Improving Time-Optimal Maneuvers of Two-Link Robotic Manipulators

Abstract

HIS Note discusses in detail numerical results of a parametric study for rest-to-rest time-optimal maneuvers of rigid two-link robotics manipulators. The problem of minimizing the time of planar maneuvers in terms of control and structure was considered parametrically. First, the time-optimal control strategy was applied. This strategy led to a bang-bang control in which the motors operated with the maximum torques changing directions at the switch time. The solutions were obtained by directly using Pontryagin’ s minimum principle (PMP). The analysis was then repeated for different lengths of particular links and for different torques applied at particular joints. The total length of the manipulator and the resultant torques generated by the shoulder and elbow motors were kept constant. For the numerical calculations, the set of data characterizing the IBM 7535 B 04 robot discussed in Refs. 1 and 2 was adapted. II. Time-Optimal Control of Two-Link Robotic Manipulators The equations derived from PMP and the corresponding boundary conditions form a two-point boundary value problem (TPBVP). Here we present the solutions generated by a numerical procedure that combinesthe forward-backwardmethod with the shooting method to directly solve the TPBVP. 3 The procedure that is capable of determining the states, the costates, and the switching functions with a high numerical accuracy was discussed in more detail in Ref. 4. The procedure was used by the authors in Ref. 5 examine the effects of orientation of the plane of motion on the time-optimal maneuvers in the gravitational e eld. That work is extended here to include the effects of the links and the torque ratios. Maneuvers of a two-link robotics manipulator are considered in plane y, z as shown in Fig. 1. Mass moments of inertia of the links with respect to their centers of mass, located at lc1 and lc2, respectively, are I1 and I2. The states are x1 = } 1, x2 = C } 1, x3 = } 2, and x4 = C