the components in the prototype is, at most, 1:20, and all parts except for the cable can be described as having 2½D geometries, as such description is currently understood in the art. 
     Actuator drives  14   a  and  14   b , and arm  18 , were lithographically manufactured using DRIE on a SOI substrate. The Z-arm of the actuator is fabricated in-plane with a tether remaining to the substrate, and is released by breaking the tether with a passive “jammer.” Arm  18  is then picked up from the substrate, rotated by 90 degrees, and vertically assembled (coupled to shuttle  30   a ) by means of a compliant snap-fastener, resulting in a vertically oriented (relative to shuttle  30   a  and substrate  26   a ), as shown in  FIG. 4 . The design of the vertical snap-fastener is similar to connectors extensively described in prior publications of the inventors. The microassembly operation is automated using the μ 3  system located at UT Arlington&#39;s Texas Microfactory. More information on the snap-fastener design and assembly methodology can be found in [16-17]. Once assembled, the joint strength of the Z-arm (strength of the connection between arm  18  and shuttle  30   a ) can be increased using UV-curable epoxy dispensed at the joint between the arm and shuttle  30   a . The joint strength of similar joints before failure has been evaluated extensively in the past [18], and has generally exceeded 50 mN when loaded in the weaker Y direction. Once bonded, the stiffness of this joint is generally much larger than the remaining flexures and/or joints of the robot, and can largely be described as and considered “rigid”. Prior to assembly, the robot die can be placed in a micropackage and the actuators driven by current inputs directed to the Au-coated pads via wirebonds. Currently, the footprint and dimensional choices for some of the robot components may not be optimum for all applications, and can be varied in any suitable fashion to adapt the configuration of the robot as suitable or desired. 
     III. Configuration of Actuator Drives, Arm, and Cable 
     A. Methodology of Design and Configuration 
       FIG. 5  depicts a flowchart outlining the design steps for the prototyped version of microrobot  10 . A 3D (e.g., cubic) workspace requirement of 50 μm along all the X, Y, and Z axes was targeted. A chevron beam electrothermal actuator (actuators  34   a  and  34   b ) was designed to produce a required planar deflections, while maintaining its torsional stiffness. XY flexure stages (actuator drives)  14   a  and  14   b  were incorporated into the design, and a Z-axis flexure was incorporated into the vertical arm  18  (between base portion  42  and cantilever portion  46 ) based on the desired TCP displacement and the planar actuation inputs (displacement) from Actuator drives (XY stages)  14   a  and  14   b . Actuator drives (XY stages)  14   a  and  14   b  were designed to provide enough support and stiffness to allow controlled displacements for the Z axis arm, including sufficient stiffness against reaction torque due to the vertical arm pitch and yaw motion. Finally, the length, diameter, angle to Z-arm  18 , and attachment location along the cantilever portion  46 , for cable  22  were selected in order to maximize transmission of the force generated by actuator drives  14   a  and  14   b . In practice, this sequence may be iterated multiple times to suit a specific force or displacement requirement at the tool tip. 
     B. In-Plane Actuator Drive Configuration 
     Actuator drives  14   a  and  14   b  (driving the microrobot) were designed to: (i) allow a large displacement of their respective shuttles  30   a  and  30   b  in the plane of their respective substrates  26   a  and  26   b  (e.g., SOI dies); (ii) resist out-of-plane bending torques when the pitch and yaw axes (motions) of cantilever portion  46  are actuated; and (iii) maximize the retention force of the assembled out of plane arm  18  in the snap-fastener socket of shuttle  30   a.    
       FIGS. 6A and 6B  depict perspective and top views, respectively, of an electrothermal chevron actuator  34  suitable for use in, and used in the prototype of, robot  10 . Because the actuator portion of actuators  34   a  and  34   b  are substantially similar in design and construction, electrothermal actuator  34  of  FIGS. 6A and 6B  is described as representative of all actuators  34   a  and  34   b . Actuator  34  is designed for a horizontal displacement of up to 50 μm. Actuator  34 , as shown, comprises seven pairs of 15 μm-wide, 1 mm-long, and 100 μm-thick beams  100 . Beams  100  are each offset or separated from one another by a distance of 10 μm, and form an angle of 3.5° to shuttle arm  38  that couples the respective actuator ( 34   a - 1 ,  34   a - 2 ,  34   b - 1 ,  34   b - 2 ) to the respective shuttle ( 30   a ,  30   b ). Actuator  34  exhibit a current draw of approximately 50 mA at 10 V (e.g., alternating current or AC) input with 18 μm steady-state displacements, and 250 mA at 19 V input with 48 μm displacements, with a stiffness of about 180N/m. The measured bandwidth of actuator  34  was 45 Hz, and is generally dictated by thermal effects (rather than mechanical resonance). Actuator  34  produces up to 50 mN of force output at maximum voltage inputs (e.g., 19-20 V). Power is provided to actuator  34  by way of pads  104 , which can, for example, be coated with gold (Au) to improve conductivity of connection to conductors such as wires and the like. 
