Method of evolving junctions: A new approach to optimal path-planning in 2D environments with moving obstacles
Wuchen Li, Shui-Nee Chow, Magnus Egerstedt, Jun Lü, Haomin Zho · The International Journal of Robotics Research · 2017
We propose a novel algorithm to find the global optimal path in 2D environments with moving obstacles, where the optimality is understood relative to a general convex continuous running cost. By leveraging the geometric structures of optimal solutions and using gradient flows, we convert the path-planning problem into a system of finite dimensional ordinary differential equations, whose dimensions change dynamically. Then a stochastic differential equation based optimization method, called intermittent diffusion, is employed to obtain the global optimal solution. We demonstrate, via numerical examples, that the new algorithm can solve the problem efficiently.