Patent Publication Number: US-8526737-B2

Title: Method and apparatus for transforming coordinate systems in a telemanipulation system

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This application is a continuation of and claims the benefit of priority from, U.S. patent application Ser. No. 11/971,984, filed Jan. 10, 2008, which is a continuation of U.S. patent application Ser. No. 10/414,814 filed Apr. 15, 2003, now U.S. Pat. No. 7,333,642 issued on Feb. 19, 2008; which is a continuation of Ser. No. 09/813,506 filed Mar. 21, 2001, now U.S. Pat. No. 6,574,355 issued on Jun. 3, 2003; which is a continuation of U.S. patent application Ser. No. 09/174,051 filed Oct. 15, 1998, now U.S. Pat. No. 6,259,806 issued on Jul. 7, 2001; which is continuation application of U.S. patent application Ser. No. 08/783,644, filed Jan. 14, 1997, now U.S. Pat. No. 5,859,934, issued on Jan. 12, 1999, which is a continuation application of U.S. patent application Ser. No. 08/239,086 filed May 5, 1994 now U.S. Pat. No. 5,631,973 issued on May 20, 1997, the full disclosures of which are incorporated herein by reference. 
    
    
     STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT 
     This invention was made with Government support under Grant No. 5-R01-GM44902-02 awarded by the National Institutes of Health. The Government has certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates to telemanipulation using telepresence, and more particularly to applications of telemanipulation to laparoscopic surgery. 
     A telemanipulation system allows an operator to manipulate objects located in a workspace from a remote control operator&#39;s station. For example, in a laparoscopic abdominal surgery procedure, the patient&#39;s abdomen is insufflated with gas, and cannulas are passed through small incisions to provide entry ports for laparoscopic surgical instruments. Laparoscopic surgical instruments include an image capture means for viewing the surgical field and working tools, such as forceps or scissors. The working tools are similar to those used in open surgery, except that the working end of each tool is separated from its handle by an extension tube. The surgeon performs surgery by sliding the instruments through the cannulas and manipulating them inside the abdomen while referencing a displayed image of the interior of the abdomen. Surgery by telepresence, that is, from a remote location by means of remote control of the surgical instruments, is a next step. A surgeon is ideally able to perform surgery through telepresence, which, unlike other techniques of remote manipulation, gives the surgeon the feeling that he is in direct control of the instruments, even though he only has remote control of the instruments and view via the displayed image. 
     The effectiveness of telepresence derives in great measure from the illusion that the remote manipulators are perceived by the operator of the system to be emerging from the hand control devices located at the remote operator&#39;s station. If the image capture means, such as a camera or laparoscope, are placed in a position with respect to the manipulators that differs significantly from the anthropomorphic relationship of the eyes and hands, the manipulators will appear to be located away from the operator&#39;s hand controls. This will cause the manipulators to move in an awkward manner relative to the viewing position, inhibiting the operator&#39;s ability to control them with dexterity and rapidity. However, it is often unavoidable in applications such as laparoscopic surgery to move the laparoscope in order to obtain the best possible image of the abdominal cavity. 
     Thus, a technique is needed for providing to the operator the sense of direct hand control of the remote manipulator, even in the presence of a substantially displaced imaging device, such that the operator feels as if he is viewing the workspace in true presence. 
     BRIEF SUMMARY OF THE INVENTION 
     According to the invention, in a telemanipulation system for manipulating objects located in a workspace at a remote worksite by an operator at an operator&#39;s station, such as in a remote surgical system, the remote worksite having a manipulator or pair of manipulators each with an end effector for manipulating an object at the workspace, such as a body cavity, a controller including a hand control at the control operator&#39;s station for remote control of the manipulators, an image capture means, such as a camera, for capturing in real-time an image of the workspace, and image producing means for reproducing a viewable image with sufficient feedback to give the appearance to the control operator of real-time control over the object at the workspace, the improvement wherein means are provided for sensing position of the image capture means relative to the end effector and means are provided for transforming the viewable real-time image into a perspective image with correlated manipulation of the end effector by the hand control means such that the operator can manipulate the end effector and the manipulator as if viewing the workspace in substantially true presence. By true presence, it is meant that the presentation of an image is a true perspective image simulating the viewpoint of an operator. Image transformation according to the invention includes rotation, translation and perspective correction. 
     The invention will be better understood by reference to the following detailed description in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a side view of a remote operator station and of a worksite station in a telemanipulation system according to the present invention. 
