On the Optimal Control of a Rolling Ball Robot Actuated by Internal Point Masses

TL;DR

This paper derives optimal control equations for a rolling ball robot actuated by internal point masses moving along arbitrary rails, using Pontryagin's minimum principle to achieve desired motion while minimizing a performance index.

Contribution

It introduces a novel optimal control framework for a rolling ball robot with internal mass actuation, extending previous models to arbitrary rail shapes.

Findings

Derived controlled equations of motion using variational principles

Achieved motion control satisfying initial and final conditions

Minimized a specified performance index

Abstract

The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. Application of the variational Pontryagin's minimum principle yields the ball's controlled equations of motion, a solution of which obeys the ball's uncontrolled equations of motion, satisfies prescribed initial and final conditions, and minimizes a prescribed performance index.