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

2025-07-07

AI Summary

This study investigates the nonlinear dynamics and multistability of Twistcar—a soft robot driven by inertial rotors and equipped with passive steering joints—subject to nonholonomic constraints. Using perturbation expansion, harmonic balance, and scaling analysis, complemented by numerical simulations and asymptotic analysis of reduced-order equations, we demonstrate that the passive steering degree of freedom induces multiple coexisting stable periodic solutions. We identify symmetry-breaking bifurcations as the fundamental mechanism governing stability transitions—first reported for this class of systems. Our theoretical framework derives existence conditions and bifurcation pathways for both symmetric and asymmetric periodic orbits, with predictions showing excellent agreement with numerical results. The work establishes a novel modeling paradigm and dynamical design principle for passively actuated soft robots, enabling systematic synthesis and control of multistable locomotion behaviors.

Technology Category

Intelligent Robots: Multi-Robot SystemsMultiagent Systems: Agent-Based Simulation and Emergent BehaviorPlanning, Routing, and Scheduling: Model-Based Reasoning

Application Category

Systems and Infrastructure for Web, Mobile and WoT: Novel mobile and WoT systems, and system-of-systemsResponsible Web: Machine-in-the-loop, human agency and autonomyWeb Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Analyzes dynamics of a rotor-actuated Twistcar with passive steering
• Explores multi-stability and bifurcations in nonholonomic robotic systems
• Studies symmetry-breaking conditions via asymptotic and numerical methods

Innovation

• Periodic oscillations of inertial rotor actuation
• Passive steering joint enables free rotation
• Perturbation expansion for symmetric periodic dynamics