Model-Free Optimization and Control of Rigid Body Dynamics: An Extremum Seeking for Vibrational Stabilization Approach

TL;DR

This paper presents a novel model-free extremum seeking control method for stabilizing rigid body systems using only measurements, demonstrated on satellite, quadcopter, and unicycle dynamics.

Contribution

It introduces a new ESC-VS approach that stabilizes rigid bodies at optimal states without requiring explicit models or prior knowledge.

Findings

Successfully stabilizes various rigid body systems in simulations.

Operates effectively with measurement delays and noise.

Uses only one vibrational signal for control.

Abstract

In this paper, we introduce a model-free, real-time, dynamic optimization and control method for a class of rigid body dynamics. Our method is based on a recent extremum seeking control for vibrational stabilization (ESC-VS) approach that is applicable to a class of second-order mechanical systems. The new ESC-VS method is able to stabilize a rigid body dynamic system about the optimal state of an objective function that can be unknown expression-wise, but assessable through measurements; the ESC-VS is operable by using only one perturbation/vibrational signal. We demonstrate the effectiveness and the applicability of our ESC-VS approach via three rigid-body systems: (1) satellite attitude dynamics, (2) quadcopter attitude dynamics, and (3) acceleration-controlled unicycle dynamics. The results, including simulations with and without measurement delays/noise, illustrate the ability of our ESC-VS to operate successfully as a new methodology of optimization and control for rigid body dynamics.