A continuation method for time-optimal control synthesis for robotic point-to-point motion

In this paper, a new computational method is developed for obtaining time-optimal control (TOC) trajectories for robotic point-to-point motions. The algorithm is composed of two phases: initialization and refinement. In the initialization phase, a two-point boundary value problem (TPBVP) resulting from the perturbed TOC problem is solved for an appropriately chosen perturbation parameter. Then, the solution obtained from the initialization phase is refined by solving a set of initial value problems (IVP) sequentially and/or in parallel until the desired solution is achieved. The proposed two-phase method is computationally efficient since the resulting TPBVP is solved once for a large perturbation parameter and the remaining problem becomes solutions to a set of IVP sub-problems. The algorithm is, therefore applicable in practice. The practicability of the method was demonstrated by computer simulations on an example robot system with different motion configurations, including both regular and singular trajectories