       FIG. 7A  depicts an embodiment of shuttle  30   a  that is suitable for use in embodiments of (and is used in the prototype of) robot  10 . As mentioned above, shuttles  30   a  and  30   b  are substantially similar, with the exception that shuttle  30   a  is configured (e.g., by way of a micro-snap fastener  108 ) to be coupled to base portion  46  of arm  18 . As such, shuttle  30   a  is described as representative of first and second shuttles  30   a  and  30   b , with the understanding that, when used as second shuttle  30   b , micro-snap fastener  108  can be (and was, in the prototype) omitted. At the center of the shuttle  30   a  is micro snap-fastener  108 , configured to receive an out-of-plane (e.g., vertical) assembly of Z axis arm  18 , such as is depicted in  FIGS. 1 ,  2 , and  4 . 
     Shuttle  30   a  has a rectangular shape with four sides. As shown, shuttle  30   a  is coupled on two sides to (and, in the prototyped embodiment, is integral to or of unitary construction with) shuttle arms  38 , which also provide some support to shuttle  30   a  (e.g., during operation of the actuator drive  14   a . In the embodiment shown, shuttle  30   a  is also coupled to (and, in the prototyped embodiment, is integral to or of unitary construction with) a passive flexure (e.g., flexure spring)  112 . Flexure  112 , in prototyped embodiment shown, is also integral to the substrate (e.g., SOI die)  26   a . Flexure  112  adds to the torsional stiffness of shuttle  30   a  (e.g, reduces twisting of shuttle  30   a  during operation of actuator drive  14   a ), and increases durability of actuator drive  14   a  (e.g., allows a larger number of cycling operations before failure). Flexure  112  can be designed and/or configured for varying numbers, n, of turns  116 ; width of each coil, w; and number of flexure elements  120 , N, for each flexure  112 . The embodiment of shuttle  30   a  shown in  FIG. 7A  depicts the configuration of shuttle  30   a  in the prototyped embodiment of  FIG. 1 . More particularly, and as shown, shuttle  30   a  is configured with a length of about 600 μm and width of about 200 μm; and flexure  112  is configured with two flexure elements  120 , each with n=9 turns, w=about 100 μm, and N=2 flexure elements  120 . 
       FIG. 7B  depicts a shuttle  30   c  that is an alternate embodiment of shuttle  30   a . Shuttle  30   c  includes four flexures  112 , two each of two different configurations. The configuration shown in this figure results in relatively low deflection (24 microns) and relatively high torsional rigidity (0.5 N-m 2 /rad) compared to the configuration shown in  FIG. 7A . Shuttle  30   c  corresponds to  FIG. 8C . 
     Actuator drive  14   a  (including drive  14   a  and flexure  112  of  FIG. 7A , and actuators  34   a  of  FIGS. 6A-6B ) was optimized and/or configured to maximize possible displacement of shuttle  30   a  while maintaining suitable torsional stiffness (e.g., during pitch and yaw actuation and/or motion of cantilever portion  46  of arm  18 ) along the pitch, yaw, and roll axes of shuttle  30   a , using finite element analysis (FEA) modeling. 
       FIGS. 8A-8D  show plots of XY displacement and stiffness along the pitch direction for different iterations of the designs of actuator drives (e.g.,  14   a ,  14   b ).  FIGS. 8A-8C  were generated from the FEA modeling of different iterations.  FIG. 8D  was generated from experimental testing of the prototype.  FIG. 8A  shows the displacement for n=8, w=10 μm and N=2, which yielded relatively high displacement (45 microns) with relatively low torsional rigidity (0.26 N-m 2 /rad).  FIG. 8B  shows displacement for n=6, w=10 μm and N=4, which yielded medium deflection (40 microns) and medium torsional rigidity (0.38 N-m 2 /rad).  FIG. 8C  is displacement profile for n=4, w=10 μm and N=2, which yielded relatively low deflection (24 microns) and relatively high torsional rigidity (0.5 N-m 2 /rad). Ideally, the motion of the shuttle should be planar, along two DOFs (X and Y), and each actuator  34  should directly control its own DOF (X or Y). However, due to the fact that the two actuators  34  are both connected to the shuttle, XY motion of the shuttle is coupled, and some amount of undesirable drift generally occurs along the axis orthogonal to the actuation axis of each actuator. The size of the shuttle arms (e.g., 38), and the stiffness of the flexures can be (and were, for the prototype) selected to be close to decoupling the XY motion of the shuttle, and then experimentally evaluated using a microscope.  FIG. 8D  depicts the experimentally measured characteristics of the configuration of  FIG. 8B , n=6, w=10 μm and N=4. For the prototyped embodiment, the torsional rigidity was 0.26 N-m 2 /rad along the pitch and roll axes and 0.12 N-m 2 /rad along the yaw axes ( FIG. 1B  depicts the pitch, yaw, and roll axes relative to the X and Y axes). Coupling compensation using kinematic identification of the microrobot X, Y, and Z stages was carried out experimentally after fabrication and assembly, as described below. This was accomplished by providing a wide range of voltage inputs to the actuators  34   a - 1 ,  34   a - 2 ,  34   b - 1 , and  34   b - 2 , and tracking the resulting position of end effector  58  for each input. The resulting input output data was used to fit an approximate model, the inverse of which provides the inputs required for a desired trajectory for end effector  58 . 
