Provably Correct Sensor-driven Path-following for Unicycles using Monotonic Score Functions

Abstract: This paper develops a provably stable sensor-driven controller for path-following applications of robots with unicycle kinematics, one specific class of which is the wheeled mobile robot (WMR). The sensor measurement is converted to a scalar value (the score) through some mapping (the score function); the latter may be designed or learned. The score is then mapped to forward and angular velocities using a simple rule with three parameters. The key contribution is that the correctness of this controller only relies on the score function satisfying monotonicity conditions with respect to the underlying state -- local path coordinates -- instead of achieving specific values at all states. The monotonicity conditions may be checked online by moving the WMR, without state estimation, or offline using a generative model of measurements such as in a simulator. Our approach provides both the practicality of a purely measurement-based control and the correctness of state-based guarantees. We demonstrate the effectiveness of this path-following approach on both a simulated and a physical WMR that use a learned score function derived from a binary classifier trained on real depth images.