Robustness and efficiency of a variable-leg-spring hopper

In a previous study, stability of a spring-mass hopping-model with variable rest length and stiffness during stance has been investigated. Here, robustness of the stable hopping solutions is addressed. For this, the basin of attraction of the stable fixed points is determined. Results show a tradeoff between maximum stability and maximum robustness. Additional velocity-dependent damping only slightly increases robustness. However, the areas of a given robustness level are enlarged. As a third criterion for successful locomotion efficiency is investigated. To do so, the work-based cost of movement as well as the work ratio between elastic and total work are estimated. Similarly to robustness, the areas of a given maximum cost of movement grow for increasing additional damping. At the same time the maximum cost of transport only slightly increases. However, the work ratio decreases drastically, i.e. less work is done passively by the spring and hopping becomes less efficient.