Approximate Time-Optimal Path Planning and Its Control Application to Differential-Drive Mobile Robot.

Abstract

This paper deals with an approximate time-optimal path planning for a differential-drive mobile robot equipped with only motors and encoders. Time-optimal trajectories to be proposed consist of a combination of both approximate trajectories in a given bounded region and trajectories that keeps the robot in the given region. Position and orientation of mobile robot are calculated using dead reckoning. Necessary conditions for optimality are derived from the Pontryagin‟ s maximum principle. An uncertainty, possibly caused by computational error,discretization effect in control input or sampling effect in robot posture measurement, is considered in this paper. Also, geometric method is used to propose the possible control inputs of two wheels, for different robot configurations. In addition mathematical model for a wheel-motor assembly of differential-derive mobile robot is proposed. The time optimal controller for this wheel-motor assembly model is driven. This motor control is applied with the algorithm of approximate time optimal trajectories to get a complete approximate time optimal control of differential drive mobile robot.