Profile Design of Parallel Rotary Compliance for Energy Efficiency in Cyclic Tasks

Compliant elements, installed in parallel with actuators, potentially contribute to the energy efficiency of legged robots. Nevertheless, finding the most appropriate compliance profile, especially over a reasonable range of locomotion speeds, is still an open topic. This article contributes to the literature on three grounds. First, it proposes optimality conditions for parallel compliance in terms of energy efficiency. Second, it introduces a class of parallel compliance termed as rotary compliance, in that recycling energy in reciprocal motions is done through continuous rotation of a compliant element. Rotary compliances have the potential to result in higher energy efficiency in cyclic tasks in comparison to reciprocating compliances. Finally, it presents a rotary compliance profile design method for energy and torque minimization. Robustness against some task frequency variations is also considered in the design process. Experimental results on implementing the rotary compliance on a robotic leg show up to 49% energy consumption improvement in absence of ground impact and up to 22% in running tests on a treadmill. Moreover, investigation of the effects of velocity variations on the efficiency of the compliance reveals an acceptable robustness level for the proposed design.