A Fast and Robust Algorithm for General Inequality/Equality Constrained Minimum-Time Problems

Abstract

the state space (s, S ) (regions for which the appropriate Abstract This paper presents a new algorithm for solving general inequalitylequality constrained minimum time problems. The algorithm's solution time is linear in the number of Runge-Kutta steps and the number of parameters used to discretize the control input history.The method is being applied to a thee 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 h m 30 to 120 seconds on a hewlett packard workstation. A zero torque history is always used in the initial guess, and the algorithm has never crashed, indicating its robustness.The algorithm solves for a feasible solution for large trajectory execution time t, and then reduces t, by a small amount and re-solves. The futed 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 convergence to a feasible solution of the full nonlinear problem.On the other hand, our method, applied to the three-link-arm path constrained problem described in the Abstract and Section 3.2.8, solves case after case, each within 30 to 120 seconds, within a graphical user interface in which the user selects the tip path with a mouse, and the initial guess always has a zero torque history.An interesting contrast to the above methods was presented by Zimmerman and Layton [18]. To generate a This work * . ' United Con tract CE-ACn4 -94ALRWO. completed in part at Sandia National Laboratories, Albuquerque, NM States D v a der i