         FIG. 1B  is a perspective view of a remote operator station and a worksite station adapted for stereoscopic viewing in a telemanipulation system according to the present invention. 
         FIG. 2  is a diagrammatic perspective view of a specific embodiment of the invention wherein the image capture means is centered and normalized relative to the viewpoint of an operator using the manipulators. 
         FIG. 3  is a diagrammatic perspective view of a specific embodiment of the invention wherein the image capture means is laterally displaced relative to the viewpoint of an operator using the manipulators. 
         FIG. 4  is a diagrammatic perspective view of a specific embodiment of the invention wherein the image capture means is at a lower position relative to the viewpoint of an operator using the manipulators. 
         FIG. 5A  is a front elevational view of the lenses of a stereoscopic image capture means where the lenses are in a normalized position relative to the viewpoint of an operator using the manipulators. 
         FIG. 5B  is a front elevational view of the lenses of a stereoscopic image capture means where the lenses are rotated relative to the viewpoint of an operator using the manipulators. 
         FIG. 6A  is a top plan view of an image of a remote manipulator in a telemanipulation system that shows a superimposed stereographic four-point coordinate element prior to calibration. 
         FIG. 6B  is a top plan view of an image of a remote manipulator in a telemanipulation system that shows a superimposed stereographic four-point coordinate element after calibration. 
         FIG. 7A  is a top plan view of an image of a remote manipulator in a telemanipulation system that shows the angle of displacement in the horizontal of the image capture means relative to the manipulators. 
         FIG. 7B  is an enlarged view of a portion of  FIG. 4A  that shows the combined effect on the position of the end effector of a manipulator after a lateral shift. 
         FIG. 8  is a geometric depiction of the image of a manipulator as a projection of a hand control. 
         FIG. 9  is a geometric depiction of the actual manipulator whose image is depicted in  FIG. 8 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1A  shows a telemanipulation system  10  according to the present invention with a remote operator station  12  where an operator  14  (a surgeon, for example) can perform telemanipulation on an object at a worksite station  16 . The remote station  12  includes a video display  20  for the operator  14  to view the worksite and an apparent workspace  22  where the operator  14  carries out the actual manipulations by grasping hand control means  24 ,  26 , such as surgical instrument handles, which are connected to position sensors  51 ,  55 . The worksite station  16  includes an image capture means  19 , including a sensor means  21  with camera lens  28  of a camera or endoscope and understanding that there is an image capture means  19  associated with that lens, which captures an image of an object located in the workspace  30 . (An endoscope would be within the body cavity.) The manipulators  32 ,  34  allow manipulation of the object in the workspace  30  correlated with a displayed image by use of end effector means  39 ,  41 . 
     The image captured at worksite  16  is transmitted through a number of stages which present to operator  14  a real-time image of the object in the workspace  30 . In particular, sensor means  21 , including optical image capture means  19 , provides a view of the manipulators  32 ,  34  through a camera lens  28 , passing such image information via path  13  to an image processor  23 . In addition, image sensor position information (camera position) may be passed on path  63  to coordinate transformer  43 . (For a fixed camera, the camera position information can be preset). Further, mechanical position sensing means  59 ,  61  sense the position of manipulators  32 ,  34  mechanically, passing on the position information to coordinate transformer  43  via path  157 . 
     The image processor  23  includes a rotation and translation means  25 , a perspective correction means  29  and a calibration means  27 . The rotator is for rotating the image and the translator is for shifting the rotated image. The perspective corrector  29  is primarily for magnifying the image and may include some tilt correction. The calibrator  27  may have various functions, depending upon the type of image input. It is in particular used to calibrate the image to a known reference coordinate system to enable an operator to coordinate motions of the hand controls and the manipulators. After the image has undergone transformation through one or more of these function blocks, the pixel data is passed on path  15  to an imager  31  which drives a video display  20 , which in this embodiment is a monoscopic device, and data about the image is passed on to the coordinate transformer  43 , whereby any processed image data potentially affecting control of the manipulators (e.g., magnification, rotation, translation) is made available for the control of the manipulators. The details of the processes which may be affected are explained hereinbelow, particularly with respect to calibration. 
     The coordinate transformer  43  is the principal processor of position information. Camera position information, manipulator position information, and hand control position information are received and processed therein. In particular, the positions of hand controls  24 ,  26  are sensed by position sensors  51 ,  51  and passed via path  47  to coordinate transformer  43 . After transformation and processing in coordinate transformer  43 , control information is applied to position-following servo  45 , which drives and controls manipulators  32 ,  34  with end effectors  39 ,  41 . The operation of each of these blocks will be described in further detail. 