     C. Z-Axis Arm Configuration 
     Referring now to  FIGS. 9A-9C ,  FIGS. 9A ,  9 B depict side and perspective views, respectively, of arm  18 ; and  FIG. 9C  depicts a side view of a prototyped arm  18 . As noted above, arm  18  comprises base portion  42  and cantilever portion  46 . As shown in more detail in  FIGS. 9A and 9B , arm  18  further comprises a flexure  124  and a compliant region  128 . Compliant region  128  is configured to enable pick-up and assembly for coupling arm  18  to micro-snap fastener  108  of shuttle  30   a . More particularly, the lower end of base portion  42  includes a pair of flexures with a micro-snap fastener configuration that is used for assembly onto (coupling to) micro-snap fastener  108  of shuttle  30   a . Base portion  42  also includes a compliant region used for gripping the part for pickup with a “jammer” during assembly, and a guide to release the gripper after mating with the snap-fastener. Details of some examples of suitable micro-snap fasteners can be found in U.S. Pat. No. 6,672,795, which is incorporated by reference in its entirety. Additional fastener examples and further information on design of this region can be found in [19]. 
     Flexure  124  was optimized and/or configured using FEA modeling to maximize the force output at the tool coordinate point (end effector  58 ). In the embodiment shown, flexure  124  is a two-axis flexure (e.g., it permits rotation of cantilever portion  46  relative to base portion  42  around at least two axes, such as, for example, up/down relative to base portion  46 , left/right relative to base portion  42 ). Further, in the embodiment shown, cantilever portion  46 , base portion  42 , and flexure  124  of arm  18  are of unitary construction (are formed as a single piece from an SOI die). As indicated in  FIG. 9A , arm  18  has a height of about 800 μm and flexure  124  has a length such that the overall dimension of base portion  42  and cantilever portion  46  is about 1.3 mm combined (the length of the cantilever portion  46  of the arm is about 800 μm). As indicated in the inset of  FIG. 9B , flexure  124  of arm  18  is formed with a depth of about 100 μm, a length of about 400 μm, and a height or width of about 150 μm, with n=9 turns, and a stiffness of about 90 N/m along the pitch φ axis and about 140 N/m on the yaw ψ axis. 
     D. Cable Angle Configuration 
     In the prototyped embodiment, cable  22  comprises copper (Cu) with a diameter of about 30 μm. In other embodiments, cable  22  can comprise carbon nanotubes, nanowires, and the like. First end  50  of cable  22  is coupled to cantilever portion  46  of the arm, and second end  54  of cable  22  is coupled to second shuttle  30   b , such that forces and motion can be transferred from shuttle  30   b  to end effector  58  of cantilever portion  46 . The attachment angle and location of coupling to cantilever portion  46  were simulated and optimized using FEA modeling. 
     As shown in  FIG. 10 , the length of cable  22  and the point-of-attachment of cable  22  to cantilever portion  46  constrain the angle at which forces are transmitted through cable  22  to cantilever portion  46  (and to end effector  58 ). The deflection produced at the cable attachment point P is amplified at the TCP by a factor of L o /d, while the output force is reduced by the same factor. Thus a smaller d (distance between point of attachment, P, and end of cantilever portion  46  adjacent to TCP) is desired to obtain higher TCP displacement outputs, while a larger d is desired for higher force outputs. Considering the flexure design discussed above, and the output force capacity from in-plane actuator actuator drive  14   b , a parametric FEA analysis on the Z axis arm was conducted to determined: optimum cable angle θ, the distance d from the end of the arm, and the cable length that results in maximum force output at the point P along the −Y p  axis. This also ensures maximum deflection of cantilever portion  46  with the TCP shown in  FIG. 10 .  FIG. 11  illustrates the variation in force transmitted for various cable angles θ at which the cable is attached to second shuttle  30   b . Maximum force is transmitted when this angle is 45 degrees. At this angle (45°), cable  22  must be attached at a distance d=200 μm from the tip of cantilever portion  46  for maximum force and displacement transmission. After determining the cable angle and d, the optimum cable length L c  was determined using Equation (1).
 
