Path-Following through Control Funnel Functions

We present an approach to path following using so-called control funnel functions. Synthesizing controllers to "robustly" follow a reference trajectory is a fundamental problem for autonomous vehicles. Robustness, in this context, requires our controllers to handle a specified amount of deviation from the desired trajectory. Our approach considers a timing law that describes how fast to move along a given reference trajectory and a control feedback law for reducing deviations from the reference. We synthesize both feedback laws using "control funnel functions" that jointly encode the control law as well as its correctness argument over a mathematical model of the vehicle dynamics. We adapt a previously described demonstration-based learning algorithm to synthesize a control funnel function as well as the associated feedback law. We implement this law on top of a 1/8th scale autonomous vehicle called the Parkour car. We compare the performance of our path following approach against a trajectory tracking approach by specifying trajectories of varying lengths and curvatures. Our experiments demonstrate the improved robustness obtained from the use of control funnel functions.