     In operation, the camera lens  28  captures the image of the object in the actual workspace  30  in a specific orientation on image capture means  19 . The video display  20  displays this image so that the operator  14  can view the object as it is manipulated. The operator  14  may then grasp hand control means  24 ,  26  located in the apparent workspace  22  to carry out the desired manipulations. The hand control means  24 ,  26  at remote station  12  under instruction of the position-following servo  45  control the manipulators  32 ,  34  at worksite station  16 , which actually manipulate the object in workspace  30 . The actual workspace  30  is thus effectively projected back to the remote operator  14  to create the illusion that he is reaching and looking directly into it and controlling the object located in workspace  30 . Properly projected, this results in natural and spontaneous control motions by the operator  14 , even if he is located in an another room or another extremely remote location. 
     The problems addressed by the present invention arise from the situation where the camera lens  28  is not placed at the same position in the real workspace  30  relative to the manipulators  32 ,  34  as the eyes of the control operator viewing the projected image in the “apparent” workspace  22  relative to the hand control means  24 ,  26 . A solution is provided by the present invention. 
     The telemanipulation system according to the present invention can also be adapted to accommodate stereoscopic viewing.  FIG. 1B  shows all the elements of  FIG. 1A , with the addition of a second camera lens  36  and image capture means  35 . The two camera lenses  28  and  36  can be separated by about 10°, which is the same interocular viewing disparity that one experiences when viewing a visual field at 40 cm separation. The stereo image is displayed on a stereo video display monitor  38  (e.g. using an electronically switched polarizer  37  over the screen) and viewed through cross-polarized stereoscopic lenses  40 , thus offering a natural image to the remote operator  14  so that the operator experiences the correct visual feedback when reaching and looking directly into the actual workspace  30  and directly manipulating the object located therein. The details of the system are explained hereinafter. 
       FIG. 2  is a diagrammatic perspective view of the elements of the worksite station  16  in workspace  30  of the telemanipulation system, showing features of  FIG. 1  which are in a control loop. The system an operator at a remote station to manipulate objects located at a centerpoint  50  in the workspace  30 . In the monoscopic system, sensor means  21  with camera lens  28  and image capture means  19  captures a real-time image of the object. The operator  14  uses dual hand control means  24 ,  26  to control left manipulator  32  and right manipulator  34 , respectively, which allow remote manipulation of the object at the workspace  30 . For hand control means  24 ,  26  and manipulators  32 ,  34 , there is in this example a fixed pivot point about which bidirectional angular motion can be effected, together with a telescopic-like extension capability for each of the manipulators and hand controllers. The correlation between the hand control means  24 ,  26  and the manipulators  32 ,  34 , combined with the image captured by the camera lens  28 , provide sufficient feedback to give the appearance to the control operator of real-time control over the object at the workspace (further improvement is possible with tactile feedback). Both left manipulator  32  and right manipulator  34  are in this example raised 30° with respect to an arbitrary plane of orientation, including a centerline axis  52  of the workspace  30 , to simulate a typical positioning of an object in the real local workspace  30 . 
     In operation, camera lens  28  is at the 0° lateral position with respect to the centerline axis  52 , such that the camera lens  28  is between left manipulator  32  and right manipulator  34 . The face of the camera lens  28  is raised at for example a 45° angle with respect to the plane containing centerline axis  52  and baseline  53 . This camera position and orientation is a close approximation to the actual eye position with respect to the manipulators  32  and  34  and represents a base or reference position. The image captured by the camera lens  28  appears as if the operator were looking at the centerpoint  50  while standing over the manipulators  32  and  34  with a 45° angle view into the workspace. Both left manipulator  32  and right manipulator  34  appear in the bottom of the displayed image (proximal to the operator&#39;s hand controls), evoking a strong sense of telepresence, which means that the operator senses direct control of manipulators  32  and  34 , allowing control with dexterity and rapidity, particularly where there is tactile feedback from the manipulators  32 ,  34  to the hand control means  24 ,  26 . 
