Our paper titled “A Monotonicity Framework for Stability Verification of Planar Path-Following Controllers” has been accepted to the IEEE Control Systems Letters journal. Benton Clark is the lead on this work.

The paper provides a new and simple method to confirm that a sensor-driven controller will achieve path-following. This method is based on checking monotonicity of the control law (velocities) with respect to the relative path variables (cross-track error and heading error). This check is easy when the control law is known in closed-form, but can also be done using observation data online.

The paper proves that a simple range-sensor-based control law will achieve path-following in curved hallways. The sensor readings are highly nonlinear functions of the state (path-error variables), but it is easy to verify monotonicity of these functions.

The value of this work is that the alternative approach for analyzing path-following relies on Lyapunov methods. To implement these methods, one needs to solve a partial differential inequality corresponding to decrease of the Lyapunov function along solutions. Moreover, the inequality depends on the closed-loop models, which are difficult for most sensor-environment combinations. As such, verifying sensor-driven control loops has been nearly impossible to date. Our methods makes it practical to say something concrete.