Stability Considerations for Variable Impedance Control

Impedance control is a commonly used control architecture for robotic manipulation. For increased flexibility, the impedance can be programmed to vary during the task. This has important implications on the stability properties of the control system, which are often overlooked in practice. In fact, the standard stability analysis is not valid in the case that the impedance parameters vary over time. Simulations show that, depending on how the impedance parameters are varied, stable or unstable behavior can arise even in regulation without contact. In this paper, we elucidate this issue and propose a state-independent stability constraint that relates the stiffness, and also the time derivative of the stiffness to the damping. Our approach is illustrated and evaluated in comparison with an online stabilization method [8] which uses a tank-based stability criterion.