     In a telemanipulation application in which positioning of elements is difficult due to obstructions, it is often necessary to move the camera lens  28  to different positions result in a different view of the object at the centerpoint  50 . Referring to  FIG. 3 , a diagrammatic perspective view of the elements in workspace  30  of the worksite station  16  of a monoscopic telemanipulation system is shown in which the camera lens  28  position is rotated by angle θ 58  laterally in the horizontal plane away from the centerline axis  52 . After rotation of the camera lens  28 , left manipulator  32  and right manipulator  34  are still inclined downward at a 30° angle relative to the plane containing centerline axis  52  and baseline  53 , and the camera lens  28  is still positioned at an angle θ above the plane formed by centerline axis  52  and baseline  53 . In order to evoke a sense of telepresence in the operator similar to the case in which the camera lens  28  is positioned directly over manipulators  32  and  34  (as in  FIG. 2 ), according to the invention, the captured image projected by the camera lens  28  is rotated about visual axis  54  through the center of the camera lens  28 . This compensates for rotation about “vertical” axis U to effect a static reorientation of the apparent manipulator positions. 
     It should be understood that camera lens  28  and image capture means  19  enjoy a full range of rotation about vertical axis U, and that the angles relative to reference planes and the like of the manipulators and the camera are dictated by the constraints of the operating environment. Additionally, camera lens  28  may be positioned at different angles relative to the plane formed by centerline axis  52  and baseline  53 . For example,  FIG. 4  shows camera lens  28  positioned at an elevation of 15° above the (arbitrary) reference plane formed by centerline axis  52  and baseline  53 . In this alignment, camera lens  28  is below manipulators  32 ,  34 . 
     If the image is purely monoscopic as depicted in  FIG. 1A , the system can effect static reorientation of the manipulators  32  and  34  about an axis  54  through a point, specifically center point  50 , by rotating the digital image through rotation means  25 .  FIG. 3  shows the relevant angles of rotation. Angle Φ 56  denotes the angle of declination of the visual axis  54  of camera lens  28  below vertical axis U. Angle θ 58  denotes the rotation of camera lens  28  position in the horizontal plane (formed by lines  52 ,  53 ) away from centerline axis  52  relative to the centerpoint  50 . 
     Rotation means  25  effects static realignment of the manipulators by rotating the real-time image pixel-by-pixel by an angle approximately equal to −θ, according to known methods. After this operation is complete, the left manipulator  32  and right manipulator  34  appear in the bottom of the displayed image (lower half of the projected screen). The camera lens  28  remains stationary, and the displayed image is rotated through image manipulation. Note that if hand control means  24 ,  26  at the operator&#39;s station are positioned above the viewpoint of the control operator, the rotation of the displayed image will correct the displayed image to the point where the manipulators appear in the top of the displayed image (upper half of the projected screen). In either case, the transformation of the displayed image allows the operator to view the manipulators as if emerging from the operator&#39;s hand controls. The remapping of the image is effected before actual control can be effected. 
     In addition to effecting static realignment through digital image transformation, transformation means  25  may effect dynamic synchronization of apparent manipulator tip positions with hand control positions by performing the following coordinate transformation on the video image data. The actual position of the manipulator tips in the workspace  30  can be transformed to an apparent position in the displayed image so that the manipulators will appear to move as though rigidly connected to the operator&#39;s hand controls. The altering of the apparent position of the manipulator tips improves the dexterity of the operator in handling the object in the workspace  30 . Because the end point of the end effector of the manipulator is known, the point (a,b,c) can be related to the angular position and length of the manipulator, and the point (p,q,r) can be related to the same parameters relative to the hand control using well-known trigonometric relationships between vectors and their endpoints. Thus: 
                              p           q           r              =                  cos   ⁢           ⁢     θ   ′             sin   ⁢           ⁢     θ   ′           0               -   sin     ⁢           ⁢     θ   ′             cos   ⁢           ⁢     θ   ′           0           0       0       1              ⁢                cos   ⁢           ⁢   Φ         0         sin   ⁢           ⁢   Φ             0       1       0               -   sin     ⁢           ⁢   Φ         0         cos   ⁢           ⁢   Φ                ⁢                cos   ⁢           ⁢   θ         0         sin   ⁢           ⁢   θ                 -   sin     ⁢           ⁢   θ           cos   ⁢           ⁢   θ         0           0       0       1              ⁢              a           b           c                        (     Eq   .           ⁢   1     )               
In connection with the transformation associated with the above equation, the image is rotated by an angle Θ′ selected by the operator to bring the apparent position of the manipulators into substantial registration with the hand controls. It is an observation that angle θ′≈−θ. This transformation describes the relationship between the position of the point represented by the end effector means at (a,b,c) (for either end effector means) relative to the point (p,q,r) of the corresponding tip of the manipulator in the apparent workspace in the displayed image on video display  20 .
 
