Design and Performance Evaluation of a μ-Synthesis-Based Robust Impedance Controller for Robotic Joints

This paper proposes a robust impedance controller to address the performance limitations of mechanical impedance rendering in robotic joints, enabling stable interaction with passive environments. Considering structured uncertainties, such as dynamic parameter perturbations, sensor noise, disturbances, and unmodeled dynamics in actuator models, the μ-synthesis method is employed to optimize closed-loop robustness performance. This approach minimizes impedance-matching errors in the frequency domain, thereby enhancing the regulation of the systems’s inherent impedance characteristics. Key performance metrics are analyzed, and the impedance-rendering accuracy is evaluated. Furthermore, the limiting factors affecting impedance-matching bandwidth are investigated to inform the selection of impedance parameters and ensure safe physical interaction. The proposed controller is validated through simulations and hardware experiments on a one-DoF modular robotic joint. Frequency domain impedance matching comparisons show that relative to H∞ control, the μ-synthesis approach reduces impedance matching errors by up to 94.6% and 97.5% under 5% and 30% inertia uncertainties, respectively. Furthermore, experimental results demonstrate that compared to classical impedance control, the proposed method reduces impedance rendering errors by an average of 85.71% across all tested configurations while maintaining superior passivity and interaction stability under diverse impedance conditions. These results validate the effectiveness of μ-synthesis in achieving safe and high-fidelity physical interaction behavior.