Robot motion planning on N-dimensional star worlds among moving obstacles

Inspired by an idea of Rimon and Koditschek [1], we develop a motion planning algorithm for a point robot traveling among moving obstacles in an N-dimensional space. The navigating point must meet a goal point at a fixed time T, while avoiding several translating, nonrotating, nonintersecting obstacles on its way. All obstacles, the goal point, and the navigating point are confined to the interior of a star-shaped set in R^N over the time interval [0, T]. Full a priori knowledge of the goal's location and of the obstacle's trajectories is assumed. We observe that the topology of the obstacle-free space is invariant in the time interval [0, T] as long as the obstacles are nonintersecting and as long as they do not cover the goal point at any time during [0, T]. Using this fact we reduce the problem, for any fixed time to ∈ [0, T], to a stationary-obstacle problem, which is then solved using the method of Rimon and Koditschek [1]. The fact that the obstacle-free space is topologically invariant allows a solution to the moving-obstacle problem over [0, T] through a continuous deformation of the stationary-obstacle solution obtained at time t₀. We construct a vector field whose flow is in fact one such deformation. We believe that ours is the first global solution to the moving-obstacle path-planning problem which uses vector fields.