     Another method of achieving static reorientation of manipulator positions is to rotate the image capture means about its visual axis. Referring again to the monoscopic system depicted in  FIG. 1A  and  FIG. 3 , camera lens  28  is rotated about its own visual axis  54 , an axis normal to the plane of the camera lens  28 , to the point where left manipulator  32  and right manipulator  34  appear in the bottom of the displayed image (lower half of the projected screen). Note again that if hand control means at the operator&#39;s station are positioned above the viewpoint of the control operator, the rotation of camera lens  28  and image capture means  19  will correct the displayed image to the point where the manipulators appear in the top of the displayed image (upper half of the projected screen). 
     To preserve the stereoscopic effect, in the case of stereoscopic imaging, as depicted in  FIG. 1B , rotations cannot be done about separate axes through each camera lens, but (referring to  FIG. 5A  and  FIG. 5B ) must be done in concert about a single axis offset from either lens. Specifically, rotation is done normal to center axis  57  passing through the centerpoint  50  and an arbitrary point on center axis  57  between the stereoscopic camera lenses  28  and  36  ( FIGS. 5A &amp; 5B ). This axis is similar to the visual axis  54  described in connection with  FIG. 2 . Referring to  FIG. 5A , the lenses of a stereoscopic device are shown in their initial position. Center axis  57  shows the fixed relation of each lens of the camera pair and is parallel to a reference axis  59  parallel to an axis in the plane formed by manipulators  32 ,  34  intersecting at the centerpoint  50 , where the axis is normal to a line bisecting the manipulators and passing through the centerpoint  50 . In order to reorient the displayed image through rotation of the image capture means, center axis  57  is canted relative to a reference plane  59  passing through centerpoint  50 , which plane includes reference axis  59 , as shown in  FIG. 5B . 
     There is a limitation on the amount of visually acceptable rotation of the stereoscopic image capture means  19 ,  35  and the elevation of the image capture means  19 ,  35  relative to the plane of the manipulators  32 ,  34 . The elevation cannot be so great as to make it impossible to change the relative view angle of each of the two manipulators relative to one another. Clearly, if angle Φ equals 90° elevation (where the viewing axis  54  lies in the reference plane formed by lines  52  and  53 ), no useful change in the relative view angle will be achieved by rotating the image. At other angles of elevation, the limitation depends on the separation angle of the manipulators  32 ,  34  and secondarily on the separation of the stereoscopic lenses  28 ,  36 . 
     In addition to achieving static reorientation of manipulator positions by rotation of the camera lens  28 , the system can effect a dynamic realignment by performing a coordinate transformation through translation means  25 . The actual position of the manipulator tips in the workspace  30  can be transformed to an apparent position in the displayed image so that the manipulators will appear to move as though rigidly connected to the operator&#39;s hand controls. The altering of the apparent position of the manipulator tips improves the dexterity of the operator in handling the object in the workspace  30 . 
       FIG. 8  and  FIG. 9  depict the image  132  of a manipulator ( 32 ) and an actual manipulator  32 , respectively, relative to a hand control  24 . In this example, and comparing  FIG. 2 , manipulators and corresponding controllers represented by hand controls are of a type utilizing a single pivot point  151 ,  161  in connection with the position sensors  51 ,  61  with two dimensional pivot about the point(s) and extension along the axis of the manipulator  32 . Other motions consistent with these actuations, such as longitudinal rotation of the manipulator about its axis is contemplated by the invention. With reference to  FIG. 8  and  FIG. 9 , movement of the hand control  24  causes the manipulator tip  72  to move to a new point (a,b,c) in workspace  30  such that the image  132  of the manipulator tip  172  moves to a new point (p,q,r) in the apparent workspace  22 , that point appearing in the view of the operator to be at the extended end of the hand control  24 . It may be preferable to express the servo commands relating the hand control and the corresponding manipulator in their polar coordinate systems (Ω,□, L) and (Ω′, □′, L′). These polar coordinates and their respective points in Cartesian coordinate systems are related by well-known polar to Cartesian transformations. 
     Referring again to  FIG. 3 , the specific angles of rotation used in calculating the coordinate transformation are shown. Angle Φ 56  denotes the angle of declination of the visual axis  54  of camera lens  28  below vertical axis U. Angle θ 58  denotes the rotation of camera lens  28  in the horizontal plane away from centerline axis  52  relative to the centerpoint  50  in the workspace  30 . Angle Γ 60  denotes the rotation of camera lens  28  about its visual axis  54 . 
     In operation of a monoscopic telemanipulation system, camera lens  28  and image capture means  19  are rotated about visual axis  54  as described above. The coordinates (a,b,c) in a reference orthogonal Cartesian coordinate system of the three-dimensional workspace  30  define the actual position of the tip of a manipulator, such as left manipulator  32 . The following matrix equation relates the desired apparent position (p,q,r in orthogonal Cartesian space) of the manipulator tip in the displayed image in video display  20  to the actual position (a,b,c) of the manipulator tip in the workspace  30 : 
                              p           q           r              =                  cos   ⁢           ⁢     Γ   ′             sin   ⁢           ⁢     Γ   ′           0               -   sin     ⁢           ⁢     Γ   ′             cos   ⁢           ⁢     Γ   ′           0           0       0       1              ⁢                cos   ⁢           ⁢   Φ         0         sin   ⁢           ⁢   Φ             0       1       0               -   sin     ⁢           ⁢   Φ         0         cos   ⁢           ⁢   Φ                ⁢                cos   ⁢           ⁢   θ         0         sin   ⁢           ⁢   θ                 -   sin     ⁢           ⁢   θ           cos   ⁢           ⁢   θ         0           0       0       1              ⁢              a           b           c                        (     Eq   .           ⁢   2     )               
When the manipulator tip is displayed at a position (p,q,r) in the displayed image in video display  20 , the manipulator will appear to the operator as if it is actually at the end of the operator&#39;s rigid hand control device. The coordinate transformation improves the ease with which the operator can handle objects in the workspace using a telemanipulation system.
 
