Multi-center impedance control

Abstract

To provide a method for controlling a robot so that a component comprising a plurality of pins or pegs is inserted into a structure comprising a plurality of holes for instance, in order to execute complicated assembling work.SOLUTION: The method uses an impedance controller including a plurality of reference centers having one gain coefficient group. Only two translational gain coefficients, one of which corresponds to spring force and the other of which corresponds to damping force, are used and rotation gain is not used. In the method, spring-damping force is calculated from a position of a reference center and a speed using a value of gain, and contact force and contact torque are measured using a sensor coupled to a space between a robot arm and a component to be manipulated. Subsequently, the calculated spring-damping force is combined with the measured contact force and the contact torque to provide combined force and combined torque at a centroid of the component. Subsequently, a posture of a new component is calculated on the basis of the combined force and the combined torque, using calculation by the impedance controller.SELECTED DRAWING: Figure 4

Description

[Technical field]

[0001] The present invention relates to the field of industrial robot motion control, and more particularly to a method of controlling a robot to perform a complex assembly task, for example to insert a two-pin component into a two-hole structure, the method including an impedance controller using multiple reference centers with a gain group, adding spring-damping forces calculated from the reference center positions and velocities to measured contact forces and contact torques, and calculating a new component pose based on the sum. [Background technology]

[0002] The use of industrial robots to perform a wide range of repetitive manufacturing and assembly tasks is well known. However, some types of assembly tasks are still performed manually, such as assembling an automobile door with two hinge pins onto an automobile body with two hinge pin holes. In such tasks, a machine lifts the weight of the door and an operator aligns the hinge pins with the holes and sinks the door into place. The reason these types of tasks are still often performed manually is because it is difficult for a robot to detect and correct the complex misalignments that can occur when trying to insert multiple pins into multiple holes simultaneously.

[0003] Conventional techniques for controlling robots in applications such as those described above use a spring-damper system model with a single reference center, with an impedance controller that defines two gain sets, one linear gain and one angular gain. The conventional technique then compares the force and torque feedback from the robot with the forces and torques calculated from the system model and attempts to adjust the robot position accordingly. However, adjusting the gains in such conventional types of system models is difficult; specifically, the angular gains and their relationship to the linear gains are not intuitive. Furthermore, a system model tuned for one assembly application cannot be applied to another application with different part geometries or structural characteristics, so the gains and gain relationships must be determined uniquely for each application.

[0004] In light of the above, there is a need for improved impedance-based feedback control techniques for robots performing alignment-sensitive assembly tasks. Summary of the Invention [Means for solving the problem]

[0005] According to the teachings of the present disclosure, a method is disclosed for controlling a robot to perform a complex assembly task, for example, to insert a component with multiple pins or pegs into a structure with multiple holes. The method uses an impedance controller that includes multiple reference centers with one set of gain coefficients. Only translational gain coefficients are used, one corresponding to spring forces and one corresponding to damping forces, and no rotational gains are used. The method calculates spring-damping forces from the position and velocity of the reference center using the gain values, and measures contact forces and contact torques by sensors coupled between the robot arm and the component being manipulated. The calculated spring-damping forces are then summed with the measured contact forces and contact torques to provide resultant forces and torques at the center of mass of the component. A new component pose is then calculated based on the resultant forces and torques. Effect of the Invention

[0006] Additional embodiments of the presently disclosed devices and methods will become apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. [Brief description of the drawings]

[0007] [Figure 1] FIG. 1 shows a diagram of a two-peg workpiece assembled into a two-hole structure and a conventional single-point impedance controller technique using translational and rotational gains, as known to those skilled in the art. [Diagram 2] FIG. 2 illustrates a two-peg workpiece assembled into a two-hole structure and an impedance controller technique using two reference centers according to an embodiment of the present disclosure. [Figure 3A] FIG. 3A is a diagram illustrating the steps involved in implementing the impedance controller technique using two reference centers shown in FIG. 2 according to an embodiment of the present disclosure. [Figure 3B] FIG. 3B is a diagram illustrating the steps involved in implementing the impedance controller technique using two reference centers shown in FIG. 2 according to an embodiment of the present disclosure. [Figure 3C] FIG. 3C is a diagram illustrating the steps involved in implementing the impedance controller technique using two reference centers shown in FIG. 2 according to an embodiment of the present disclosure. [Figure 3D] FIG. 3D is a diagram illustrating the steps involved in implementing the impedance controller technique using two reference centers shown in FIG. 2 according to an embodiment of the present disclosure. [Figure 4] FIG. 4 is a flow chart diagram illustrating a method for controlling a robot performing an assembly task, including a multiple reference center impedance controller, according to an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0008] The following discussion of disclosed embodiments of an impedance controller for a robot using multiple centers of reference is merely exemplary in nature and is in no way intended to limit the disclosed apparatus and techniques, or their applications or uses.

