In human-robot cooperative tasks, the robot is required to memorize different trajectories for different assignments, and retrieve a proper one from them in real-time for the robot to follow when an assignment is repeated. A three-point representation of the space curves is translation/rotation/scaling invariant. Schemes of matching positions by vectors, and orientations by matrices are efficient in that computing time is short enough for real-time implementations. Physical experiments are performed to illustrate and verify the analytical results.

Trajectory/profile in human-robot cooperative tasks is investigated for real-time identification and learning. The method of three-distances and its association with specific spherical and Cartesian coordinates are presented which are invariant to rotation/translation, and insensitive to disturbance. These methods are illustrated via computer simulations.

When a cooperative task is performed jointly by a human and a robot manipulator, it is reasonable to have the human mainly making decisions and the manipulator carrying the physical load. To carry out the task successfully, the robot must be trained to possess the necessary experiences to work with the human on the assigned tasks. This goal may be achieved by real-time identification and learning of robot's position/orientation trajectories and force/moment profiles. The model of human's action, however, is also needed to help the design and analysis of the interactive system. In this paper, a variety of different cases are considered for both robot and human. Three different cases of robot's force/torque contributions are considered. An extreme case is that the robot contributes no force/moment except balancing the load so that it becomes a burden to the human. Such a situation could happen when the robot controller breaks down. Another case is that the robot furnishes enough torque/force so that the task progresses at a constant acceleration. Practically speaking, the robot contributes a nearly constant force/torque. The final case involves the real-time identification and learning of the robot's position/orientation trajectories and force/moment profiles so that they may be retrieved for future use. Five different cases are considered for the human. The first case is the open-loop approach in which his/her trajectories and profiles are preplanned. This is usually true when the human performs a daily routine after many many times. If the human cares about only the final goal position/orientation, a PD controller model suffices. A third case is to adopt a fuzzy controller model for the human. The membership function may be constructed based on the observation of the human's reaction. An interactive case may be represented by re-planning with time-delay. At each selected time instant, the human revises the actual trajectory/profile based on his/her judgement. The final case involves the simulation of the human interaction using physically the "mouse" movement. This is however restricted to the two-dimensional motion on the "mouse pad". A variety of combinations of different cases of robot and different models of human is analyzed and simulated. A comparison is made among the various combinations from which a conclusion is drawn.

In the process of human-robot interaction, effective representation and real-time learning of manipulator's trajectory/profile in response to human's motion are presented. Method of obtaining approximate solutions during the learning stage are introduced to circumvent the noise effect caused by numerical inaccuracy and computational errors. Perturbed solutions are derived as an alternative approach to overcome the noise effect. Simulation examples are given to illustrate every stage of the presentation.

The task of coordinating and controlling a group of small mobile robots may be decomposed into five subtasks: formation of geometric pattern, alignment of each robot's orientation, coordination of the robots in the group, motion realization and stability of the formation in motion. The technique of imposing constraint conditions is utilized to coordinate and control the formation. Group stability is presented in terms of the bound of the transient response of the formation system.>

This paper investigates the motion control issues involved in distributing the task of transporting an object over a group of homogeneous mobile robots. We assume that each individual robot has no advanced sensory or communication capability. The motion control here refers to that of the robots to form some geometric pattern before they start moving and to maintain the geometric pattern while the robots are moving towards a goal location. The motion control of the robots is implemented in a distributed fashion. A distributed, concurrent algorithm for forming geometric patterns is discussed. Different control methods are presented and the simulation results from resting these methods are examined. The objective is to study the complexity of motion coordination of the robots in performing the overall task. The ultimate goal is to identify a method that requires minimum real-time inter-robot communication and computational effort to achieve the group goal.>

A truncation technique has been presented to reduce the computational complexity of optimal scheduling in the context of timed Petri nets. A number of problems associated with the Petri net truncation technique remain unsolved. This work concentrates on the issue of how the global criteria function (viz. the minimum time makespan) may be incorporated in the subnet-wide search, so that merging the sub-schedules would yield an overall optimum schedule. A new and comprehensive algorithm is developed for the subnet-wide search, and is tested by two scheduling examples.