 L   c =( L   x   −d )/cos θ,  (1)
 
where L x  is the distance between the center of second shuttle  30   b  (which drives the cable) and the tip of cantilever portion  46  projected onto the plane of the die, for d=200 μm and θ=45°. Using Equation (1), it was determined that L c =3.2 mm.
 
     E. Alternate Embodiments 
     The prototyped embodiment comprises two in-plane actuator drives  14   a  and  14   b . Other embodiments of the present robots can comprise any suitable number of in-plane actuator drives. For example, some embodiments of the present robots can comprise three actuator drives with two as in the prototyped embodiment, and a third actuator drive positioned to the side of the arm such that an additional cable is at a greater angle (e.g., up to 90 degrees), relative to the side of the cantilever portion of the arm, to increase the forces in lateral directions that can be imposed or created at the end effector of the arm. In other embodiments, the cantilever portion of the arm can be provided with a telescoping configuration, and an additional in-plane actuator or actuator drive can be provided to increase or decrease the length of the cantilever portion of the arm. In other embodiments, robots can comprise any combination of in-plane actuator drives to provide translations, rotations, and/or combinations thereof, of the arm, cantilever portion of the arm, and/or the end effector of the arm. In other embodiments, actuators and/or actuator drives can be formed in the plane of the arm (e.g., an actuator in the plane of the arm can be coupled by a cable to the cantilever portion of the arm to provide pitch motion of the cantilever portion relative to the base portion). In another example, an actuator in the plane of the arm can provide actuation to telescope the cantilever portion of the arm. 
     IV. Experimental Results 
     A. Cable Attachment 
     The cable used in constructing the prototype of microrobot  10  was a 30 μm diameter copper wire with a PVC coating. The coating provided some added strength, and cable  22  behaved more like a tight rod than a flexible tether. The cable was sliced to a length of 3.2 mm using an EXCIMER 248 nm laser. The cable was gripped using a Femto Tools® FT100 electrostatic microgripper mounted on a terminal roll degree of freedom of one of the robots in the μ 3  system referenced above. Using machine vision through a microscope, cable  22  was oriented at approximately 45 degrees relative to the SOI die substrate  26   b  (and thereby to shuttle  30   b ), and ends  50  and  54  of the cable were epoxy bonded to cantilever portion  46  of the arm and second shuttle  30   b  of actuator drive  14   b , respectively. The connection of cable  22  to cantilever portion  46  is shown in an enlarged view in  FIG. 12 . 
     B. Workspace Measurement 
     Post assembly, the microrobot work volume, which is the volume in 3D space reached by the TCP, was determined. When all four actuators  34   a - 1 ,  34   a - 2 ,  34   b - 1 , and  34   b - 2  were sequentially swept from their respective zero positions to their respective maximum-displacement positions, the TCP passed through the 3D shape shown in  FIG. 13 . Using two high zoom (10× and 4.5×) cameras (one mounted directly above the TCP looking down at the TCP, and one mounted to the side looking directly at the side of cantilever portion  46 ), the locations reached by the TCP were recorded. As shown in  FIG. 13 , the workspace volume is not a parallelepiped, but shows a reduction in the achievable vertical displacements towards the end of the maximum horizontal displacement (along the X axes). The discrete points in  FIG. 13  mark actual positions reached by the TCP. 
     C. System Jacobian 
       FIGS. 14A-14D  depict sample snap-shots (pictures) of the TCP during various stages of actuation.  FIGS. 14A and 14B  show side view when X D  (actuator  34   b - 1 ) was actuated.  FIGS. 14C and 14D  show top views when Y C  (actuator  34   b - 2 ) was actuated. As noted above, the four degrees of freedom of microrobot  10  are highly coupled and it was desirable to establish the kinematics that relate inputs at the actuator level (at actuators  34   a  and  34   b ) to the corresponding output motion of the TCP. The data used to determine the work volume was also used to approximate the microrobot Jacobian. To characterize the motion of the TCP, the four actuators ( 34   a - 1 ,  34   a - 2 ,  34   b - 1 ,  34   b - 2 ) were powered using various voltages. The two high-magnification microscopes (10× and 4.5×) were used to track the output motion of the features noted in  FIG. 14 . The top view camera was used to measure Y and yaw of the TCP (end effector  58  of cantilever portion  46 ), and the side view camera measures X and pitch of the TCP. The data recorded is shown in Table 2. The coordinates referenced correspond to the coordinates illustrated in  FIG. 3 . 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Sample measured displacement data at TCP 
               
