Summary
Underactuated wheeled vehicles are commonly studied as nonholonomic systems with periodic actuation. Twistcar is a classical example inspired by a riding toy, which has been analyzed using a planar model of a dynamical system with nonholonomic constraints. Previous analyses of the Twistcar model also revealed the possibility of reversing the direction of motion depending on the geometric and mass properties of the vehicle. In this work, we present new experimental results using a two-link robotic prototype of the Twistcar vehicle. An important finding from experimental measurements is that the vehicle’s motion reaches bounded oscillations, in contrast to previous analyses that predicted unrealistic results of unbounded divergence of vehicle’s speed, as well as the amplitude of body angle oscillations. In order to improve the predictive power of our analysis, we consider a modified version of the Twistcar model with added viscous dissipation due to rolling resistance. Numerical analysis of the dissipative Twistcar model leads to convergence to bounded oscillations of the vehicle motion, which agrees with experimental observations. We also present asymptotic analysis, which enables obtaining explicit expressions that highlight the influence of various parameters on the motion, including reversal of the direction.