[0009] The use of industrial robots for a variety of manufacturing and assembly tasks is well known. However, some types of assembly tasks, such as those in which the initial part position is highly uncertain or where the assembly task is sensitive to even minor misalignment of one part relative to another, are difficult for robots to perform reliably. Examples of such types of assembly tasks include inserting an electronic component with multiple pins into a socket on a circuit board and assembling an automobile door with two hinge pins into an automobile body with two hinge pin holes. These types of tasks are still often performed manually because it is difficult for a robot to detect and correct any complications resulting from even minor misalignments that may occur when attempting to simultaneously insert multiple pins into multiple holes.

[0010] 1 illustrates how a two-peg workpiece is assembled into a two-hole structure and a conventional single-point impedance controller technique using translational and rotational gains, as known to those skilled in the art. The assembly 100 includes a door 110 and a vehicle body 120. The door 110 includes two vertically aligned pegs 112 and 114. The body 120 includes vertically aligned holes 122 and 124. The task of a robot (not shown) is to manipulate the door 110 to insert the pegs 112 and 114 into the holes 122 and 124, thereby forming a hinged joint between the door 110 and the body 120. This assembly operation, of course, requires that the door 110 be moved so that the tips of the pegs 112 and 114 simultaneously align with and enter the tops of the holes 122 and 124, and then the door 110 is lowered so that the pegs 112 and 114 are fully inserted into the holes 122 and 124.

[0011] Conventional robot control techniques, in applications such as the one shown in FIG. 1, involve using a spring-dampener impedance controller model with one reference point or reference center 116 and defining two gain groups, one translational gain and one rotational gain. The conventional technique then compares the force and torque feedback from a force sensor 130 (coupled between the robot and the door 110) with the forces and torques calculated from the spring-dampener system model and attempts to adjust the robot position accordingly. However, adjusting the gains in such a conventional type of system model is difficult; specifically, the angular gains and their relationship to the linear gains are not intuitive. In addition, traditional single reference center impedance controllers are sensitive to the choice of the location of the reference center 116.

[0012] Furthermore, a controller tuned for one application, such as assembly 100, may not be applicable to another application with different component geometries or structural characteristics, so gains and gain relationships must be uniquely determined for each application. For example, if a spring-dampener impedance controller has translational and rotational gains tuned for a door assembly operation for assembly 100, the same controller will not be properly tuned for a door assembly operation for assembly 140, where the hinge pegs are farther apart, or for assembly 150, where the hinge pegs are closer together.

[0013] The present disclosure overcomes the limitations of single reference center impedance controllers by providing an impedance controller with multiple reference centers defined at key points. Each reference center in the presently disclosed technique contains only translational spring-damping gain, and the same gain coefficients are used at all of the reference centers. This simplifies tuning and provides other advantages as described below.

[0014] FIG. 2 illustrates a two-peg workpiece being assembled into a two-hole structure and an impedance controller technique using two reference centers according to an embodiment of the present disclosure. The system 200 includes an industrial robot 202 tasked with assembling a vehicle door member 210 into a vehicle body 220, similar to the previous example shown in FIG. 1. The robot 202 typically communicates with a controller 204 via cables, but possibly wirelessly, as known to those skilled in the art. The robot 202 may be a traditional multi-axis articulated industrial robot with arms connected in series at rotary joints (as shown in simplified form in FIG. 2), or a "delta" type pick-and-place robot with multiple parallel links, or any other variety of robots or machines capable of performing specified movements of a workpiece based on instructions from a controller.

[0015] It is emphasized that the door assembly operation of FIG. 2 and subsequent figures is but one example of an assembly operation that is sensitive to misalignment, even if it is minor, and that may benefit from the impedance controller techniques of the present disclosure. Other examples, such as plugging multi-pin electronic components into circuit boards or other components, will occur to those skilled in the art of robotically performed assembly operations. Also, while FIG. 2 and subsequent figures depict the door assembly operation in two dimensions, it will be understood that all of the forces, torques, positions, and motions described in the following discussion are three-dimensional in nature, and include both forces and motions that are considered to be in the X and Y directions "in the plane of the page," and forces and motions "into and out of the page" (Z direction).

