A near-minimum time controller for two coordinating robots grasping an object

Abstract

This paper is concerned with the development of a nearminimum time controller for two coordinating robots manipulating an object in a workspace. Optimal control theory is used to derive the feedback controller which will enable the two robots to move an object from one place to another in nearminimum time. A dynamic model for the two robots and the load is first established and then linearized using the average dynamics method. The model is continuously updated at every control interval making it suitable for high speed applications such as minimum-time problems. Bang-bang control theory in conjunction with synchronization of execution time for each joint is used to derive the near-minimum time controller. The model and the control law are simulated for two distinct schemes. One is a master/slave configuration of the two robots while the other is based on an optimal controller for both robots. The simulation results indicate that the proposed controller implemented for both schemes behaves favorably. l "A thorough survey of the literature indicates that some attempts have been made at developing a suboptimal controller for a single robot, but none for a dual robot system. Lynch [SI developed a minimum-time controller for sequential axis operation. In this method, only one link moves at one time. Although this simplifies the dynamics greatly, the sequential control requires much more time than the simultaneous control of all joints. A perturbation model was used by DeHoff and Lock [6] to linearize the nonlinear dynamics. The linearization is performed near a set of steady-state operating conditions. Although linearization is achieved, this design method does not employ the full capability of the manipulator (application of maximum torque).The problem in this paper involves the determination of a near-minimum time controller for two coordinating robots manipulating a rectangular box type object. The workspace in which the two robots move is assumed to be free of any obstacles. Furthermore, it is assumed that the two robots do not interfere with each other or themself. Figure 1 shows the two robots and the object. The solution for the minimum-time problem is bang-bang with a certain switching curve which is difficult to compute. The average dynamics method, which linearizes the system dynamics, is introduced to overcome such difficulties.Using the Euler-Lagrange method, the dynamics of an n-joint manipulator may be represented as follows:CH2876-1/90/0000/1184$01.00 @ 1990 IEEE Figure 1 : Two-Robot Model and Load z(t) = DOQ(0 + UQ,b + QOwhere &(t), i t ) , i t ) are the n X 1 position, velocity, and acceleration vectors, respectively. Also, z(t) is an n X 1 applied torque vector, D(a) .is an n X n inertia matrix, H(Q, Q) is an n X 1 coriolis and centrifugal torque vector, G(a) is an n X 1 gravity torque vector.When two robots grasp an object and attempt to move it in the workspace, there will be certain klnematic constraints that govern their motion. The relative position and orientation between the end-effectors of ...

Coordination of multiple robots via supervisory control

“…In addition, the determination of internal fmes and load-sharing between the two robots become significant. Kinematic closed-chain implies that the relative position and orientation between the endeffectors of the two robots holding a common object remain invariant during the entire motion [17]. This constraint guarantees that the two robots neither lose grasp of the payload, nor collide with each other.…”

Hybrid adaptive control of two-link flexible manipulators grasping a payload

“…The main contribution of this paper is first the detailed development and analysis of qybrid adaptive controller in which the cpntrol parameters are updated infrequently for al twolink flexible robot with a payload (seeFigdre 1As stated previously[8], the lineqzed dynamic model for the rigid body motion lof a flexible robot with one elastic link is: at position, velocity, and the previous ikput z(t-dt) where dt denotes the sampling pediod. [ ';;t(tf ), p ( t f ) IT are the function of the in.1 target states which can be computed a priori by using the final target position and velocity.…”