The Boltzmann-Hamel Equations for Optimal Control

TL;DR

This paper extends the Boltzmann-Hamel equations to optimal control problems, providing a unified framework for both kinematic and dynamic nonholonomic systems with a minimal set of differential equations.

Contribution

It introduces a novel formulation of the Boltzmann-Hamel equations tailored for optimal control, reducing the complexity of dynamic problems to 4n-2m equations.

Findings

Unified equations for kinematic and dynamic nonholonomic control

Reduced the dynamic optimal control problem to 4n-2m differential equations

Provides a minimal set of equations for practical computation

Abstract

We extend the Boltzmann-Hamel equations to the optimal control setting, producing a set of equations for both kinematic and dynamic nonholonomic optimal control problems. In particular, we will show the dynamic optimal control problem can be written as a minimal set of 4n-2m first order differential equations of motion.