Modeling posture-dependent leg actuation in sagittal plane locomotion

The spring loaded inverted pendulum template has been shown to accurately model the steady locomotion dynamics of a variety of running animals, and has served as the inspiration for an entire class of dynamic running robots. While the template models the leg dynamics by an energy-conserving spring, insects and animals have structures that dissipate, store and produce energy during a stance phase. Recent investigations into the spring-like properties of limbs, as well as animal response to drop-step perturbations, suggest that animals use their legs to manage energy storage and dissipation, and that this management is important for gait stability. In this paper, we extend our previous analysis of control of the spring loaded inverted pendulum template via changes in the leg touch-down angle to include energy variations during the stance phase. Energy variations are incorporated through leg actuation that varies the force-free leg length during the stance phase, yet maintains qualitatively correct force and velocity profiles. In contrast to the partially asymptotically stable gaits identified in previous analyses, incorporating energy and leg angle variations in this manner produces complete asymptotic stability. Drop-step perturbation simulations reveal that the control strategy is rather robust, with gaits recovering from drops of up to 30% of the nominal hip height.