            
           
           
               
               
               
               
               
            
               
                   
                 X d  Y d  X c  Y c   
                   
                 Side View 
                 Top View 
               
               
                   
                 (Volts) 
                   
                 ΔX, Δφ 
                 ΔY, Δψ 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 0, 0, 0, 0 
                 0 μm, 
                 0° 
                 0 μm, 
                 0° 
               
               
                   
                 20, 0, 0, 0 
                 −25 μm, 
                 11.1° 
                 7.1 μm, 
                 2.3° 
               
               
                   
                 20, 0, 20, 0 
                 −45.1 μm, 
                 1.7° 
                 6.8 μm, 
                 0° 
               
               
                   
                 0, 0, 0, 20 
                 8.1 μm, 
                 0° 
                 27.1 μm, 
                 6.2° 
               
               
                   
                 0, 20, 0, 20 
                 0 μm, 
                 0° 
                 42.8 μm, 
                 0° 
               
               
                   
                 20, 20, 20, 20 
                 46.5 μm, 
                 0° 
                 44.9 μm, 
                 0° 
               
               
                   
                 0, 0, 0, 10 
                 3.2 μm, 
                 0° 
                 12.2 μm, 
                 2.2° 
               
               
                   
                 0, 10, 0, 10 
                 0 μm, 
                 0° 
                 21.3 μm, 
                 0° 
               
               
                   
                 10, 0, 0, 0 
                 −12.1 μm, 
                 3.1° 
                 3.1 μm, 
                 0.9° 
               
               
                   
                 10, 0, 10, 0 
                 −23.1 μm, 
                 1° 
                 3.8 μm, 
                 0° 
               
               
                   
                   
               
            
           
         
       
     
     The TCP velocity in global coordinates relates to the individual actuator inputs by a robot Jacobian J, given by: 
                     [           Δ   ⁢           ⁢       X   .     f                 Δ   ⁢                 ⁢   Y     .     f                 Δ   ⁢           ⁢       Z   .     f                 Δ   ⁢               ⁢   φ     .                 Δ   ⁢     ψ   .             ]     =     J   ⁡     [           Δ   ⁢           ⁢       X   .     D                 Δ   ⁢           ⁢       Y   .     D                 Δ   ⁢           ⁢       X   .     C                 Δ   ⁢           ⁢       Y   .     C             ]               (   2   )               
The Jacobian is state dependent, but a simple approximation using a constant can be useful for visual servoing. Using a total of 50 data points, the Jacobian entries in Equation (2) are approximated through a linear data fit as:
 
                   J   =     [         0.1       0         -   0.92         1.1           1.76       2.1       0.02       0.87           0       1.7         3.12   ′           -   2.67             2.1       3.12         -   2.67         1.76           0       0.92       2.43       0.86         ]             (   3   )               
Knowledge of the Jacobian allows implementing largely decoupled robot joint operation for the microrobot using a servoing command input given by:
 
                     [           Δ   ⁢           ⁢     X   D                 Δ   ⁢           ⁢     Y   D                 Δ   ⁢           ⁢     X   C                 Δ   ⁢           ⁢     Y   C             ]     =     -     h   .       J   +     ⁡     [           Δ   ⁢           ⁢     X   f                 Δ   ⁢           ⁢     Y   f                 Δ   ⁢           ⁢     Z   f                 Δ   ⁢           ⁢   φ               Δ   ⁢           ⁢   ψ           ]                   (   4   )               
Where h=0.18 is a scaling constant. This command input was used to generate drive input voltages in order to move the microrobot TCP between repeated locations 25 μm apart as described below.
 
