Analyzing and Improving Cartesian Stiffness Control Stability of Series Elastic Tendon-Driven Robotic Hands

Robust and dexterous manipulation is identified as one of the critical challenges in the field of robotic hand design and control. A key requirement of dexterous manipulation is the ability to modulate fingertip force directions and magnitudes. Cartesian stiffness control is a strategy to generate position dependent fingertip forces. However the stability conditions for the Cartesian stiffness controllers vary nonlinearly because of dependency on the manipulator's configuration and loading forces. The challenge is enhanced in case of tendon-driven robotic hands due to passive joint coupling. In this work, we derive a generalized passivity based stability boundary for Cartesian stiffness. We then present a methodology to analyze the stability boundaries of Cartesian stiffness controlled series elastic tendon-driven robotic fingers. We also present a solution to improve stability by optimizing the arrangement of optimized passive compliance in parallel to the actuators based on the stability criteria. Our analysis not only allows for informed design of new robotic hands but also applies to improving performance of existing robotic hands.