Time-optimal control of multiple cooperating manipulators with trajectory and motion program constraints

Two types of problems associated with time-optimal control of multiple manipulators moving a commonly held object along specified trajectories are studied. The first problem involves finding the minimum traveling time and the optimal control torques for any desired motion programs of the given trajectory. The second problem involves finding the optimal velocity distribution along the trajectory such that the motion can be completed in the minimum time. To solve these problems, a parametric form of the generalized dynamic equation is derived. An iterative search procedure is developed for solving the first problem. During the search, the lower bound of the traveling time at any point of the given trajectory is determined by using the linear programming technique. The second problem is solved by integrating the parametric dynamic equation along the given trajectory based on the phase-plane switching curve approach. The maximum acceleration and the upper bound of the operation speed at each integration instance are determined from two linear programs. The proposed methods are applicable to various complex multi-robot systems and can handle nonlinear torque-speed characteristics of the joint actuators. © 1996 John Wiley & Sons, Inc.     

Dynamics and control of space free-flyers with multiple manipulators

This paper studies the motion control of a multiple manipulator free-flying space robot chasing a passive object in near proximity. Free-flyer kinematics are developed using a minimum set of body-fixed barycentric vectors. Using a general and a quasi-coordinate Lagrangian formulation, equations of motion for model-based controllers are derived. Two model-based and one transposed Jacobian control algorithms are developed that allow coordinated tracking control of the manipulators and the spacecraft. In particular, an Euler parameter model-based control algorithm is presented that overcomes the non-physical singularities due to Euler angle representation of attitude. To ensure smooth operation, and reduce disturbances on the spacecraft and on the object just before grasping, appropriate trajectories for the motion of spacecraft/manipulators are planned. The performance of model-based algorithms is compared, by simulation, to that of a transposed Jacobian algorithm. Results show that due to the complexity of space robotic systems, a drastic deterioration in the performance of model-based algorithms in the presence of model uncertainties results. In such cases, a simple transposed Jacobian algorithm yields comparable results with much reduced computational burden, an issue which is very important in space.     

Dynamics of cooperating manipulators for fixtureless assembly and robust control based on fuzzy logic

This article presents the modeling of the dynamics of two cooperating robot manipulators performing assembly tasks such as the peg‐in‐hole job while coordinating the payload along the desired trajectory. The system has uncertainty due to unknown mass and moment of inertia of the manipulators and the payload, and has disturbances due to coupling forces between manipulators and due to frictional forces during the assembly process. To control the uncertain system, a robust control algorithm with computed torque control is proposed. The robust control algorithm includes fuzzy logic that has two functions: one is to regulate the magnitude of the input torque of the manipulators to not go beyond the torque saturation. The other function is to reduce trajectory tracking errors. To validate the proposed control algorithm, a numerical example using dual 3 degree‐of‐freedom manipulators is shown. ©1999 John Wiley & Sons, Inc.     

Distribution of dynamic loads for multiple cooperating robot manipulators

For the situation of multiple cooperating manipulators handling a single object, a formulation is presented which allows load distribution of the combined system to be made while taking manipulator dynamics into account. First, object dynamics are used to transform the motion task. An integrated procedure for modeling arm dynamics is detailed. Then a method is introduced which transforms the object load to the joint level. At this level, various methods of load distribution that allow subtask performance are proposed. These methods allow desired object motion while selecting loads desirable to alleviate manipulator dynamic loads.     

柔性臂协调运动系统的动态反馈镇定

研究柔性臂协调运动系统分布参数模型的镇定问题.基于系统能量关系和正实引理,提出一种构造性的设计方法.所设计的控制器由前馈和动态反馈两部分构成,其中动态反馈部分的传递函数是严格正实的.通过线性算子半群理论和LaSalle不变集原理,证明了闭环系统是渐近稳定的.     

Adaptive robust coordinated control of multiple mobile manipulators interacting with rigid environments

In this paper, we consider multiple mobile manipulators grasping a common object in contact with a rigid surface, and propose a new version of adaptive robust control extended to the actuator level for multiple mobile manipulators carrying a common object in a cooperative manner. The proposed controls are robust not only to parametric uncertainties including mass variation and electrical parameters but also to external disturbances. Simulation results are presented to validate that the motion/force tracking errors converge to zero whereas the internal force tracking error remains bounded and can be made arbitrarily small.     

