Computing Minimum Time Paths With Bounded Acceleration

Abstract

Solving for the minimum time bounded acceleration trajectory with prescribed position and velocity at endpoints is a highly nonlinear problem. The methods and bounds developed in this paper distinguish when there is a continuous acceleration solution and reduce the problem of computing the optimal trajectory to a search over two parameters, planar rotation $-π/2<θ<π/2$ and spatiotemporal dilation $0<α<Λ(θ)$.