Zero-Error Tracking for Autonomous Vehicles through Epsilon-Trajectory Generation

This paper presents a control method and trajectory planner for vehicles with first-order nonholonomic constraints that guarantee asymptotic convergence to a time-indexed trajectory. To overcome the nonholonomic constraint, a fixed point in front of the vehicle can be controlled to track a desired trajectory, albeit with a steady-state error. To eliminate steady state error, a sufficiently smooth trajectory is reformulated for the new reference point such that, when tracking the new trajectory, the vehicle asymptotically converges to the original trajectory. The resulting zero-error tracking law is demonstrated through a novel framework for creating time-indexed Clothoids. The Clothoids can be planned to pass through arbitrary waypoints using traditional methods yet result in trajectories that can be followed with zero steady-state error. The results of the control method and planner are illustrated in simulation wherein zero-error tracking is demonstrated.