Analysis of Stability and Energy Efficiency of Legged Running Based on the Two-Segmented Leg Model

The running of animals and humans often exhibits a spring-like leg behavior, which is abstractly explained by the Spring-Loaded Inverted Pendulum (SLIP) model. However, such an equivalent model neglects the nonlinear characteristics generated by the spring-like behavior localized at the joint level, leading to a substantial difference from those in the real system when analyzing locomotion stability and energy efficiency. The segmented leg model introduces the stiffness and rest angle of the virtual torsion spring at the joint into the dynamics to demonstrate the nonlinear relationship between the leg force and the leg compression. Due to the introduction of multiple parameters, it is of great significance to determine the optimal parameter combination. In this paper, we present a method to analyze the effects of the model parameters on the self-stability and energy efficiency. The nonlinear relationship between leg force and leg compression, and the hybrid dynamics of a two-segmented leg model are built, the apex return map is introduced to set up the self-stable constraints based on passive dynamics, and the effects of model parameters on the running energy efficiency are investigated via numerical simulation. The simulation results reveal that the highest energy efficiency is achieved when the stiffness is set to be the maximum value allowed and achievable, and the target running pattern is located at the fixed point corresponding to the largest angle to attack. The methodology to determine the model parameters is concluded based on the simulation results.