Adaptive control for robot manipulators using multiple parameter models

In this paper, we propose multiple parameter models based adaptive switching control system for robot manipulators. We first uniformly distribute the parameter set into a finite number of smaller compact subsets. Then, distributed candidate controllers are designed for each of these smaller compact subsets. Using Lyapunov inequality, a candidate controller is identified from the finite set of distributed candidate controllers that best estimates the plant at each instant of time. The design reduced the observer-controller gains by reducing modeling errors and uncertainties via identifying an appropriate control/model via choosing largest guaranteed decrease in the value of the Lyapunov function energy function. Compared with CE based CAC design, the proposed design requires smaller observer-controller gains to ensure stability and tracking performance in the presence of large-scale modeling errors and disturbance uncertainties. In contrast with existing adaptive method, multiple model based distributed hybrid design can be used to reduce the energy consumption of the industrial robotic manipulator for large scale industrial automation by reducing actuator input energy. Finally, the proposed hybrid adaptive control design is experimentally tested on a 3-DOF Phantom^TM robot manipulator to demonstrate the theoretical development for real-time applications.

     

Adaptive control of multiple mobile manipulators transporting a rigid object

International Journal of Control, Automation and Systems - This paper presents a nonlinear control scheme for multiple mobile manipulator robots (MMR) moving a rigid object in coordination. The...     

Two-time scale control and observer design for trajectory tracking of two cooperating robot manipulators moving a flexible beam

In this paper, we present two-time scale control design for trajectory tracking of two cooperating planar rigid robots moving a flexible beam, which does not require vibration measurement for the beam. First, the kinematics and dynamics of the robots and the object are derived. Then, using the relations between different forces acting on the object by the manipulators’ end-effectors, dynamics equations of the robots and the object are combined. The resulting equations show that the coupled dynamics including beam vibration and the rigid motion take place in two different time domains. By applying two-time scale control theory on the combined dynamics, a composite control scheme is elaborated which makes the beam orientation and its center of mass position track a desired trajectory while suppressing the beam vibration. For the controller algorithm, first a slow controller is utilized for the slow (rigid) subsystem and then a fast stabilizing controller is considered for the fast (flexible) subsystem. To avoid requiring measurement of beam vibration for the fast control law, a linear observer is also designed. The simulation results show the efficiency of the proposed control scheme.     

Combined direct and indirect adaptive control of robot manipulators using multiple models

A novel methodology is proposed for the adaptive control of rigid robotic manipulators. The proposed method utilizes multiple adaptive models for the identification and control of the manipulator. The present study is an extension of our previous work which utilized an indirect adaptive control approach with multiple models for better transient performance. The proposed scheme uses a composite approach where both prediction and tracking errors are used in a combined direct and indirect adaptive control framework. Simulation results are given to demonstrate the efficient use of the methodology.     

Adaptive motion/force control of multiple manipulators with jointflexibility based on virtual decomposition

In this paper, a virtual decomposition-based adaptive motion/force control scheme is presented to deal with the control problem of coordinated multiple manipulators with flexible joints holding a common object in contact with the environment. The control scheme is essentially a generalized Newton-Euler approach in which the original system is virtually decomposed into several subsystems, including the held object, the rigid links, and the flexible joints, so that the control problem of the original system can be greatly simplified. An interesting result is that the dynamic coupling between every two physically connected subsystems is completely represented by the so-called virtual power flow (VPF) at the cutting point between them. The VPF takes a very simple form and is very easy to handle. Control design of the constraint/internal forces can be performed with respect to the held object. Asymptotic stability of the overall system is ensured in the sense of Lyapunov. Computer simulations of two manipulators transporting an object in the plane are given to show the validity of the proposed scheme     

Position synchronised control of multiple robotic manipulators based on integral sliding mode

In this study, a new position synchronised control algorithm is developed for multiple robotic manipulator systems. In the merit of system synchronisation and integral sliding mode control, the proposed approach can stabilise position tracking of each robotic manipulator while coordinating its motion with the other manipulators. With the integral sliding mode, the proposed approach has insensitiveness against the lumped system uncertainty within the entire process of operation. Further, a perturbation estimator is proposed to reduce chattering effect. The corresponding stability analysis is presented to lay a foundation for theoretical understanding to the underlying issues as well as safely operating real systems. An illustrative example is bench tested to validate the effectiveness of the proposed approach.     

Nonlinear repetitive control with application to trajectory control of manipulators

In this article, a new control scheme named repetitive control is proposed for a class of nonlinear systems described by x(t) = Ax(t) + Bu(t) + n(x(t)) and y(t) = Cx(t), in which the controlled variables follow periodic reference commands. The stability condition is derived by applying the passivity theorem. We show how to apply the repetitive control scheme to the trajectory control of a manipulator. A simple repetitive control scheme is developed for the trajectory control of a manipulator by using nonlinear compensation and feedbacks of position and velocity signals. Experimental results for a three link manipulator verify that the proposed repetitive control reduces the tracking error to a very low level.     

