SDRE- Suboptimal Approach for Robust Control of Multiple Arms Carrying a Load in Cooperation

Document Type : Research Article

Authors

1 Faculty of Electrical,Biomedical and Mechatronics Engineering,Qazvin Branch,Islamic Azad University,Qazvin,Iran

2 Department of Electrical, Biomedical and Mechatronics Engineering, Qazvin Branch, Islamic Azad University

3 Department of Electrical Engineering, Amirkabir University of Technology, Hafez Ave.,15875-4413, Tehran, Iran

Abstract

In this paper, a new application of State- Dependent Riccati Equation (SDRE) is proposed as a framework to design a robust controller for the system of multiple cooperative arms with parametric uncertainties. The cooperative arms are tracking a trajectory holding a mass. Transforming the complicated robust control design to a parallel auxiliary sub-optimal design, leads to a considerable facility in design and extensive applicability specifically for complex systems. An auxiliary system with a modified performance criterion is firstly introduced. The modification in performance criterion is through incorporation of uncertainties upper bounds obtained from stability proof. Uncertain

State- Dependent Coefficient (USDC) regarding joints’ friction for the robotic system is utilized to obtain the auxiliary USDC structure. Two control policies are considered: independent control of each arm and simultaneous control of overall multiple manipulators. The sub-optimal problem for the auxiliary system is solved. The achieved optimal control input for auxiliary system is the robust input for the equivalent uncertain system. Simulation results in both policies verify the effectiveness and satisfactory robustness (30%) of the proposed scheme in load carrying. Moreover, considering the same trajectory, payload and design parameters controlling the overall robotic system is superior with respect to separately controlling each arm. Finally, a comparison study is presented for the proposed scheme and Mixed SDRE-SMC (MiSS) for the overall robotic system carrying the same payload through simulation results.

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AUT Journal of Modeling and Simulation
Volume 55, Issue 2
December 2023
Pages 299-316

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