Parameter Study of Compliant Elements for a Bipedal Robot to Increase Its Walking Efficiency

In this paper, we introduce a method to place compliant elements with parameters that can be adjusted during operation in the joints of the bipedal walker to improve its energy efficiency. The bipedal walking robot is modelled with five rigid segments and driven by electric motors in its revolute joints. Minimizing the energy consumption of locomotion is formulated as a numerical optimization problem. An Euler-Bernoulli beam is used to describe the nonlinear behavior, caused by large deflections, of a compliant element loaded with forces and moments. The static problem for the beam deflection for given boundary conditions is solved numerically. Four parameters defining either the undeformed geometry or the boundary conditions are varied to modify the torque that this compliant element exerts on two robot segments connected by a revolute joint. The torque-deflection dependence and its dependence on the four different parameters is approximated by simple ansatz functions via fitting. The fitted functions are then included in a numerical optimization problem to determine the optimal parameters of the compliant element and the corresponding energy optimal gait simultaneously. ... mehrWe evaluate the optimized energy efficiency at different walking speeds, where the robot has different optimal gaits or parameters of the compliant elements. Two kinds of elastic couplings are investigated: the elastic coupling between the robot’s upper body and its thighs; or between the robot’s thighs and shanks. These specific compliant elements show a negligible performance gain from nonlinearity due to the small active operating range of these joints. However, the practicability of the proposed method for combining the detailed, model-based description of manufacturable compliant elements and the optimization of the overall robot system to achieve maximum energy efficiency is successfully demonstrated.