Planar length-optimal paths under acceleration constraints
V. Aneesh, Sanjay P. Bhat · 2006
This paper considers the problem of finding minimum length trajectories for a particle moving in a two-dimensional plane from a given initial position and velocity to a specified terminal heading under a magnitude constraint on the acceleration. Unlike previous work on related problems, variations in the magnitude of the velocity vector are allowed. Pontryagin's maximum principle is used to show that the length-optimal paths possess a special property whereby the angle bisector between the acceleration and velocity vectors is a constant. This property is used to obtain the optimal acceleration vector and to show that the length-optimal paths are arcs of alysoids. A numerical example is presented and the solutions of the length-optimal problem are compared with those of the corresponding time-optimal problem