Nonholonomic Dynamics of the Twistcar Vehicle: Asymptotic Analysis and Hybrid Dynamics of Frictional Skidding

Abstract

The Twistcar vehicle is a classic example of a nonholonomic dynamical system. The vehicle model consists of two rigid links connected by an actuated rotary joint and supported by wheeled axles, where nonholonomic constraints are assumed to impose no skidding of the wheels. Recent experimental measurements conducted with a robotic Twistcar prototype have shown disagreements with previous theoretical analyses. In particular, significant skidding has been observed, in addition to discrepancies with respect to theoretical predictions of divergence in oscillations of the vehicle’s speed and orientation, as well as direction reversal depending on the vehicle’s structure. The goal of our research is to resolve this disagreement by generalizing the theoretical analysis. First, we extend previous asymptotic analysis by incorporating the effects of links’ inertia and oscillation amplitude of the input angle on the direction of net motion. Next, we formulate the vehicle’s hybrid dynamics under frictional bounds and skid-state transitions. Using numerical analysis, we obtain optimal values for the vehicle’s mean speed and energetic cost-of-transport as a function of the input frequency. Our results improve the agreement between theory and experiments and suggest directions for further experimental investigation.