We present two schemes for planning the time-optimal trajectory for cooperative multi-manipulator system (CMMS) carrying a common object. We assume that the desired path is given and parameterizable by an arclength variable. Both approaches take into account the dynamics of the manipulators and object. The first approach employs linear programming techniques, and it allows us to obtain the time-optimal execution of the given task utilizing the maximum torque capacities of the joint motors. The second approach is a sub-time-optimal method that is computationally very efficient. In the second approach the given load is divided into a share for each robot in the CMMS in a manner in which the trajectory acceleration/deceleration is maximized, hence the trajectory execution time is minimized. This load distribution approach uses optimization schemes that degenerate to a linear search algorithm for the case of two robots manipulating a common load, and this results in significant reduction of computation time. The load distribution scheme not only enables us to reduce the computation time, but also gives us the possibility of applying this method in real-time planning and control of CMMS. Further, we show that for certain object trajectories the load distribution scheme yields truly time-optimal trajectories.

A control scheme to perform force/position control with flexible joint robots when the end effector is constrained to move along a frictionless curved surface represented by algebraic constraints is developed. The control scheme described involves the exact cancellation of the nonlinear terms of the projected end effector dynamics in the position and force controlled directions. It is shown that it is not necessary to employ end-effector force sensors in order to control a desired force trajectory in the force controlled directions and a desired end-effector position trajectory along the position controlled directions. Measurements of joint acceleration and jerk are also not necessary.>

The problem of controlling multiple flexible joint robots during cooperative manipulation of a rigidly grasped common load (denoted as the CMFJR problem) is addressed. The dynamic model of the CMFJR shows the interaction between the manipulators in the closed chain is analogous to a single manipulator interacting with frictionless (algebraic constraint) surface, while in motion along the surface. It is assumed that each flexible joint robot is equipped with joint velocity and position sensors and also actuator mounted position and velocity sensors. It is shown that it is not necessary to employ force sensors mounted on the robot wrist in order to track a desired load trajectory and an internal force trajectory. The transient response of the position error and the internal force error can be arbitrarily assigned even though the force sensors are not employed.>

Redundant robots that are kinematically controlled by using Jacobian pseudoinverses may not have repeatable joint motions. This problem was initially observed and analyzed by C.A. Klein and C.H. Huang (1983). T. Shamir and Y. Yomdin (1988) analyzed this problem using a differential geometric approach. Both studies arrived at conditions under which a cyclic path in the work space does not result in a cyclic path in the joint space. It is shown that these criteria are equivalent. A measure for the drift motion of planar kinematically redundant manipulators is presented. A mathematical analysis that determines the predictable properties of drift motion for planar manipulators operating under pseudoinverse control is presented. In fact, it is shown that the Lyapunov stability analysis and phase portrait techniques can be used to predict the stability behavior of drift utilizing the drift density measure. The information-such as how much drift will occur and which configurations are drift stable-can be obtained from the analysis.>

Dynamic feedback control strategies are proposed for the asymptotic stabilization and asymptotic output tracking problems, associated with the operation of flexible joint manipulators. Smooth dynamical linearizing feedback controllers, as well as dynamical sliding mode regulators, are derived within the context of M. Fliess's (1989) generalized observability canonical form (GOCF). The GOCF is obtained by means of a state elimination procedure, carried out on the system of differential equations describing the manipulator dynamics. The remarkable feature of this new approach lies in the fact that a truly effective smoothing of the sliding mode controlled responses is possible while substantially reducing the chattering in the control input torque. Simulation examples are given that illustrate the performance of the proposed controllers.>

Redundant robots which are kinematically controlled by using Jacobian pseudo-inverses may not have repeatable joint motions. This problem was initially observed and analyzed by C.A. Klein and C.H. Huang (1983). T. Shamir and Y. Yomdin (1988) recently analyzed this problem using a differential geometric approach. The above papers arrived at conditions under which a cyclic path in the work space does not result in a cyclic path in the joint space. However, it was not clear that these conditions were equivalent. It is presently shown that these two criteria are indeed equivalent. A measure for the drift motion is presented. The mathematical analysis given in the present paper can determine these predictable properties of drift motion. It is shown that the Lyapunov analysis and phase portrait techniques can be used to predict the stability behavior of drift utilizing the drift density measure described here. Information about how much drift will occur and which configurations are stable can be obtained from the analysis.>

