The effect of leg impedance on stability and efficiency in quadrupedal trotting

Numerous legged robots have demonstrated the effectiveness of tuned leg impedance to achieve dynamically stable running and hopping. However, selecting appropriate impedance values for new machines remains challenging. This paper investigates the effect of joint impedance selection on locomotion stability and efficiency by analyzing a simulation model of the MIT Cheetah quadruped robot performing a trot gait. An exhaustive search of impedance parameters of the knee and hip shows that locomotion stability is highly sensitive to knee impedance and insensitive to hip impedance. Inspection of simulations operating during a ground-height disturbance reveals why: During a disturbance response most of the variation in work performed in the legs occurs in the knee joints. Mechanical work data from the MIT Cheetah exhibits close experimental agreement with the simulation predictions. The exhaustive search also reveals that, within the range of impedance parameters that can achieve stable locomotion, joint impedance values do not have a significant effect on the mechanical cost of transport. These results indicate that the dynamic response of the leg-extension degree of freedom is of primary importance to achieving dynamically stable running, and that robust stability may be achieved with minimal compromise of locomotion efficiency.