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

Abstract

This work has developed a new robust and reliable O(N) algorithm for solving general inequality/equality constrained minimum-time problems. To our knowledge, no one has ever applied an O(N) algorithm for solving such minimum time problems. Moreover, the algorithm developed here is new and unique and does not suffer the inevitable ill-conditioning problems that pre-existing O(N) methods for inequality-constrained problems do. Herein we demonstrate the new algorithm by solving several cases of a tip path constrained three-link redundant robotic arm problem with torque bounds and joint angle bounds. Results are consistent with Pontryagin’s Maximum Principle. We include a speed/robustness/complexity comparison with a sequential quadratic programming (SQP) code. Here, the O(N) complexity and the significant speed, robustness, and complexity improvements over an SQP code are demonstrated. These numerical results are complemented with a rigorous theoretical convergence proof of the new O(N) algorithm.