     In the case of stereoscopic imaging, the stereo image capture means  19 ,  35  is rotated relative to a reference axis  59  parallel to an axis in the plane formed by manipulators  32 ,  34  intersecting at the centerpoint  50 , where the axis is normal to a line bisecting the manipulators and passing through the centerpoint  50 , as shown in  FIG. 5B . Angle Γ 60  measures the amount of rotation of the stereoscopic lenses  28 ,  36 , and its value can be used in Eq. 2 to calculate the proper coordinate transformation for stereoscopic viewing. 
     In order to ensure that the movements of the manipulators  32 ,  24  in workspace  30  properly track the movements of the hand controls  24 ,  26  in the operator&#39;s apparent workspace  22  even without complete knowledge of all angles and positions, the operator can establish a calibration reference for manipulators  32 ,  34  as they are viewed in the displayed image in video display  20  in connection with the position-following servo. Referring to  FIG. 6A , which shows the image displayed in video display  20 , a four-point coordinate graphic element  62  for example in the form of a tetrahedron or cube structure in three-dimensional view may be superimposed in three-dimensional space on the stereo image display, providing a coordinate reference in the three-dimensional image space. To calibrate the position of a single manipulator with respect to its corresponding hand control, the system “opens” the control loop, and the operator  14  moves hand control  24 , for example, while observing the motion of the tip of manipulator  32 , steering the tip until it appears to be touching a first reference point  64  of superimposed graphic element  62 , as shown in  FIG. 6B . (Since the motion of the hand control and manipulator tip have not yet been coordinated, the alignment of the tip with the first reference point may require very deliberate effort.) The operator  14  then indicates to the system that superposition of manipulator and reference point has been achieved (e.g., a “set” signal is sent to the system). 
     The system then locks the manipulator  32  into place, opens the control loop by decoupling it from the hand control  24  and instructs the operator  14  to release the hand control  24 . The system adjusts the extension L ( FIGS. 8 and 9 ) of the hand control to match that of the manipulator by inserting the offset σ 3 =L−L′, so that when the control loop is closed, there will be no reactive motion by either device. That is, the apparent extension positions of the hand control  24  and manipulator  32  must be identical when compared in the control loop. The system then closes the control loop and unlocks the manipulator  32 , returning control to the operator  14 . 
     The operator then moves the hand control about its pivot point to an angular orientation (Ψ, Ω) at which the operator senses that the image of the manipulator appears to emerge from the operator&#39;s hand control. Similar to the process described above, the system computes transformations which ensure that there will be no reactive motion by either master or slave when the control loop is closed. The system calculates angular offsets σ 1 =Ψ−Ψ′ and σ 2 =Ω−Ω′ and transforming the apparent position of the master or the slave prior to closing the control loop. The system now records the positions in three-dimensional space of the hand control master (Ψ 1 , Ω 1 , L 1 ) and the manipulator slave (Ψ 1 , Ω 1 , L′ 1 ). 
     The operator repeats the elements of this process with the remaining reference points of the superimposed graphic element  62 . The system may then derive and install the following linearized equation relating incremental changes in the position of the hand control masters  24 ,  26  to incremental changes in the position of the manipulator slaves  32 ,  34 , using the data sets to determine the coefficients of the equations relating the positions:
 
