Stiffness Decomposition and Design Optimization of Under-Actuated Tendon-Driven Robotic Systems

We present a novel systematic design framework for general under-actuated tendon-driven (UATD) robotic systems to exhibit desired behaviors both during the free motion and the contact task. For this, we propose stiffness decomposition, which enables us to completely decompose the configuration space of the UATD robotic systems into the actuated space (with full actuation via active tendons) and the un-actuated space (with no actuation, only with passive compliance and contact wrench). The behavior in the actuated space is then fully-controllable, thus, the attainment of the desired behaviors, particularly those during the contact task, hinges upon that in the un-actuated space. For this, relying on the stiffness decomposition, we optimize the design parameters (e.g., tendon routing, pulley radius, passive compliance, etc.) to ensure the deformation in the un-actuated space as directional (e.g., for adaptive grasping) and minimized (e.g., pushing with posture maintained) for different contact wrench sets as possible, while also rendering the free motion to be as compliant and backdrivable as possible. The presented framework is then applied to design a UATD robotic finger and experimentally verified with the robot able to mimic the behavior of human index finger both during the free motion and pinch-pushing.