Chaotic Dynamics of the Chaplygin sleigh with a passive internal rotor

TL;DR

This paper investigates how adding a passive internal rotor to the Chaplygin sleigh induces complex, chaotic dynamics, significantly altering its motion and potential control strategies for nonholonomic robotic systems.

Contribution

It demonstrates that a passive internal rotor causes chaotic behavior in the Chaplygin sleigh, a novel insight into the system's dynamics with implications for robotic motion control.

Findings

Presence of a passive rotor induces chaotic attractors.

Trajectory exhibits two transient phases before chaos.

Small inertia rotor significantly alters sleigh dynamics.

Abstract

The Chaplygin sleigh is a classic example of a nonholonomically constrained mechanical system. The sleigh's motion always converges to a straight line whose slope is entirely determined by the initial configuration and velocity of the sleigh. We consider the motion of a modified Chaplygin sleigh that contains a passive internal rotor. We show that the presence of even a rotor with small inertia modifies motion of the sleigh dramatically. A generic trajectory of the sleigh in a reduced velocity space exhibits two distinct transient phases before converging to a chaotic attractor. We demonstrate this through numerics. In recent work the dynamics of the Chaplygin sleigh have also been shown to be similar to that of a fish like body in an inviscid fluid. The influence of a passive degree of freedom on the motion of the Chaplygin sleigh points to several possible applications in controlling the motion of the nonholonomically constrained terrestrial and aquatic robots.