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.

The mechanical design of robotic hands has been converging towards low-inertia, tendon-driven strategies. As tendon driven robotic fingers are serial chain systems, routing strategies with compliant tendons lead to multi-articular coupling between the degrees of freedom. We propose a generalized analysis of such serial chain linkages with coupled passive joint stiffnesses. We analyze the effect of such coupling on maximum achievable stiffness control boundaries while maintaining passivity at the actuators by analytically deriving the boundaries. We believe that we can use this information to form mechanical design guidelines for intelligently selecting arrangements of compliance elements (mechanical springs) and transmission strategies, i.e. tendon routing and pulley radii, to provide intrinsic stability and customizable controller stiffness limits for high performance manipulation in robotic hands.