A fast and robust algorithm for general inequality/equality constrained minimum-time problems

This work has developed a new robust and reliable O(N) algorithm for solvin g general inequality/equality constrained minimum-time problems. To our kno wledge, 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 far 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 bound s. Results are consistent with Pontryagin's Maximum Principle. We include a speed/robustness/complexity comparison with a sequential quadratic program ming (SQP) code. Here, the O(N) complexity and the significant speed, robus tness, and complexity improvements over an SQP code are demonstrated. These numerical results are complemented,vith a rigorous theoretical convergence proof of the new O(N) algorithm.