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 $-\pi /2<\theta <\pi /2$ and spatiotemporal dilation $0<\alpha <\Lambda (\theta )$.