Discontinuous energy shaping control of the Chaplygin sleigh
It provides a robust control solution for nonholonomic mechanical systems, which are known to be difficult to stabilize with smooth controllers.
The paper presents a discontinuous energy shaping control law for set-point regulation of the Chaplygin sleigh, achieving robust asymptotic stabilization despite nonholonomic constraints.
In this paper we present an energy shaping control law for set-point regulation of the Chaplygin sleigh. It is well known that nonholonomic mechanical systems cannot be asymptotically stabilised using smooth control laws as they do no satisfy Brockett's necessary condition for smooth stabilisation. Here, we propose a discontinuous control law that can be seen as a potential energy shaping and damping injection controller. The proposed controller is shown to be robust against the parameters of both the inertia matrix and the damping structure of the open-loop system.