Optimization-based Robot Compliance Control: Geometric and Linear Quadratic Approaches

Impedance control is a compliance control strategy capable of accommodating both unconstrained and constrained motions. The performance of impedance controllers depends heavily upon environment dynamics and the choice of target impedance. To maintain performance for a wide range of environments, target impedance needs to be adjusted adaptively. In this paper, a geometric view on impedance control is developed for stiff environments, resulting in a “static-optimized” controller that minimizes a combined generalized position and force trajectory error metric. To incorporate the dynamic nature of the manipulator-environment system, a new cost function is considered. A classic quadratic optimal control strategy is employed to design a novel adaptive compliance controller with control parameters adjusted based upon environment stiffness and damping. In steady state, the proposed controller ultimately implements the static-optimized impedance controller. Simulation and experimental results indicate that the proposed optimal controller offers smoother transient response and a better trade-off between position and force regulation.