     D. Preliminary Precision-Metrics Evaluation 
     The prototype repeatability along the four coordinate axes of the TCP was measured, as a preliminary step, using a Veeco® NT 1100 DMEMS surface profiler. Using the system Jacobian shown in Equations (3)˜(4), the TCP was guided between two locations in the work volume multiple times (&gt;30) and the sub-micron motion data was captured and processed at 20× magnification to evaluate repeatability of the prototype. At this magnification, the surface profiler provided a resolution of 350±σ x,y     —     error  nm along the X and Y axes, and 15±σ z     —     error  nm along the Z axis. The bidirectional repeatability determined along the four axes are as shown in Equation set (5). The use of a surface profiler for planar XY motion data, however, limits the repeatability measurements. Further investigation of the system repeatability and resolution will require as scanning electron microscope, as described below. 
     However, the resolution can be estimated to be on the order of 15˜30 nm, based on the electrothermal actuator resolution [20]. The preliminary repeatability measurements indicate that:
 
σ repeat     —     X ≦450 nm; σ repeat     —     Y ≦560 nm
 
σ repeat     —     φ ≦0.009°; σ repeat     —     ψ ≦0.015°  (5)
 
     V. Implementation and Further Study 
     Characteristics of the present microrobots  10  exceed those of other MEMS positioners in categories such as such as range of motion vs. exerted force, and range of motion vs. precision. Details of the robot&#39;s configuration and design, fabrication, assembly, and preliminary precision measurement using a Veeco® surface profiler, are provided above. The remainder of this disclosure describe the precision metrics of the robot prototype, including resolution, repeatability and accuracy, and application of the microrobot for nano-indentation on polymer thin films. 
     A. AFM Tip Mounting 
     In order to investigate and demonstrate applications of microrobot  10  a nano-manipulation scenario, a Veeco® DP-10 AFM (atomic force microscope) probe was mounted onto the Tool Center Point (e.g., in place of end effector  58 ), as shown in  FIGS. 15A-15E . More particularly,  FIG. 15A  depicts a portion of the overall robot  10 ;  FIG. 15B  depicts the TCP (tip or end effector  58 ) of cantilever portion  46  of the arm;  FIG. 15C  depicts arm  18  with an AFM tip mounted to cantilever portion  46 ;  FIG. 15D  depicts an enlarged view of an AFM cantilever (tip); and  FIG. 15E  depicts a 2 μm AFM tip. The AFM tip of  FIG. 15E  is attached to a micro-fixture on cantilever portion  46  configured with a triangular groove that fits the thin arms of the AFM cantilever of  FIG. 15D . Once the AFM cantilever is in place on the micro-fixture, epoxy is dispensed along the groove to bond the AFM cantilever to the micro-fixture. The micro-fixture is coupled to the TCP of cantilever portion  46  of the arm with a compliant snap fastener. 
     In this way, robot  10  can be configured to replace the traditional cantilever of an atomic force microscope (AFM), or to replace and/or carry the probe and/or probe tip of other scanning probe microscopes (SPM). Embodiments of the present AFMs comprise: a robot (e.g., robot  10 , comprising: a first actuator drive having a first shuttle and one or more in-plane actuators coupled to the first shuttle, the first actuator drive configured such that the one or more actuators are actuatable (can be powered or driven) to move the first shuttle along a first plane; an arm having a base portion and a cantilever portion movably coupled to and extending from the base portion, the base portion coupled in fixed relation to the first shuttle of the first actuator drive, the cantilever portion having a distal end with a probe tip; a second actuator drive having a second shuttle and one or more in-plane actuators coupled to the second shuttle, the second actuator drive configured such that the one or more actuators are actuatable (can be powered or driven) to move the second shuttle along a second plane; a cable having a first end coupled to the second shuttle of the second actuator drive and a second end coupled to the cantilever portion of the arm); and a detector module (not shown, but individually known in the art) coupled to the robot for sensing the position of the probe tip. For example, the sensor module can comprise: any suitable imaging sensor(s) (e.g., photodiode(s)), any suitable control electronics, and/or any suitable light sources (e.g., light emitting diode(s)). Examples of commercially available AFM&#39;s include the Dimension Icon® from Veeco Instruments [21], XE-150® system from Park Systems [22], and Cypher® from Asylum research [23]. These systems typically span 6˜8 ft 3 . 
     Using the described configuration setup, robot  10  was driven (actuated) to create nano indents on a 2 μm-thick PARYLENE layer. The robot Jacobian described above was used to derive the actuation required for the tip to reach the target locations shown in  FIGS. 16A-16B . Finally, the indent locations reached by the robot were used to determine the robot accuracy and repeatability. 
     B. Accuracy and Repeatability 
     To estimate the accuracy of the robot, the letters “ARRI” were indented, and before every indent, the AFM tip was brought back to the same initial condition (position). Following the indentation operation, the error in the indent location compared to the target locations desired was used to determine accuracy. In the example shown on  FIGS. 16A-16B , a total of 27 points were indented. Using this technique, the average accuracy of the microrobot prototype was measured to be around 500 nm. 
     To measure the repeatability of the microrobot, the pattern indented was repeated and the actual positions reached were measured by analyzing the polymer surface with a scanning electron microscope (SEM). The repeatability is defined as the variance in the actual positions reached. This is a function of the operating point in the robot&#39;s workspace. 
       FIGS. 17A-17B  illustrates the repeatability obtained using the Jacobian derived above, along the XY plane of the polymer. Referring still to  FIGS. 17A-17B , the measured repeatability indices σ cal     —     x,y,z  vary as follows in Equation (6):
 
