Software Method for Analysis of the Performance of Anthropomorphic Manipulator

Abstract

A universal anthropomorphic manipulator with six rotational degrees of mobility is considered. The nodal points S0, ..., S6 are selected on the trajectory of movement of the manipulator grip. The kinematic analysis of the manipulator was carried out by the method of transforming the coordinates of Denavit - Hartenberg. The mathematical model of the manipulator is compiled by the Lagrange-Euler method. The problem of maximum performance for each generalized coordinate qi (t) is solved using the Pontryagin maximum principle. Mathematical modeling was carried out in the Mathcad environment. The software method for analyzing the speed of the manipulator allows us to consider for each nodal point of the trajectory S0, ..., S6 the set of admissible configurations of the manipulator, solve the problem of maximum speed for each generalized coordinate qi (t) and estimate the minimum time for the implementation of the sequence of state vectors. When solving the problem of maximum speed, the switching time ti1 and the minimum turning time tik are calculated for each generalized coordinate qi (t). The minimum time for the configuration implementation can be found by summing the minimum rotation time tik over six generalized coordinates. Similar calculations are carried out for each nodal point S0, ..., S6 and the corresponding sets of permissible manipulator configurations. The developed software makes it possible, on the basis of the data obtained, to synthesize a sequence of control commands for the manipulator drives. The research results can be used at the design stage, implementation and modernization of robotic systems and manipulators.