Dynamics of a multilink wheeled vehicle: partial solutions and unbounded speedup

TL;DR

This paper develops a nonholonomic mathematical model for a multilink wheeled vehicle, analyzes its inertial motion, stability, and invariant manifolds, and investigates unbounded speedup phenomena in certain trajectories.

Contribution

It introduces a detailed analysis of the vehicle's dynamics, including fixed points, stability, invariant manifolds, and unbounded velocity growth, especially for a three-link configuration.

Findings

Identification of fixed points and their stability.

Existence of trajectories with unbounded velocity components.

Asymptotic behavior of unbounded speedup trajectories.

Abstract

A mathematical model featuring the motion of a multilink wheeled vehicle is developed using a nonholonomic model. A detailed analysis of the inertial motion is made. Fixed points of the reduced system are identified, their stability is analyzed, and invariant manifolds are found. For the case of three platforms (links), a phase portrait for motion on an invariant manifold is shown and trajectories of the attachment points of the wheel pairs of the three-link vehicle are presented. In addition, an analysis is made of motion in the case where the leading platform has a rotor whose angular velocity is a periodic function of time. The existence of trajectories for which one of the velocity components increases without bound is established, and the asymptotics for it is found.