An efficient algorithm for solving time-optimal point-to-point motion control problems

Time-optimal point-to-point motion trajectories are typically computed by solving a sequence of linear feasibility problems and using a bisection algorithm. This paper presents a more efficient iterative algorithm, inspired by Newton-Raphson´s root-finding algorithm, to solve time-optimal point-to-point motion control problems for discrete-time linear time-invariant systems with linear system constraints. In each iteration a maximum range problem is solved, maximizing the travel range of a system for a given motion time and system constraints. Although each iteration of the proposed algorithm is computationally more expensive than an iteration of the bisection algorithm, the presented approach is generally more efficient thanks to a great reduction in the number of optimization problems to be solved.