A three-dimensional spring-loaded inverted pendulum walking model considering human movement speed and frequency

The spring-loaded inverted pendulum (SLIP) model is an effective model to capture the essential dynamics during human walking and/or running. However, most of the existing three-dimensional (3D) SLIP model does not explicitly account for human movement speed and frequency. To address this knowledge gap, this paper develops a new SLIP model, which includes a roller foot, massless spring, and concentrated mass. The governing equations-of-motion for the SLIP model during its double support phase are derived. It is noted that in the current formulation, the motion of the roller foot is prescribed; therefore, only the equations for the concentrated mass need to be solved. To yield model parameters leading to a periodic walking gait, a constrained optimization problem is formulated and solved using a gradient-based approach with a global search strategy. The optimization results show that when the attack angle ranges from 68° to 74°, the 3D SLIP model can yield a periodic walking gait with walking speeds varying from 0.5 to 2.0 m s^-1. The predicted human walking data are also compared with published experimental data, showing reasonable accuracy.