Analytical time-optimal trajectories for an omni-directional vehicle

We present the first analytical solution method for finding a time-optimal trajectory between any given pair of configurations for a three-wheeled omni-directional vehicle in an obstacle-free plane. The mathematical model of the vehicle bounds the velocities of the wheels independently. The timeoptimal trajectories can be divided into two categories: singular and generic. An analytical solution method has previously been presented for singular trajectories; this paper completes the work and presents the solution for generic trajectories. The speed and precision of the algorithm allow dense sampling of the configuration space, to determine how the time and structure of time-optimal trajectories change across configurations. Simulation results show that time-optimal trajectories tend to be ten to twenty percent faster than a simple but practical driving strategy: turn until the fastest translation direction faces the goal, drive to the goal, and turn to the current angle.