Purpose: This paper presents an impedance control method with mixed H 2 /H ∞ synthesis and relaxed passivity for a cable-driven series elastic actuator to be applied for physical human-robot interaction.Design/methodology/approach: To shape the system's impedance to match a desired dynamic model, the impedance control problem was reformulated into an impedance matching structure. The desired competing performance requirements as well as constraints from the physical system can be characterized with weighting functions for respective signals. Considering the frequency properties of human movements, the passivity constraint for stable human-robot interaction, which is required on the entire frequency spectrum and may bring conservative solutions, has been relaxed in such a way that it only restrains the low frequency band. Thus, impedance control became a mixed H 2 /H ∞ synthesis problem, and a dynamic output feedback controller can be obtained.Findings: The proposed impedance control strategy has been tested for various desired impedance with both simulation and experiments on the cable-driven series elastic actuator platform. The actual interaction torque tracked well the desired torque within the desired norm bounds, and the control input was regulated below the motor velocity limit. The closed loop system can guarantee relaxed passivity at low frequency. Both simulation and experimental results have validated the feasibility and efficacy of the proposed method.Originality/value: This impedance control strategy with mixed H 2 /H ∞ synthesis and relaxed passivity provides a novel, effective and less conservative method for physical human-robot interaction control.

Impedance control and specifically stiffness control are widely applied for physical human-robot interaction. The series elastic actuator (SEA) provides inherent compliance, safety and further benefits. This paper aims to improve the stiffness control performance of a cable-driven SEA. Existing impedance controllers were designed within the full frequency domain, though human-robot interaction commonly falls in the low frequency range. We enhance the stiffness rendering performance under formulated constraints of passivity, actuator limitation, disturbance attenuation, noise rejection at their specific frequency ranges. Firstly, we reformulate this multiple frequencyband optimization problem into the H∞ synthesis framework. Then, the performance goals are quantitatively characterized by respective restricted frequency-domain specifications as norm bounds. Further, a structured controller is directly synthesized to satisfy all the competing performance requirements. Both simulation and experimental results showed that the produced controller enabled good interaction performance for each desired stiffness varying from 0 to 1 times of the physical spring constant. Compared with the passivity-based PID method, the proposed H∞ synthesis method achieved more accurate and robust stiffness control performance with guaranteed passivity.

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