Time optimal trajectories for a two wheeled robot

Abstract

This paper addresses the problem of time-optimal motions for a mobile platform in a 2-D planar environment. The platform is assumed to be of the skid-steer type, with two non-steerable independently driven wheels. The overall mission of the robot is expressed in terms of a sequence of via points at which the platform must be at rest in a given configuration (position and orientation). The objective is to plan time-optimal trajectories between these configurations assuming an unobstructed environment. Using Pontryagin's maximum principle, we formally demonstrate that the time optimal motions of the platform are bang-bang (at each instant, the acceleration on each wheel is either at the upper or lower limit). The optimal trajectories can be characterized by a set of unique parameters corresponding to the switch times (the times at which the wheel accelerations change sign). We show numerically that trajectories with three switch times (two on one wheel, one on the other) can reach any position, while trajectories with four switch times can reach any configuration. Given the desired final configuration of the platform, we can search the parameter space and find the switch times that will produce particular paths to the configuration. We show numerically that a more » uniquely defined subset of these paths are time optimal by calculating the dual variables required by the maximum principle. 26 refs., 12 figs. « less