Finding Multiple Local Solutions to Trajectory Optimization Problems Using a Saddle-Point Search Method

This paper presents a numerical method for finding multiple locally optimal solutions to multi-modal trajectory optimization problems. Starting from an already-found local solution, a saddle-point search algorithm finds a surrounding saddle point of the constrained optimization problem, from which a new local solution is obtained by applying a gradient-based optimizer. Although the developed method is not rigorously guaranteed to produce the global solution, it is applicable to large-scale generic trajectory optimization problems, which makes it a practically beneficial technique. In addition, saddle-point trajectories sometimes yield insightful information on the relationships and reasons of the obtained local optimal trajectories. Validity and utility of the proposed methodology are demonstrated by solving simple but illustrative example problems.