  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.
