Title: Path-Following through Control Funnel Functions,
Abstract: 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.