When hyper redundant robots are used in complex and unpredictable environments such as human living space, they should deal with various contact conditions between surrounding objects. Robots thus should plan and optimize not only applying force to the object but also its distribution among contact area. This paper defines the ability to optimize stiffness distribution of a number of contact points as "Flexibility" and proposes elastic closed-loop mechanism which has a serial chain of revolute joints with torsion coil springs as a lightweight and supple hyper redundant mechanism. Output stiffness is formulated based on the minimization of potential energy, the balancing of internal force and the velocity constraint to construct a closed-loop mechanism. Joint input to obtain both the desired stiffness distribution and desired output position simultaneously is derived from partial derivative of the output stiffness and compensation by a learning control scheme. Motion control experiments with a 10R elastic closed-loop robot demonstrate the effectiveness of the proposed control scheme.
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