Fast and Robust Algorithm for general inequality/equality constrained minimum time problems

摘要

This paper presents a new algorithm for solving general inequality/equality constrained minimum time problems. The method is being applied to a three link redundant robotic arm with torque bounds, joint angle bounds, and a specified tip path. It solves case after case within a graphical user interface in which the user chooses the initial joint angles and the tip path with a mouse. Solve times are from 30 to 120 seconds on a Hewlett Packard workstation. he algorithm solves for a feasible solution for large trajectory execution time t(sub f) and then reduces t(sub f) and then reduces t(sub f) by a small amount and re-solves. The fixed time re-solve uses a new method of finding a near-minimum-2-norm solution to a set of linear equations and inequalities that achieves quadratic convegence to a feasible solution of the full nonlinear problem.