Frequency-shaped μ-synthesis with force-guided reference shaping for robust impedance control of robots

Physical human–robot interaction requires impedance controllers to simultaneously achieve high-fidelity impedance rendering, robust stability against multi-source uncertainties, and compliant contact transition, all of which are critical to collaborative robotics. This paper proposes a robust impedance control method based on frequency-shaped μ-synthesis, integrated with a force-guided online reference shaping (RS) strategy for series elastic actuator (SEA) joints. A three-mass dynamic model of the SEA joint is developed, and multiple structured uncertainties are systematically characterized within a linear fractional transformation (LFT) framework. A hybrid stability criterion combining the passivity theory and the small-gain theorem is incorporated into the proposed loop-shaping framework to guarantee robust interaction stability during contact with stiff environments. By formulating the impedance control problem as a port impedance matching μ-synthesis problem, the proposed approach enables a more independent design of trajectory tracking and impedance rendering, thereby alleviating the intrinsic coupling between motion tracking and impedance behavior in conventional impedance control. An online force-guided RS strategy is further integrated to improve compliant interaction performance during unintended human–robot contact. Extensive numerical simulations and experimental validations on a 1-degree-of-freedom (DOF) force-controlled robotic joint platform with SEA-equivalent compliant dynamics demonstrate the effectiveness of the proposed method in achieving high-fidelity impedance rendering, stable contact transition, and robust performance against model uncertainties. The proposed framework provides a practical and effective solution for high-performance compliant control of collaborative robots.