Global Exponential Stabilization of the Kinematic Bicycle Model of a Car in Polar Coordinates

What the math gives to ML

The paper provides a transferable mechanism rather than merely a vehicle-specific controller: a discontinuous polar coordinate change removes the Cartesian nonholonomic obstruction, and the resulting range-normalized dynamics expose a strict-feedback structure suitable for nonconventional backstepping. A neural policy can use these coordinates as its control state and be trained with a Lyapunov-decrease residual, while an analytic backstepping term supplies a stabilizing nominal controller. The key falsifiable prediction is that closed-loop radial and angular errors should exhibit exponential decay in the transformed coordinates, and that removing either the coordinate transform or the Lyapunov residual should produce a sharp loss of stability near low-speed or near-goal regimes.