Open AccessA fast and Robust Algorithm for general inequality/equality constrained minimum time problems
Author(s) -
B. Briessen,
Nader Sadegh
Publication year - 1995
Language(s) - English
Resource type - Reports
DOI - 10.2172/225042
Subject(s) - discretization , mathematics , robustness (evolution) , time complexity , variational inequality , quadratic equation , nonlinear system , mathematical optimization , path (computing) , algorithm , triangle inequality , linear inequality , running time , computer science , combinatorics , inequality , mathematical analysis , geometry , biochemistry , chemistry , physics , quantum mechanics , gene , programming language
This paper presents a new algorithm for solving general inequality/equality 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 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. 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{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