Dynamics and multi-stability of a rotor-actuated Twistcar robot with passive steering joint

TL;DR

This paper investigates the complex dynamics of a Twistcar robot with passive steering, driven by a rotor, revealing multiple stable solutions, bifurcations, and the influence of passive variables on nonholonomic robotic motion.

Contribution

It introduces a novel analysis of Twistcar dynamics with passive steering and rotor actuation, combining asymptotic methods and simulations to uncover multi-stability and bifurcations.

Findings

Identification of multiple periodic solutions including symmetric and asymmetric types

Demonstration of stability transitions and bifurcations as a function of actuation frequency

Validation of asymptotic analysis with numerical simulations

Abstract

The nonlinear dynamics of many under-actuated wheeled platforms are governed by nonholonomic constraints of no-skid for passively rolling wheels, coupled with momentum balance. In most of theoretical models, the shape variables, i.e. joint angles, are directly prescribed as periodic inputs, such as steering angle of the Twistcar. In this work, we study a variant of the Twistcar model where the actuation input is periodic oscillations of an inertial rotor attached to the main body, while the steering joint is passively free to rotate. Remarkably, the dynamics of this model is extremely rich, and includes multiplicity of periodic solutions, both symmetric and asymmetric, as well as stability transitions and bifurcations. We conduct numerical simulations as well as asymptotic analysis of the vehicle's reduced equations of motion. We use perturbation expansion in order to obtain leading-order dynamics under symmetric periodic solution. Then, we utilize harmonic balance and further scaling assumptions in order to approximate the conditions for symmetry-breaking pitchfork bifurcation and stability transition of the symmetric periodic solution, as a function of actuation frequency and structural parameters. The asymptotic results show good agreement with numerical simulations. The results highlight the role of passive shape variables in generating multi-stable periodic solutions for nonholonomic systems of robotic locomotion.