The inertias of the parallel and serial connections of two robots in the operational space are studied in this paper. First, it is reviewed that the symmetry between the velocity and force in a robotic chain results in velocity-force duality of the parallel and serial connections. The possible duality in the operational inertia matrix is then investigated. From the dynamic equations of the two connections, it is found that there does not exist a real duality in the operational inertia matrix. However, the real duality becomes possible when the coupling effects between the two robots are negligible. This conditional duality is called "quasi-duality" in this paper. As a result of this study, the duality behaviors of the two connections in velocity, force and inertia are completely obtained.>

The method of relaxation labeling, which is a parallel distributed processing mechanism, is presented. Relaxation labeling is able to integrate the sensor data with some known knowledge. Such an integration is implemented by forcing constraint satisfaction. One type of constraint satisfaction in intelligent robotic systems is described. A relaxation labeling algorithm is presented. The local convergence properties of a labeling process are established. Its global behavior was examined numerically. To illustrate its potential applications in robotic workstations, the relaxation labeling algorithm was applied to perform an object identification task in an intelligent robotic workstation with two cameras.>

The stability of position and force control of an uncertain multiple-robot system is presented. The main objective is to obtain the bounded stable tracking performances for position and force simultaneously when the dynamic system is not exactly known. To perform tasks in a system of multiple redundant robots, the coordination among the robots may be incorporated within the position and force controls of the robots, and the constraints among the end-effectors and the rigid object grasped by the end-effectors. When the physical parameters of the robots are known, control laws which are linear in position/orientation errors may be applied to achieve asymptotic stability in both position/orientation of the object, and interactive force/torque among the object and end-effectors. When the physical parameters are not exactly known, robust control laws may be applied to compensate for the errors caused by the uncertainties. The bounds of the errors are dependent on the bounds of the uncertainties and some design factors that can be specified.>

A closed-loop state feedback motion-control scheme has been developed for manipulators with redundant joints. The scheme is based on the well-known Hamilton-Jacobi-Bellman algorithm of optimal control. Self motion of the linkage is utilized for optimizing a quadratic performance criteria over the entire trajectory of the end-effector. A linearized model of the dynamics of the manipulator is used in the control algorithm. The algorithm requires solving the algebraic matrix Riccati equation. Simulation results are presented.>

Two different control schemes, position model referenced control (PMRC) and force model referenced control (FMRC), are developed for a simplified two robots model with one interacting axis. The dynamic stability of the position (or force) control under the FMRC (or PMRC) is analyzed. Results indicate that PMRC, although providing better dynamic performance of the position control, may degrade the dynamic performance of the force control. However, FMRC can provide better dynamic performance of both position and force control.>

The commenter points out that two sets of equations in the above-titled paper by Luh et al. (see ibid., vol.RA-1, no.2, p.95-103, June (1985)) are confusing as they give different solutions for the second time-derivative of q/sup 0/. Luh points out that one of the equations does not include the constraints included in the other, as one is for an open-chain and the other for a closed-chain mechanism.>

When two robots execute coordinated motion in industrial application such as assembly, not only is the specification of the desired motion of each robot's end effector required, but also that of the desired contact force exerted on the end effectors. The involvement of the forces is the motivation for a consideration of compliance. The compliant coordination control scheme of two moving robots is presented. One robot is equipped with a force/torque sensing wrist, which provides force feedback signals and permits the fine coordinated motion control of complex assembly tasks. A control strategy is derived so that the measured force/torque can be used to modify the trajectory of one of the robots. This control scheme can be realized in real time by using the proposed computational structure. The system stability is related to the force-displacement conversion gain in the forward path. An experiment that screws a moving nut onto a moving bolt has been carried out as an illustration.>

The authors present a solution to the optimal force distributions for two redundant coordinating robots. Two coordinating robots whose end-effectors firmly grasp a common inertial load form a closed-chain structure. In these closed kinematic chains, the two robots must observe a set of constraint conditions on the end-effectors' positions, orientations, linear and angular velocities and the forces and torques inserted onto the end-effectors by the load. To achieve the maximum load capability, the optimal force distribution under the known posture is developed. If both robots are redundant, joint solutions may be obtained if some optimization criterion such as manipulability is imposed. The singularity, manipulability, and force ellipsoid are investigated for the two coordinating redundant robots in terms of the two manipulator Jacobian matrices. The manipulability is shown to correspond to the cascade structure while the force ellipsoid corresponds to the parallel structure in terms of their manipulator Jacobian matrices. Null-space contributions towards singularity escapement and mechanical advantage are found.>

