Motion Planning with Reversal Manoeuvres for a Non-Holonomic Constrained Robot

Abstract

This paper presents a new motion planning approach, including reversal manoeuvres, for car-like robots subject to non-holonomic constraints. The paper presents a complete path planning algorithm and describes the procedure for constructing a collision-free path for a mobile robot constrained by its rectangular shape and kinematics. Emphasis is made on the techniques of reversal transfers, which are used to compensate the limited manoeuvrability of a car-like robot. The approach works entirely in the workspace, as opposed to building a higher dimensional configuration space (C-space). It starts by constructing a visibility graph and finding the shortest path for a point robot and then detects areas where collision may occur by minimum distance calculations between obstacles and between the selected path and obstacles. Robot configurations are placed along the shortest path and lemmas are developed for ascertaining transfers from one robot configuration to another. The transfer techniques include direct, indirect and reversal manoeuvres, and ensure that the path is feasible for the robot to travel with a given steering limit. The process runs in time O(nk + n log n) for k obstacles and n vertices. The algorithm is tested in computer simulations and results are given, demonstrating the versatility of the algorithm.