[0016] The door member 210 includes a hinge peg 212 and a hinge peg 214. The door member 210 has a pseudo center of gravity 211. The pseudo center of gravity is a point defined based on the centers of gravity of the pegs 212 and 214. The body 220 includes a hinge hole 222 and a hinge hole 224. The task of the robot 202 is to manipulate the door member 210 to simultaneously insert the pegs 212 and 214 into the holes 222 and 224, thereby forming a hinge joint connection between the door 210 and the body 220. The robot arm 230 forms the outer arm and wrist joint of the robot 202. The arm 230 manipulates the vertical and horizontal position and the tilt angle of the door member 210. A force and torque sensor 240 is coupled between the robot arm 230 and the door member 210 and provides a force and torque signal to the controller 204 via a wired (as shown) or wireless connection.

[0017] This disclosure describes an impedance controller technique using multiple centers of reference. Impedance control is an approach to dynamic control related to force and position. Impedance control is often used in applications where a manipulator interacts with its environment and force-position relationships are involved. Mechanical impedance is the ratio of force output to motion input. The "spring constant" defines the force output for a spring extension or compression. The "damping constant" defines the force output for a velocity input. Controlling the impedance of a mechanism means controlling the resistance to an external motion imposed by the environment. Mechanical admittance is the inverse of the impedance, which defines the motion resulting from a force input. The key theory behind the impedance control method is to treat the environment as an admittance and the manipulator as an impedance. This disclosure describes an impedance controller method using multiple centers of reference with advantages over prior art methods.

[0018] In system 200, a reference center 216 is defined at the tip of peg 212, and a reference center 218 is defined at the tip of peg 214. An impedance controller defines spring-damping forces at each of reference centers 216 and 218, including a displacement-based spring force and a velocity-based damping force. The spring force at reference center 216 is calculated based on the displacement of reference center 216 from a target reference point 226 at the bottom center of hole 222. Similarly, the spring force at reference center 218 is calculated based on the displacement of reference center 218 from a target reference point 228 at the bottom center of hole 224.

[0019] The following discusses how the spring-damping forces at the reference centers 216 and 218 are calculated within the impedance controller of the present disclosure. 216 and the position of the reference center 218 is expressed as p 218 Position p 216 and p 218 has three-dimensional (e.g., X, Y, and Z) coordinates. The velocity of the reference center 216 is v 216 and the velocity of the reference center 218 is v 218The velocity v 216 and v 218 is a vector with three-dimensional (e.g., X, Y, and Z) components. 216 and p 218 and speed v 216 and v 218 is calculated by the controller 204 based on the known geometry of the robot 202, including the position and orientation of the arm 230, along with the geometry of the door member 210.

[0020] The position of the target reference point 226 is p 226 The position of the target reference point 228 is expressed as p 228 Position p 226 and p 228 also have three-dimensional (e.g., X, Y, and Z) coordinates, with at least lateral and vertical components fixed relative to the base of the robot 202. In addition, while Figure 2 shows a static view of the members in the system 200, it should be noted that the techniques of this disclosure may be applied when the vehicle body 200 is moving along a conveyor, and the longitudinal (Z) velocity of the conveyor is factored into the three-dimensional motion of the robot arm 230.

[0021] According to the impedance controller of the present disclosure, the spring-damping force at the reference center 216 is calculated as the following equation (1):

[0022]

number

[0023] Similarly, the spring-damping force at the reference center 218 is calculated as equation (2) below:

[0024]

number

[0025] K p is the spring constant or spring gain factor, and D pis the damping constant or damping gain coefficient, and the other variables are defined above. The same spring gain coefficient K p and the same attenuation gain coefficient D p is used in calculating the spring-damping forces for all of the reference centers and may be empirically determined and fine-tuned as necessary to achieve the best controller results. Because the multiple reference center impedance controller does not use rotational gain coefficients, the translational gain coefficients selected for a particular application (e.g., automobile door assembly) are likely to be highly effective for other applications of the same type having different member geometries. The use of a single set of gain coefficients without rotational gains provides a significant advantage of the multiple center impedance controller of the present disclosure over the prior art.

[0026] Equation (1) can be explained as follows: the spring force at reference center 216 is the spring constant multiplied by the displacement (position difference) of reference center 216 from target reference point 226, and the damping force at reference center 216 (subtracted from the spring force) is the damping constant multiplied by the velocity of reference center 216. Equation (2) is explained similarly. The spring-damping forces at reference centers 216 and 218 are three-dimensional force vectors.