ΔΩ′= k   11   ΔΩ+k   12   ΔΨ+k   13   ΔL  
 
ΔΨ′= k   21   ΔΩ+k   22   ΔΨ+k   23   ΔL  
 
Δ L′=k   31   ΔΩ+k   32   ΔΩ+k   33   ΔL  
 
The solution to the above linearized equation is as follows:
 
                             k   11           k   12           k   13               k   21           k   22           k   23               k   31           k   32           k   33                =                  Δ   ⁢           ⁢     Ω   1   ′             ΔΩ   2   ′           ΔΩ   3   ′               Δ   ⁢           ⁢     Ψ   1   ′             ΔΨ   2   ′           ΔΨ   3   ′               Δ   ⁢           ⁢     L   1   ′             Δ   ⁢           ⁢     L   2   ′             Δ   ⁢           ⁢     L   3   ′                  ⁢                  Δ   ⁢           ⁢     Ω   1                     ΔΩ   2                   ΔΩ   3                       Δ   ⁢           ⁢     Ψ   1                     ΔΨ   2                   ΔΨ   3                       Δ   ⁢           ⁢     L   1                     Δ   ⁢           ⁢     L   2                     Δ   ⁢           ⁢     L   3                            -   1                 (     Eq   .           ⁢   3     )               
The system installs these coefficient values in the coordinate transformer  43  which controls servo  45 , with appropriate offsets σ 1 , σ 2  and σ 3 , so that there is no reactive motion when the loop is closed.
 
