A Fuzzy Cascaded Proportional-Derivative Controller for Under-actuated Flexible Joint Manipulators Using Bayesian Optimization

TL;DR

This paper introduces a fuzzy cascaded PD controller for under-actuated flexible joint manipulators, utilizing Bayesian Optimization for offline tuning, and demonstrates its stability and effectiveness through simulation results.

Contribution

It presents a novel fuzzy cascaded PD control scheme with Bayesian Optimization-based tuning for flexible joint manipulators, including stability proof and simulation validation.

Findings

Controller achieves stable and valid control in simulations.

Bayesian Optimization effectively tunes controller parameters offline.

The method can be extended to other under-actuated systems.

Abstract

This paper proposes a novel fuzzy cascaded Proportional-Derivative (PD) controller for under-actuated single-link flexible joint manipulators. The original flexible joint system is considered as two coupled $2^{nd}$-order sub-systems. The proposed controller is composed of two cascaded PD controllers and two fuzzy logic regulators (FLRs). The first (virtual) PD controller is used to generate desired control input that stabilizes the first $2^{nd}$-order sub-system. Solving the equation by considering the coupling terms as design variables, the reference signal is generated for the second sub-system. Then through simple compensation design, together with the second PD controller, the cascaded PD controller is derived. In order to further improve the performance, two FLRs are implemented that adaptively tune the parameters of PD controllers. Under natural assumptions, the cascaded fuzzy PD controller is proved to possess locally asymptotic stability. All the offline tuning processes are completed data-efficiently by Bayesian Optimization. The results in simulation illustrate the stability and validity of our proposed method. Besides, the idea of cascaded PD controller presented here may be extended as a novel control method for other under-actuated systems, and the stability analysis renders a new perspective towards the stability proof of all other fuzzy-enhanced PID controllers.