The load distribution problem for two coordinating industrial robots handling a single object is studied. When two industrial robots grasp a single object, the total number of degrees of freedom is usually greater than six. Thus, the joint torques of two robots for a required motion of the object is not unique. The redundant degrees of freedom may be used to optimize certain kind of performance. The least energy consumption is selected as the optimization criterion. Optimal algorithms without and with a bound on the joint torques are investigated. The results show that the algorithms are computationally complicated and not suitable for real-time applications. Alternatively, optimal algorithms are proposed for load distribution with minimum exerted forces on the object. These algorithms require less computational time, which makes them attractive for real-time applications.>

The joint velocities required to move the robot end-effector with a desired speed depend on the direction of motion. Robot's mobility, i.e., its ability to move, is better in the directions requiring lower joint velocities. When the robot is near a singularity configuration, the joint velocities required to attain the end-effector velocity in certain directions are extremely high. Thus arbitrary directional changes become more difficult. Robot's flexibility, defined as its ability to change the direction of the end-effector motion, is low in the vicinity of singular configurations. Addition of redundant joints can greatly enhance their flexibility. However, this requires a proper utilization of redundancy. A control scheme is presented to improve the flexibility of redundant robots. The feasibility and effectiveness of this control scheme are demonstrated through simulation.

The design of a distributed computer system for coordinated-motion control of two industrial robots is discussed. The control mechanism for the coordinated-motion control has a hierarchical nature. For hierarchically related computational tasks, a tree-structured multicomputer system is selected as the architecture of the distributed computer system (DCS). The emphasis of the work is on the design of a distributed operating system (DOS) called REKCOR, which stands for REal-time Kernel for Coordinating Robots. It provides transparent operations to the users, and maintains the flexibility and modularity of the system. The successful design of REKCOR is verified by a practical experiment, in which the distributed computer system controls two industrial robots to successfully execute a coordinated-motion.

In robotics, to deal with coordinate transformation in three-dimensional (3D) Cartesian space, the homogeneous transformation is usually applied. It is defined in the four-dimensional space, and its matrix multiplication performs the simultaneous rotation and translation. The homogeneous transformation, however, is a point transformation. In contrast, a line transformation can also naturally be defined in 3D Cartesian space, in which the transformed element is a line in 3D space instead of a point. In robotic kinematics and dynamics, the velocity and acceleration vectors are often the direct targets of analysis. The line transformation will have advantages over the ordinary point transformation, since the combination of the linear and angular quantities can be represented by lines in 3D space. Since a line in 3D space is determined by four independent parameters, finding an appropriate type of "number representation" which combines two real variables is the first key prerequisite. The dual number is chosen for the line representation, and lemmas and theorems indicating relavent properties of the dual number, dual vector, and dual matrix are proposed. This is followed by the transformation and manipulation for the robotic applications. The presented procedure offers an algorithm which deals with the symbolic analysis for both rotation and translation. In particular, it can effectively be used for direct determination of Jacobian matrices and their derivatives. It is shown that the proposed procedure contributes a simplified approach to the formulation of the robotic kinematics, dynamics, and control system modeling.

Tasks for two coordinated industrial robots always bring the robots in contact with a same object. Physically the three form a closed kinematic chain mechanism. When the chain is in motion, the positions and orientations of the two robots must satisfy a set of holonomic equality constraints for every time instant. To eliminate motion errors between them, one of them is assigned to carry the major part of the task. Its motion is planned accordingly. The motion of the second robot is to follow that of the first robot as specified by the relations of the joint velocities derived from the constraint conditions. Thus if any modification of the motion is needed in real time, only the motion of the first robot is modified. The modification for the second robot is done implicitly through the constraint conditions. Specifically, when the joint displacements, velocities, accelerations and torques/forces of the first robot are known for the planned or modified motion, the corresponding variables for the second robot can be determined through the constrained relations.

In a physical 3-dimensional free space at most six degrees of freedom can be independent, i.e. three for position and three for orientation. Intuitively robots with six joints are adequate to execute any tasks. However, in reality, constraints often exist under the complex environment so that six joints are not quite enough for the robots. An insertion of an additional joint into the robot may solve the problems. This paper discusses only the singularity problem at which the robot degenerates. The analysis, which is a continued investigation of a previous study, shows how the degeneracy entrapment could be escaped as rapidly as possible if the robot has seven joints; between which two joints the redundant joint should be inserted; and which type of joint (i.e revolute or prismatic) should be employed.

