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

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.

💡 Research Summary

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The paper introduces a novel model‑free, real‑time optimization and control framework called Extremum Seeking for Vibrational Stabilization (ESC‑VS) that is specifically tailored for a class of rigid‑body dynamics. Traditional extremum‑seeking control (ESC) techniques either rely on multiple low‑amplitude, high‑frequency perturbations or require explicit knowledge of the system model. In contrast, ESC‑VS uses a single high‑amplitude, high‑frequency vibrational signal as both a probing input and a stabilizing actuator. The method drives the system toward the extremum (minimum) of an objective function J(q) that may be unknown analytically but can be measured online (e.g., an error‑quaternion norm).

Theoretical Development
The authors start from a generic second‑order mechanical system
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