The problem of multiple robots manipulating a rigid object cooperatively is addressed. An adaptive controller based on Lyapunov's second method is proposed. This controller takes into account the dynamics of both the object and the manipulators. The controller does not require feedback of joint accelerations and inversion of inertia or Jacobian matrices. The global stability, in the sense of Lyapunov, of the overall system is shown. The effects of bounded disturbances the multirobot system are also considered. An adaptive control law which guarantees the convergence of the tracking error to a bounded set is proposed. The size of the set is shown to depend on the be bounds of the disturbances.>

The commenters point out that the derivation of the closed-form solution to the homogeneous transform equation AX=XB by Y.C. Shiu and S. Ahmad (see ibid., vol.5, no.1, p.16-27, Feb.1989), although containing many useful ideas, is somewhat lengthy. It can be presented much more compactly using quaternion algebra. Direct benefits of such an approach are presented. In their reply, Shiu and Ahmad admit that the commenters' method has significant advantages over the original solution for the rotational part. However, it does not provide the geometric insight that the solution for AX=XB has a rotational degree of freedom about k/sub A/ (the axes of rotation of A). The solution to the translational part of X discussed in the original paper is not affected by this discussion since its computation is not dependent on how the rotational part is computed.>

An algorithm to modify the trajectories of multiple robots in cooperative manipulation is developed. If a given trajectory results in joint torques that exceed the admissible torque range for one or more joints, the algorithm slows down or speeds up the trajectory so as to maintain all the torques within the admissible boundary. The proposed trajectory-modification algorithm uses the concept of time scaling developed by Hollerbach (1984) for single robots. The trajectory scaling scheme described in this paper requires the use of linear programming techniques and is designed to accommodate the internal force constraints and payload distribution strategies. The actuator torques may be found from the quadratic minimization that has the effect of lowering energy consumption for the trajectory. A scheme for generating a robust multirobot trajectories when the carried load mass and inertia matrix are unknown but vary within a certain range is described.>

A process for shape recovery from robot contour-tracking operations with force feedback is described. Shape recovery is an important task for self-teaching robots and for exploratory operations in unknown environments. An algorithm which directs a position controlled robot around an unknown planar contour using the steady-state contact force information is described. A compensation process is explored for purposes of planar shape recovery. It is found through experimentation that the joint compliance is most conveniently compensated for in practice. Improvements in the shapes recovered from robot contouring are seen with the compensations. Experimental details and difficulties are also discussed.>

An algorithm is developed to modify the trajectories of multiple robots in cooperative manipulation. If a given trajectory results in joint torques which exceed the admissible torque range for one or more joints, the trajectory speed is scaled so as to maintain all the torques within the admissible boundary. The trajectory scaling scheme described requires the use of linear programming techniques and is designed to accommodate the internal force constraints and payload distribution strategies. As the multirobot system is usually redundantly actuated, the actuator torques can be found from the quadratic minimization, which has the effect of lowering energy consumption for the trajectory. Several examples are given to show the effectiveness of the multirobot trajectory scaling scheme.>

Mathematics is presented for using monocular model-based vision to find 3D positions of circular and spherical model features, and, for the circular case, orientations as well. Monocular model-based vision here refers to the use of a single projective image of modeled objects to solve for the 3D positions and orientations of the objects in the scene. A novel closed-formed solution for the 3D position and orientation of a circular features and the 3D position of a spherical feature is described. There are two general solutions for the circular feature bu there is only one solution when the surface normal of the circular feature passes through the center of projection. There is only one solution for the circular case. Advantages of this method are: (1) it handles spherical as well as circular features; (2) it has a closed-form solution; (3) it gives only the necessary number of solutions (no redundant solutions); (4) it uses simple mathematics involving 3D analytic geometry; and (5) it is geometrically intuitive.>