205 nm≦σ cal     —     x ≦100 nm, 0≦ x ≦50 μm
 
220 nm≦σ cal     —     y ≦100 nm, 0≦ y ≦50 μm
 
210 nm≦σ cal     —     z ≦100 nm, 0≦ z ≦50 μm  (6)
 
     C. Resolution 
     The resolution of the prototype was determined using a laser interferometer setup as shown in  FIG. 18A . In the particular embodiment shown,  FIGS. 18A-18C  illustrates measurement of pitch. Using the Jacobian described above, the electrothermal actuators associated with causing pitch motion were actuated (voltage was increased) until the Keyence LK-G10 laser interferometers detect minimum motion. This voltage varied nonlinearly with pitch actuation between 0.01 V at the center of the work volume to 0.03 V upon reaching extreme points in the 3D envelope (depicted in  FIG. 13 ). Using this setup, the measured resolution can be summarized as shown in Equation (7):
 
110 nm≦σ res     —     x ≦50 nm, 0≦ x ≦50 μm
 
105 nm≦σ res     —     y ≦50 nm, 0≦ y ≦50 μm
 
0.035°≦σ res     —     φ,ψ ≦0.018°, 0≦φ,ψ≦9°  (7)
 
     These measurements represent conservative estimates of the microrobot resolution limited by the Keyence sensor resolution (10 nm+noise). 
     VI. Nanofactory Configuration Using Multiple AFAM and ARRIpdede Microrobots 
     The present robots  10  can be coupled to or used in conjunction with ARRIpede robots (e.g., in nanofactories). The ARRIpede robot is described in U.S. patent application Ser. No. 12/583,331, filed Aug. 18, 2009, which is incorporated by reference in its entirety. Embodiments of the present microrobots can be used individually or in parallel on a single substrate, and/or can replace other nanomanipulators (e.g., when the arm is fitted with or comprises other microgrippers). 
       FIG. 19  illustrates an embodiment of a microfactory  200 , and in the inset, an embodiment of a manipulation module  250 . In the embodiment shown, each manipulation module  250  comprises multiple AFAM microrobots  10  with AFM probe tips  254  attached as end effectors, disposed around an inverted ARRIpede microrobot  300 . 
     This permits multiple AFM probes to simultaneously be employed for sensing and manipulation. Thus each nanomanipulation module  250  comprises scanning and manipulation sub modules, as detailed further in Table 3. In this way, for example, a given task can be distributed amongst all modules available or within a sub group. In some embodiments, the nanomanipulation modules will generally (but not necessarily always) operate in a calibrated open loop mode. The microrobot Jacobians can be used to repeatedly drive the probes through a pre-determined trajectory. The elimination of closed loop control can decrease cycle time and increase throughput. The throughput or processing trajectory may vary between robots belonging to the same module  250  and between different modules. The throughput trajectories will, of course, be product specific and include interplay between manipulation and processing. For example, one module  250  can be assigned a first task (e.g., nanotube bending, which might require fixturing the nanotubes using probes and impinging a suitable gas such as oxygen or the like at the specific bend location). 
     The operation of the nanomanipulation module can be modeled as a stochastic process. Scanning modules that consist of high resolution scanning using scanning probe microscopy (SPM) or imaging using scanning electron microscopy (SEM) can be configured to monitor the state of the nano parts/assemblies before transfer between modules  250 . Thus, factory  200  can be housed within a typical SPM or SEM station. In embodiments where the nano-manipulation modules  250  are not actively controlled, the scanning task can also gather information on (and/or monitor) the yield of the processing. Closed-loop manipulation using the scanning module can also be employed as a secondary manipulation process when necessary or otherwise desirable (e.g., for calibration, monitoring, etc.). 