Control and communications for multiple, cooperating robots

There is an increasing need for the flexible integration and control of multiple robots of different types and manufacturers in a single workstation. These robots must coordinate their actions with each other in order to improve throughput, to simplify the process of programming them and to accommodate variations in the working environment. We propose a flexible architecture for the control system of multiple, cooperating robots in an integrated, multiple robot system. Our new architecture has major advantages in that it provides for asynchronous operations in and between control modules at the higher levels, retaining synchronous control only at the lowest level where each robot is servoed at its own pose-clock rate. We have outlined a communications and task management architecture which calls for only a simple run-time operating system at the lower levels of the hierarchy. We have shown that the inter-task communication load at the low levels, which is where the worst case occurs, could be handled, at the speeds necessary for robot control, by at least one current message-passing operating system.     

The control of robot manipulators with bounded input

The problem of tracking a desired trajectory in the state space of ann-link robotic manipulator with bounds on the allowable input torque is considered. Using a so-called optimal decision strategy (ODS), a pointwise optimal control law is derived which, at each timet, minimizes the deviation between the vector of joint accelerations and a desired joint acceleration vector, subject to the input constraints. The design of the optimal control law is reduced to the solution of a quadratic programming problem which is solved using the primal-dual method. The solution gives an on-line feedback control scheme for trajectory following in the presence of input constraints. In addition, we extend the above optimal decision strategy to the case where the controller design is based on a simplified model or where the plant itself is imprecisely known. The resulting torque optimization scheme may be incorporated into any existing control scheme to account for input bounds. This has important implications for the problem of deriving robust control schemes that take into account parameter uncertainty and model simplification. Simulations are presented for the case of a three-link manipulator with bounded torque, and our results are compared to the computed torque method. Our simulations show that by optimally adjusting the input torque to each joint when one or more of them saturates, significant improvement in tracking performance can result.     

Adaptive control of robot manipulators with flexible joints

Presents an adaptive control scheme for flexible joint robot manipulators. Asymptotic stability is insured regardless of the joint flexibility value, i.e., the results are not restricted to weak joint elasticity. Moreover, the joint flexibility is not assumed to be known. Joint position and velocity tracking errors are shown to converge to zero with all the signals in the system remaining bounded     

Robust control of robot manipulators with parametric uncertainty

This paper proposes a robust control law for n-link robot manipulators with parametric uncertainty whose upper bound is not assumed to be known. The proposed robust control based on the Corless-Leitmann approach includes a simple estimation law for the upper bound on the parametric uncertainty and an additional control input to be updated as a function of the estimated value. Using the Lyapunov stability theory, the uniform ultimate boundedness of the tracking error is proved     

Neural-network control of mobile manipulators

In this paper, a neural network (NN)-based methodology is developed for the motion control of mobile manipulators subject to kinematic constraints. The dynamics of the mobile manipulator is assumed to be completely unknown, and is identified online by the NN estimators. No preliminary learning stage of NN weights is required. The controller is capable of disturbance-rejection in the presence of unmodeled bounded disturbances. The tracking stability of the closed-loop system, the convergence of the NN weight-updating process and boundedness of NN weight estimation errors are all guaranteed. Experimental tests on a 4-DOF manipulator arm illustrate that the proposed controller significantly improves the performance in comparison with conventional robust control.     

Dynamic control of redundant manipulators

Redundant manipulators provide increased flexibility for the execution of complex tasks. Redundancy is often required to maintain manipulability and avoid obstacles while completing the required task. Self-motion is the internal (joint) motion of the manipulator that does not contribute to the end effector motion. In this article we provide a dynamic feedback control law that guarantees the tracking of a desired end effector trajectory and provides redundancy resolution by making the self-motion of the manipulator flow along the projection of a given arbitrary vector field. By choosing this vector field to be the gradient of a cost function, for example, the manipulator can be made to seek an optimum configuration. The effectiveness of the control law is illustrated with simulation results.     

Decentralized adaptive control of manipulators

This article presents two new adaptive schemes for motion control of robot manipulators. The first controller possesses a partially decentralized structure in which the control input for each task variable is computed based on information concerning only that variable and on two “scaling factors” that depend on the other task variables. The need for these scaling factors is eliminated in the second controller by exploiting the underlying topology of the robot configuration space, and this refinement permits the development of a completely decentralized adaptive control strategy. The proposed controllers are computationally efficient, do not require knowledge of either the mathematical model or the parameter values of the robot dynamics, and are shown to be globally stable in the presence of bounded disturbances. Furthermore, the control strategies are general and can be implemented for either position regulation or trajectory tracking in joint-space or task-space. Computer simulation results are given for a PUMA 762 manipulator, and these demonstrate that accurate and robust trajectory tracking is achievable using the proposed controllers. Experimental results are presented for a PUMA 560 manipulator and confirm that the proposed schemes provide simple and effective real-time controllers for accomplishing high-performance trajectory tracking. © 1994 John Wiley & Sons, Inc.