[0027] 3A, 3B, 3C, and 3D are diagrams illustrating the steps involved in implementing the impedance controller technique using the two reference centers shown in FIG. 2 according to an embodiment of the present disclosure. FIG. 3A illustrates the first step in the process. The first step is to calculate the spring-damping forces at the reference centers 216 and 218 described above. In FIG. 3A, the force vector 310 is calculated as f (calculated in equation (1)). 216 and the force vector 312 represents f 218 The spring-damping force in this first step is a given value K p and D. p , and the reference center position and velocity known by the controller 204 as described above.

[0028] 3B shows the second step in the process. A combination of contact force and contact torque is measured by sensor 240. Force vector 320 represents the force measured by sensor 240, and torque vector 322 represents the torque measured by sensor 240. Force vector 320 and torque vector 322 represent the force and torque, respectively, applied by door member 210 to robot arm 230. The values ​​of force vector 320 and torque vector 322 are provided as sensor signals from sensor 240 to controller 204.

[0029] Figure 3C shows the third step in the process. Controller 204 calculates the sum of the spring-damping forces at reference centers 216 and 218 (from Figure 3A) and the contact forces and torques measured by sensor 240 (from Figure 3B). Summing the force vectors and torques about center of gravity 211 results in a resultant force vector 330 and a resultant torque vector 332 applied to center of gravity 211.

[0030] 3D shows the fourth step in the process. The controller 204 calculates the new pose of the door section 210 under the forces and torques resulting from the third step (resultant force vector 330 and resultant torque vector 332). Using known impedance controller techniques, the controller 204 solves an equation (Equation 3) of the type used for a spring-mass-damper system.

[0031]

number

[0032] However, since the spring and damping forces are already included in the calculated force F, the equations simplify to Equation 4 for translational motion and Equation 5 for rotational motion.

[0033]

number

[0034]

number

[0035] Using the known mass properties and inertia of door member 210, controller 204 determines the motion of door member 210 due to resultant force vector 330 (F) and resultant torque vector 332 (T). Controller 204 then moves robot arm 230, via robot 202, so that door member 210 undergoes the motion that was just calculated. This motion is shown in Figure 3D. Door member 210 is rotated (arrow 340) into extremely close alignment with holes 222 and 224, and translated (arrow 342) so that it is almost fully inserted within holes 222 and 224.

[0036] The above-described multi-center impedance controller in conjunction with the door assembly example has several advantages over conventional single-center impedance controllers. First, with a multi-center controller, the selection of reference centers and their corresponding target points is intuitive and simple. When inserting a multi-peg component into a corresponding hole, the tip of the peg can be easily defined as the reference center point. Also, the multi-center controller eliminates the need for rotational gain constants, which are difficult to determine and unintuitive. In addition, a single set of spring and damping gain coefficients is used for all of the reference centers (two or more), and gain coefficients used in one application of the multi-center controller can be applied to other applications of similar members with different geometries.

[0037] 4 is a flow chart diagram 400 illustrating a method of controlling a robot performing an assembly operation including a multiple reference center impedance controller according to an embodiment of the present disclosure. The assembly operation described in the method of FIG. 4 involves using a robot 202 (having an outer robot arm 230) to simultaneously insert multiple pins or pegs of a first workpiece 210 into multiple recesses of a second workpiece 220, as shown in FIGS. 2 and 3. However, as noted above, the multiple reference center impedance controller of the present disclosure can be applied to other types of assembly operations.

[0038] In box 402, a reference point is defined at the tip of each pin in the first workpiece 210, and a corresponding target point is defined in the recess in the second workpiece 220. Each of the pins corresponds to a particular one of the recesses, and the relationship between the reference point and the target point is defined accordingly. In box 404, the spring-damping force at each reference point is calculated by the robot controller 204 based on the velocity of the reference point and the displacement of the reference point relative to the corresponding target point. Specifically, the spring-damping force at the first reference point is calculated using equation (1) above, or the like. The position and velocity of the reference point are known by the controller 204 based on the robot kinematics and the workpiece geometry. A spring gain factor K p and the damping gain coefficient D p may be empirically determined and fine-tuned as necessary to achieve the best controller results, and the same spring gain coefficients and the same damping gain coefficients are used in calculating the spring-damping forces for each of the reference points.

