Modeling robot discrete movements with state-varying stiffness and damping: A framework for integrated motion generation and impedance control

Successful execution of many robotic tasks requires precise control of robot motion and its interaction with the environment. In robotics these two problems are mainly studied separately in the domain of robot motion generation and interaction control, respectively. Existing approaches rely on two control loops: a motion generator (planner) that provides a reference trajectory in the outer loop, and an active impedance controller that tracks the reference trajectory in the inner loop. Ensuring stability of the closed-loop system for this control architecture is nontrivial. In this paper, we propose a single-loop control architecture that performs motion generation and interaction control at once. We model robot discrete motions with a time-invariant dynamical system, which is expressed as a nonlinear combination of a set of linear spring-damper systems. This formulation represents the nominal motion and the impedance properties with a single set of parameters, simplifying stability analysis of the closed-loop system. We provide sufficient conditions to ensure global asymptotic stability of this system for movements in free-space, and its passivity during persistent contact with a passive environment. We validate our approach in simulation using the 7-DoF KUKA LWR-IV robot.