Time Optimal Trajectories for a Car-Like Mobile Robot

Abstract

This article studies the time optimal paths of a car-like mobile robot navigating in an obstacle-free planar environment. The robot, with forward and backward speeds, is controlled by bounded acceleration and limited front-wheels steering rate. The article extends previous results that solved this problem for a simplified car-robot model controlled by bounded speed and limited heading rate. The simplified car-robot model forms a unicycle with coupled bounds on the control inputs, while the full car-robot model has independent control inputs. The problem is analyzed as an optimal control problem by the minimum principle and by singular control theory. While the simplified car-robot model gives six time optimal path primitives, the optimality conditions for the full car-robot model yield <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">twelve path primitives</i> that form the time optimal paths. Three primitives involve singular controls of the steering front wheels that asymptotically align the robot along a straight line motion. All path primitives are analytically characterized and representative examples are studied in order to demonstrate how the path primitives combine to form the time optimal paths.