[0039] In box 406, the contact forces and torques are measured by sensors 240 coupled between the robot 202 and the first workpiece 210 and the contact forces and torques are communicated to the controller 204. In box 408, the resultant forces and torques at the center of gravity 211 are calculated by the controller 204 as the sum of the spring-damping forces (box 404) and the contact forces and torques (box 406). Summing the force vectors 310 and 312 with the force vectors 320 and torque 322 about the center of gravity 211 results in a resultant force vector 330 and a resultant torque vector 332 applied to the center of gravity 211.

[0040] In box 410, a new orientation of the door member 210 is calculated by the controller 204 based on the resultant force 330 and the resultant torque 332. The new orientation of the door member 210 is calculated using equation (6).

[0041]

number

[0042] In box 412, in response to a signal from the controller 204, the door member 210 is moved by the robot 202 to the new pose (calculated in box 410). The impedance controller of the present disclosure is implemented as a real-time feedback control system. This means that after the door member 210 is moved to the new pose in box 412, the process continually loops back to box 404 to calculate new spring-damping forces. The looping continues until the pegs 212 and 214 of the door member 210 are fully seated within the holes 222 and 224 of the vehicle body 220.

[0043] For clarity, again, the above discussion of assembling door members with hinge pins into corresponding hinge holes is by way of example only: the disclosed techniques can be applied to any type of workpiece with pins that must be simultaneously inserted into corresponding holes, or to other types of assembly activities that are sensitive to even minor misalignment.

[0044] Various computers and controllers are mentioned or alluded to throughout the foregoing discussion. It will be understood that the software applications and modules of these computers and controllers execute on one or more computing devices having a processor and memory modules. In particular, this includes the processor within the robot controller 204 described above. In particular, the processor within the controller 204 is configured to employ impedance feedback control techniques with multiple reference centers of the type described above.

[0045] As outlined above, the disclosed technique of an impedance controller for a robot using multiple reference centers improves the performance of robotic assembly operations where part positions are significantly uncertain, or where the assembly operation is sensitive to even minor misalignment of one part relative to another.

[0046] Having described numerous aspects and embodiments of an impedance controller for a robot using multiple reference centers, modifications, permutations, additions, and subcombinations thereof will be apparent to those skilled in the art, and therefore, the following appended claims, and any claims hereafter issued, are intended to be construed as including all such modifications, permutations, additions, and subcombinations as fall within the true spirit and scope thereof.

Claims

1. 1. A method of controlling a robot to perform an assembly operation to insert a plurality of pins of a first workpiece into a plurality of recesses of a second workpiece, the method comprising: defining reference points at the tips of each of the pins in the first workpiece and defining corresponding target points for each of the reference points within the recesses in the second workpiece; calculating, by a robot controller, spring-damping forces at each of the reference points based on the velocity of the reference points and the displacement of the reference points relative to the corresponding target points; measuring a contact force and a contact torque with a sensor coupled between the robot and the first workpiece and communicating the contact force and contact torque to the robot controller; calculating by the robot controller a resultant force and a resultant torque as the sum of the spring-damping force and the contact force and contact torque; calculating, by the robot controller, a new pose of the first workpiece based on the resultant force and resultant torque; and moving the first workpiece by the robot to the new pose in response to a signal from the robot controller; A method for controlling a robot, comprising:

2. The method of claim 1 , wherein a single damping gain factor and a single spring gain factor are used in calculating the spring-damping forces at all of the reference points.

3. 3. The method of claim 2, wherein the damping gain factor and the spring gain factor are translational gain factors, and no rotational gain factor is used in calculating the spring-damping force at the reference point.

4. 3. The method of claim 2, wherein the spring-damping force at each of the reference points is calculated as the damping gain factor multiplied by the velocity of the reference point plus the spring gain factor multiplied by the displacement of the reference point relative to the corresponding target point.

5. 2. The method of claim 1, wherein the velocity of the reference point and the displacement of the reference point relative to the corresponding target point are determined using kinematic calculations based on known robot positions and velocities and known geometry of the first workpiece relative to the robot.

6. 2. The method of claim 1, wherein calculating resultant forces and torques as the sum of the spring-damping forces and the contact forces and torques comprises summing all of the spring-damping forces and the contact forces and torques about a pseudo center of gravity of the first workpiece.

7. 2. The method of claim 1, wherein calculating a new pose of the first workpiece comprises using an impedance controller calculation to calculate the new pose of the first workpiece based on the resultant force and resultant torque applied to a pseudo center of gravity of the first workpiece.

