Extension of impedance matching to nonlinear dynamics of robotic tasks

The concept of impedance matching for linear electric circuits is extended to nonlinear position-dependent circuits that express nonlinear dynamics of robotic tasks such as holding an object of soft material and handling a rigid object with soft fingers. At the first step, impedance control is realized by negative-feedback connection of two passive (hyper-stable) blocks, one is in the forward path expressing position control of the tool endpoint and the other is in the feedback path expressing force control of pressing the object. This negative-feedback framework is naturally introduced owing to the situation that both the tool mass and the nonlinear characteristics of reproducing force of the soft material are unknown. Extension of the concept of impedance matching to such nonlinear circuits is fulfilled by optimizing the regulation of impedance control and subsequently choosing optimal parameters from the viewpoint of both the transient and stead-state responses. The relations of this extension with the well-known theorem of maximum power supply and the H-infinity tuning for disturbance attenuation are also presented.