Dynamic optimization of tendon tensions in biomorphically designed hands with rolling constraints

Biomorphic structures for robotic manipulation based on tendon-driven mechanisms have been considered in robotic design for several decades, since they provide lightweight end-effectors with high dynamics. Following this trend, many new robot designs have being proposed based on tendon driven systems. Quite noticeably, the most advanced ones include also higher kinematic pairs and unilateral types of constraints. In this paper, we present a general framework for modeling the above class of mechanical systems for robotic manipulation. Such systems, including biomorphically designed devices, consist of articulated limbs with redundant tendinous actuation and unilateral rolling constraints. Methods based on convex analysis are applied to attack this broader class of mechanisms, and are shown to provide a basis for the dynamic control of co-contraction and internal forces that guarantee the correct operation of the system, despite limited friction between contacting surfaces or object fragility. An algorithm is described and tested that integrates a computed torque law, and allows to control tendon actuators to "optimally" comply with the prescribed constraints.