     Based on the precision data outlined in the previous sections, embodiment of the present modules  250  occupying a volume of 30 mm 3  can be configured to have an almost cylindrical work volume with cylinder diameter of 100 microns and a height of 50 microns or more (e.g., 75 microns), as illustrated conceptually in  FIG. 20 . For example, such a module  250  can be configured, with five (5) AFAMs  10  and one (1) ARRIpede  300 , to have up to 23 DOFs. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Nano factory scanning and manipulation attributes 
               
            
           
           
               
               
               
            
               
                 Operation 
                 Scanning 
                 Manipulation 
               
               
                   
               
               
                 Technique 
                 SPM, SEM 
                 Probing using 
               
               
                   
                   
                 MEMS robots + SPM 
               
               
                 Control 
                 Closed loop (SPM) 
                 Hybrid (open + closed) 
               
               
                   
                   
                 Open loop using micro 
               
               
                   
                   
                 robot repeatability or 
               
               
                   
                   
                 closed loop using SPM tip) 
               
               
                 Bandwidth 
                 High 
                 Low 
               
               
                 Frequency of 
                 Intermittent between 
                 Continuous 
               
               
                 tool usage 
                 manipulation steps 
               
               
                 Sensory 
                 Laser, Electron Beam/ 
                 Force sensor (designed 
               
               
                   
                 Tunneling current for 
                 with micro robot for in-situ 
               
               
                   
                 TEM 
                 sensing) 
               
               
                   
               
            
           
         
       
     
     In summary, AFAM microrobot  10  has a measured repeatability (in open loop operation) ranging between 100 nm˜200 nm and a positioning resolution smaller than 50 nm, and can thus be used for dexterous manipulation and assembly at the nano scale. Due to its force output capacity of up to 100 mN at the end-effector (TCP), embodiments of robot  10  can also be configured to carry various types of nano grippers or sensors. The ARRIpede microrobot has an un-tethered motion repeatability of 6˜12 μm, and a resolution of 20 nm along the direction of motion, and can thus complement AFAM robot  10  as a nano-mobile stage. In some embodiments, microfactory  200  can be configured to manufacture microrobots (e.g., AFAM robot  10  or ARRIpeded  300 ) on a nano-scale, enabling un-tethered operation of such robots. 
     The various illustrative embodiments of devices, systems, and methods described herein are not intended to be limited to the particular forms disclosed. Rather, they include all modifications, equivalents, and alternatives falling within the scope of the claims. For example, in embodiments, such as the ones depicted above, embodiments of the present robots can comprise piezoelectric actuators in place of the electrothermal actuators (e.g.,  34   a - 1 ,  34   a - 2 ,  34   b - 1 ,  34   b - 2 ). Another example is the use of alternatives to the cable  22 , such as rigid body based mechanisms comprising of revolute joints and links. 
     The claims are not intended to include, and should not be interpreted to include, means-plus- or step-plus-function limitations, unless such a limitation is explicitly recited in a given claim using the phrase(s) “means for” or “step for,” respectively. 
     REFERENCES 
     The following references, to the extent that they provide exemplary procedural or other details supplementary to those set forth herein, are specifically incorporated by reference at the locations at which they have been cited.
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