Extension of the Deflection-Domain Passivity Approach for Variable Stiffnesses to SO(3)

Abstract

Recently, the deflection-domain passivity approach (DDPA) was introduced which does not control a system?s energetic behavior over time but over the deflection of the coupling controller?s virtual spring. So far, it has been applied to guarantee passivity in variable stiffness systems and for chattering-free force attenuation. When compared to time-domain based approaches as the Time Domain Passivity Approach or energy-tanks, the DDPA yields a more continuous and proactive variation of the controller force since the required dissipative action is distributed over the deflection of the spring applied in the coupling controller. In contrast, time-based approaches behave non-proactively and often attenuate control signals such as commanded forces completely. This attenuation happens suddenly when no energy is left available with regards to passivity. The DDPA was the first method to ensure passivity and non-zero stiffnesses for arbitrary unknown stiffness profiles. Here, we extend the DDPA to the control of three energetically coupled rotations in SO(3). Experiments in a teleoperation setup confirm the functionality of the approach.