Model-based monocular vision has been used to recognize and locate 3-D objects by matching image corners (or lines) to model corners (or lines). These algorithms typically have high computational complexities. Grouping of visual features has been used to reduce the computational complexity. In this work point image features are grouped into loops and object loops that have similar viewpoint-invariant characteristics. Examples of viewpoint-invariant characteristics of loops are the number of lines and vertices, the number of convex and concave curves, and the sequence in which the lines, curves, and vertices are linked together. Grouping into loops also facilitates model matching by ellipses, in addition to corners and lines. Experiments are performed to extract loops from images and segmenting them into lines and elliptical curves. Distinguishable loops are used to find 3-D locations of the objects in scenes.>

The problem of coordinating a positioning table and a seven-axis manipulator is examined. The method described is based on subdivision of tasks. The welding table is coordinated to align the weld point surface normal antiparallel to the direction of gravity. The seven-axis robot (a six-axis Cybotech WV 15 robot and a track) is constrained to move the weld torch along the weld trajectory. The robot coordination is achieved by keeping the six-axis arm in good maneuverability position, i.e. far from its singular configurations and far from the motion limits of the six-axis arm and the track. The singularity configurations of the Cybotech WV 15 are expressed in terms of Cartesian coordinates. As a result, the redundancy coordination is expressed as an optimization of the maneuverability in Cartesian coordinates. An analytic solution to the optimization is found; it gives the Cartesian positions of the track and the robot end-effector. These positions are used to generate the joint angles of the arm by inverse kinematics.>

To use a wrist-mounted sensor (such as a camera) for a robot task, the position and orientation of the sensor with respect to the robot wrist frame must be known. The sensor mounting position can be found by moving the robot and observing the resulting motion of the sensor. This yields a homogeneous transform equation of the form AX=XB, where A is the change in the robot wrist position, B is the resulting sensor displacement, and X is the sensor position relative to the robot wrist. The solution to an equation of this form has one degree of rotational freedom and one degree of translation freedom if the angle of rotation of A is neither 0 nor pi radians. To solve for X uniquely, it is necessary to make two arm movements and form a system of two equations of the form: A/sub 1/X=XB/sub 1/ and A/sub 2/X=XB/sub 2/. A closed-form solution to this system of equations is developed and the necessary conditions for uniqueness are stated.>

The problem of designing a high-performance robot controller with multiple arithmetic processing units (APUs) is addressed. One attractive feature of the controller is that a minimum number of special-purpose hardware components are needed, and off-the-shelf components can be used. One main processor unit (MPU) schedules a number of APUs to produce the computational throughput. The depth-first/initial-heuristic-search (DF/IHS) algorithm is an efficient algorithm that solves the difficult nonpolynomial- (NP-) complete problem of scheduling a set of ordered computational tasks onto a multiprocessor system. When interprocessor communication overheads are appreciable, however it is not very effective in providing a practical near-optimum schedule, it fails to consider the problem of contention for shared resources. A multiprocessor scheduling algorithm which minimizes the effects of overhead and thus reduces the effect of contention is presented. The algorithm is used to derive the operational instructions for the APUs and the MPU for a multiple-APU-based robot controller. Simulations show that six MC68881 APUs can be used to generate the robot control computations in approximately 2.5 ms.>

To understand the dual-arm coordination process and expose some engineering issues, a simple model of the dual-arm part handling process is presented. In this model, it is assumed that each manipulator has joint flexibility. The manipulators may be holding the same rigid object. Based on this mode, the issue of robustness, stability and interaction force accommodation are considered. A dual-arm coordination scheme is also proposed and simulation results are presented. >