     In an alternative embodiment, calibration of the manipulators is achieved through virtual movement with the assistance of the system. Referring to  FIG. 6B , the system moves manipulator tip  32 , rather than the operator guiding the manipulator tip  32 , to one of four defined points in the three-dimensional workspace  30 , such as reference point  64  as seen by the operator. Using the hand control  24 , the operator  14  then dynamically calibrates the position of the manipulator  32  by steering an overlaid graphic dot until it appears superimposed on the manipulator tip  32 . The operator  14  then indicates to the system that superposition of manipulator tip  32  and reference point  64  has been achieved, and the coordinates of the manipulator  32  and hand control  24  are recorded. The process is repeated for the remaining reference points, after which the system derives and installs a coordinate transformation formula in the coordinate transformer  43 , as described in the above embodiment. 
     In actual practice, it is preferable for the surgeon, rather than the system, to initiate the calibration process if the invention is being used in laparoscopic surgery. During surgery, the calibration process is being carried out within a patient&#39;s abdomen, where there is little room to maneuver. Hence, automatic movements of the manipulator, however small, may be considered less desirable than operator-controlled movements. 
     Another method for evoking a sense of telepresence in a telemanipulation system involves the use of a specific coordinate transformation to compensate for other changes in the displayed image, such as a lateral shift or a scale change. The camera may undergo a lateral or angular displacement, causing the displayed image to shift. In addition, the camera may be capable of magnifying the object in the workspace, which causes a scale change and a displacement of the apparent pivot point of the manipulator. 
       FIGS. 7A and 7B  show the combined effect of a lateral shift of the image and a scale change brought about by magnification of the image.  FIG. 7A  shows a portion of the displayed image, including a manipulator  32 , in a two-dimensional field. The center of the image is at coordinates (0,0). The operator experiences the best possible sense of telepresence if the manipulator tip  72  at coordinates (u,v) in the image field appears to move as if it were rigidly attached to the control device in the operator&#39;s hand. The control device is pivoted at point (m,n) in the figure. The manipulator lies at an angle α 74  to the y-axis, and the distance from pivot point (m,n) to manipulator tip (u,v) is length L  76 . 
       FIG. 7B  shows what the operator would see if the image were magnified by a factor M. The center of the image is shifted laterally by a distance of Δx and Δy, and the new apparent coordinates of the manipulator tip  72  are (u′,v′). In order to ensure a desired level of telepresence, angle α 74  and length L  76  are remapped through perspective correction means  29  in the displayed image to give the operator the impression that the manipulator tip  72  is still rigidly attached to the hand control device. The following pair of equations describe the remapping of angle α 74  into angle α′ 78  and length L  76  into length L′ 80 :
 
α′=arctan [( u′−m )/( v′−n )] and
 
 L ′=[( u′−m ) 2 +( v′−n ) 2 ] 1/2  
 
where:
 
 u′=M ( u−Δx )  v′=M ( v−Δy ) and where
 
 u=L (sin α)+ m v=L (cos α)+ n  
 
When α and L are remapped according to the above equations, the manipulator tip  72  appears in the displayed image to move as if it were rigidly connected to the operator&#39;s hand control device.
 
     The above relationships can be extended to include transformations in three dimensions in order to compensate for displacement of the manipulators when the camera lens  28  is rotated about its own visual axis  54 , as in the embodiment described with respect to  FIG. 3 . In all cases, the desired goal of maintaining the perceived plane containing the two manipulators coincident with the plane of the two hand controls is achieved. 
     The invention has now been explained with reference to specific embodiments. Other embodiments will be apparent to those of ordinary skill in the art upon reference to the present description. For example, the invention can be extended to articulated manipulators with multiple points of rotation and translation or with pivot points at locations not physically attached to the manipulators. It is therefore not intended that this invention be limited, except as indicated by the appended claims.