8. 2. The method of claim 1, wherein the first workpiece is a vehicle door member and the second workpiece is a vehicle body.

9. 9. The method of claim 8, wherein said plurality of pins are two hinge pins of said vehicle door member, and said assembly operation is simultaneously inserting said two hinge pins into two hinge openings of said vehicle body.

10. 10. The method of claim 8, wherein the vehicle body moves on a conveyor during the assembly operation and the robot controller includes movement of the conveyor in a signal to the robot to move the vehicle door member.

11. 1. A method for controlling a robot to assemble a vehicle door member to a vehicle body by inserting two hinge pins of the vehicle door member into two hinge openings of the vehicle body, the method comprising: defining reference points at the tips of each of the hinge pins of the vehicle door member, and defining corresponding target points for each of the reference points within two hinge openings of the vehicle body; calculating, by a robot controller, spring-damping forces at each of the reference points based on the velocity of the reference points and the displacement of the reference points relative to the corresponding target points; measuring contact forces and contact torques with sensors coupled between the robot and the vehicle door member and communicating the contact forces and contact torques to the robot controller; calculating by the robot controller a resultant force and a resultant torque as a sum of the spring-damping force and the contact force and contact torque about a center of gravity of a hinge pin of the vehicle door member; calculating, by the robot controller, a new pose of the vehicle door member using an impedance controller calculation based on the resultant force and resultant torque; and moving the vehicle door member by the robot to the new position in response to a signal from the robot controller; A method for controlling a robot, comprising:

12. 12. The method of claim 11, wherein one damping gain factor and one spring gain factor are used in calculating the spring-damping forces at both of said reference points, said damping gain factor and said spring gain factor being translational gain factor, and the spring-damping force at each of said reference points is calculated as said damping gain factor multiplied by the velocity of said reference point plus said spring gain factor multiplied by the displacement of said reference point relative to said corresponding target point.

13. 1. A system for performing an assembly operation in which a plurality of pins of a first workpiece are inserted into a plurality of recesses of a second workpiece, the system comprising: an industrial robot configured to move the first workpiece; a force and torque sensor coupled between the first workpiece and the industrial robot; A robot controller having a processor and a memory, the robot controller in communication with the industrial robot and receiving signals from the force and torque sensor, the robot controller comprising: defining reference points at the tips of each of the pins on the first workpiece and defining corresponding target points for each of the reference points in recesses in the second workpiece; calculating a spring-damping force at each of the reference points based on the velocity of the reference points and the displacement of the reference points relative to the corresponding target points; - calculating the resultant force and torque as the sum of the spring-damping force and the contact force and contact torque measured by the force-torque sensor; calculating a new pose of the first workpiece based on the resultant force and torque; sending a signal to the industrial robot to cause the industrial robot to move the first workpiece to the new pose; a robot controller configured to perform steps including:

23. A system for performing an assembly operation, comprising:

14. 14. The system of claim 13, wherein one damping gain factor and one spring gain factor are used in calculating the spring-damping forces at all of the reference points, and the gain factors are translational gain factors.

15. 15. The system of claim 14, wherein the spring-damping force at each of the reference points is calculated as the damping gain factor multiplied by the velocity of the reference point plus the spring gain factor multiplied by the displacement of the reference point relative to the corresponding target point.

16. 14. The system of claim 13, wherein the velocity of the reference point and the displacement of the reference point relative to the corresponding target point are determined using kinematic calculations based on known robot positions and velocities and known geometry of the first workpiece relative to the industrial robot.

17. 14. The system of claim 13, wherein calculating resultant forces and torques as the sum of the spring-damping forces and the contact forces and torques comprises summing all of the spring-damping forces and the contact forces and torques about a pseudo center of gravity of the first workpiece.

18. 14. The system of claim 13, wherein calculating a new pose of the first workpiece includes using an impedance controller calculation to calculate the new pose of the first workpiece based on the resultant force and resultant torque applied to a pseudo center of gravity of the first workpiece.

19. 14. The system of claim 13, wherein the first workpiece is a vehicle door member, the second workpiece is a vehicle body, and the plurality of pins are two hinge pins of the vehicle door member, and the assembly operation is simultaneously inserting the two hinge pins into two hinge openings of the vehicle body.

20. 20. The system of claim 19, wherein the vehicle body moves on a conveyor during the assembly operation and the robot controller includes movement of the conveyor in a signal to the industrial robot to move the vehicle door member.

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