Geometric Construction of Time Optimal Trajectories for Differential Drive Robots

We assume a differential drive mobile robot: two unsteered coaxial wheels are independently actuated. Each wheel has bounded velocity, but no bound on torque or acceleration. Pontryagin’s Maximum Principle gives an elegant description of the extremal trajectories, which are a superset of the time optimal trajectories. Further analysis gives an enumeration of the time optimal trajectories, and methods for identifying the time optimal trajectories between any two configurations. This paper recapitulates and refines the results of [1] and [2] and presents a simple graphical technique for constructing time optimal trajectories.