The authors analyze the singularity states of robot manipulators; only the manipulator inverse kinematic relationships are considered. In such relationships, three types of triangular equations arise for the kinematically general manipulator with the nominal decoupling conditions as found in conventional robots. These equations reveal the manipulator structural properties and the Cartesian configurations of the end effector in which the manipulator is singular; they may be used to determine the singularity states of a given trajectory. The method of singularity analysis presented is applicable to robots with six or less degrees of freedom.>

The authors consider the problem of coordinating multiple motion devices for welding purposes. They focus on the problem of controlling a positioning table and a seven-axis manipulator, given the parametric definition of a trajectory on a weld piece. The problem is complex as there are more than nine axes involved and a number of permutations are possible which achieve the same motions of the weld torch. The system is redundant and the robot has singular configurations. As a result, manual programming of the robot system is rather complex. The authors illustrate an approach to redundancy control and coordination of a multiple-robotic-device arc welding system that does not require manual teaching of the intermediate trajectory points. The system requires only the start and end points of the trajectory for setting up and calibration. The redundancy coordination scheme is based on constrained optimization of the maneuverability of the manipulator in Cartesian space. To bypass accuracy issues related to joint rate control, inverse kinematics is directly used in the kinematic control of the manipulator.>

A mathematical model of the kinematic nonlinear drive-train errors, which reduce the absolute static positioning accuracy of robot arms, is presented. This kinematic inaccuracy renders robot manipulators less effective when programmed offline, though they might be programmed to successfully perform the same task by teach playback schemes. The kinematic drive-train inaccuracy model presented can be used to predict and compensate for these nonlinear effects online, without resorting to sensor-based programming techniques, which are often expensive and may be difficult to implement in an industrial environment. The drive-train error model presented is based on gear backlash, eccentricity, and drive-shaft compliance. That the effects of these nonlinearities severely impact the robot's repeatability and absolute positioning accuracy is mathematically proven.>

In this paper we discuss preliminary design considerations for the optimal design of multiple-apu (arithmetic processing unit) based robot controllers. We justify this design interms of its ability to adopt to various different control, kinematic and trajectory computation methods which are being developed. We then show that with eight apu's, it is possible to compute the inverse kinematics, inverse dynamics and the trajectory for the PUMA arm in less then 3ms. In this design we assume the floating point processing times of a relatively slow 16.7 MHZ 68881.

Flexibilities in the manipulator structure limits its ability to perform high precision manipulation. In this paper, the effects of joint flexibility on the positioning performance of the end effector are considered. A "realistic" lumped-parameter dynamic model of the servo-mechanism is presented in order to develop a control structure to regulate the apparent torsional stiffness of the joint. The joint compliance can be compensated by using adequate feed-forward control. Computer simulation results are provided to illustrate this formulation.

This paper considers the real-time computational capability requirements of modern robot controllers. The control tasks are analyzed to obtain a lower bound on the number of mathematical operations required to generate the control signal. Then the stability of the sampled data control system is considered to estimate the maximum sample time based on stability. These bounds together with the analyses of the interprocessor communication channel bandwidth and the computation wordsize, a quantitative method of designing a (parallel or serial) computational structure for robot control is proposed. This analysis is applicable to a design utilizing custom VLSI or for a systolic array based system or a design with conventional discrete microprocessors.

This paper presents an algorithm which may be used to determine a static grasp for an "n" fingered robot hand. A static grasp is one in which the object being manipulated does not move with respect to the gripper throughout the entire operation. The following grasping algorithm is used during the program generation stage of the assembly process. It is based on the available object surfaces at each stage of manipulation, on the gripper characteristics, and on the assembly task to be performed. An example is solved in detail to illustrate the procedure of this algorithm.

This paper presents a mathematical model of the nonlinear kinematic effects, which reduce absolute static positioning accuracy of robot arms. This kinematic inaccuracy renders robot manipulators ineffective when programmed off-line, though they might be programmed to successfully perform the same task by "Teach Play back" schemes. The kinematic inaccuracy model, presented in this paper can be used to predict and compensate for these second order effects on-line, without resorting to sensor based programming techniques, which are often expensive and difficult to implement in an industrial environment.