Efficient Robot Hopping Mechanisms with Compliance Using Evolutionary Methods

This paper presents as a study of a single leg of a quadruped robot with a compliance mechanism in its foot. The objective is to optimize the hopping behavior in terms of maximum jump height, least impact force for a minimum jump height, and power consumed in the actuators of the leg as a function of the compliance in the foot. The paper consists of numerical simulations of the leg in the MuJoCo environment and experimental results obtained in hardware. In order to find the optimum, a two-stage algorithm is used. In the first stage, an exhaustive coarse grid search of the parameter space, consisting of the compliance in the foot and controller gains at the hip and knee actuators, is done to arrive at a set of parameters. Next, an evolutionary algorithm is used to conduct a more focused search beginning from the best set of parameter values found in the first phase. Simulation results show that there is an optimum value of the compliance in the foot, which can give efficient hopping behavior with the highest jump height and lesser impact force on hitting the ground. Experimental results obtained from hardware also show an optimum spring stiffness and are in reasonable agreement with the simulation results.