A three-dimnensional vision system for on-line operation that aids a collision avoidance system for an industrial robot is developed. Because of the real-time requirement, the process that locates and describes the obstacles must be fast. To satisfy the safety requirement, the obstacle model should always contain the physical obstacle entirely. This condition leads to the bounding box description of the obstacle, which is simple for the computer to process. The image processing is performed by a Machine Intelligence Corporation VS-100 machine vision system. The control and object perception is performed by the developed software on a host Digital Equipment Corporation VAX 11/780 Computer. The resultant system outputs a file of the locations and bounding descriptions for each object found. When the system is properly calibrated, the bounding descriptions always completely envelop the obstacle. The response time is data-dependent. When using two cameras and processed on UNIX time sharing mode, the average response time will be less than 2 s if eight or fewer objects are present. When using all three cameras, the average response time will be less than 4 s if eight or fewer objects are present.

In some comercially available industrial robots such as the Cincinnati T3, and the Bendix MA-510, the actuator of the third joint, which is one of the larger actuators, is mounted on the same platform as that of the second joint in order to reduce the load on the second joint. With this arrangement, the torque that moves the third moving link is transmitted through a four-bar or five-bar linkage mechanism, which is a closed-chain structure having a planar motion. Although a variety of computational schemes for the input joint torques/forces of industrial robots having open-chain mechanisms can be found in the literature, an efficient method of computation for robots with closed kinematic chain mechanisms is not available. A computationally efficient scheme is presented for industrial robots having three-dimensional closed-chain linkages. First the closed-chain is virtually cut open, and the kinematics of the virtual open-chain mechanism are analyzed. The holonomic constraints are applied to the virtually cut joint. As a result, the spatial closed-chain linkage can be considered as a tree-structured open-chain mechanism with kinematic constraints. Based on the known recursive Newton-Euler formulation, a computational scheme is developed for industrial robots having three-dimensional closed kinematic chain mechanisms. Two examples are given illustrating the approach.

To approximate a preplanned robot path in Cartesian coordinates, such as the seam in arc welding, by functions of joint displacements, enough points on the path must be selected and transformed into joint coordinates. Instead of joining the adjacent, transformed joint points by a straight line, lower degree polynomials are first determined and then splined together. The approximation functions are required to have continuous second derivatives with specified boundary conditions so that the robot's position, orientation, velocity, and acceleration are all continuous along the path. To reduce the approximation error, cubic and quartic polynomials are used with least-squares fit. A comparison of the approximation errors of the methods is presented with an illustration by a numerical example.

Industrial robots are serial link manipulators whose dynamic characteristics are highly nonlinear. By controlling each link or joint individually, employing the conventional technique to design linear feedback controllers for the robot is possible. The gravitational force and force interactions between joints are suppressed by precalculated feedforward compensation. To ease the computational burden, the compensating signals are either approximated or their computational formulas are simplified.

The physical compactness of the microcomputer has made it feasible to mount the controller and the mechanical manipulator together as a single unit. By using a computer with multiple central processing units (CPU's), parallel computations may be executed to achieve a minimum computing time so that a real-time control is possible. The parallel processing system utilizes one CPU for each link of the manipulator. Because of the dynamic coupling between adjacent links, precedence relations appear among the subtasks to be executed in CPU's. Under the series-parallel precedence constraints a method of "variable" branch-and-bound has been developed which determines an optimum ordered schedule for each of the CPU's. It consists of, alternatively, forward and backward search procedures with an aid of pushdown-stacks. In each forward search procedure, it seeks the currently feasible schedule with shorter computing time which updates the upper bound of the optimum schedule, while in each backward search procedure it discards those schedule-branches that will not provide improvements. A Fortran program has been written for a manipulator based on the Newton-Euler formulation of dynamic equations and is applied to the Stanford manipulator as an illustration.

The advantage of using a Multiprocessor controller for a mechanical manipulator is that parallel computations may be arranged to achieve a minimum computing time so that a reat time control is possible. The parallel processing scheme utilizes a number of CPU's and pursues the following steps. First divide the entire task into subtasks. Based on the precedence relations, an optimum order of execution for each CPU is obtained by using an algorithm which includes, afternatively, forward and backward phases. in each forward phase it seeks the currently available, shorter computing time, while in each backward phase it seLects a better alternative. A FORTRAN program has been written for a manipulator and is being applied to the Stanford maniputator with a Z.8000 microcomputer.