Stabilization of the wheeled inverted pendulum on a soft surface

TL;DR

This paper investigates the stability of a wheeled inverted pendulum on various surfaces, including soft terrain, using a PID controller, and introduces a differential inclusion model to analyze semi-stable solutions and their practical implications.

Contribution

It presents a novel differential inclusion approach to model semi-stability of the inverted pendulum on soft surfaces, extending stability analysis to more realistic terrains.

Findings

Identifies oscillatory regions and stability conditions on different surfaces.

Finds semi-stable stationary solutions that appear as limit cycles in simulations.

Demonstrates the impact of perturbations and numerical errors on stability observations.

Abstract

We study dynamics of an wheeled inverted pendulum under a proportional-integral-derivative controller on horizontal, inclined and soft surfaces. An oscillatory area and conditions of the stability for the control are shown on the phase portraits of the dynamical systems. Particularly, we study a differential inclusion for moving on the soft surface, and we find semi-stable stationary solutions in our mathematical model. Due to rounding errors of the numerical modelling or external perturbations of robotics equipment the semistability looks as a limit cycle in simulations.