Analysis of Foot Slippage Effects on an Actuated Spring-Mass Model of Dynamic Legged Locomotion

Abstract

The classical model of spring-loaded inverted pendulum (SLIP) and its extensions have been widely accepted as a simple description of dynamic legged locomotion at various scales in humans, legged robots and animals. Similar to the majority of models in the literature, the SLIP model assumes ideal sticking contact of the foot. However, there are practical scenarios of low ground friction that causes foot slippage, which can have a significant influence on dynamic behaviour. In this work, an extension of the SLIP model with two masses and torque actuation is considered, which accounts for possible slippage under Coulomb's friction law. The hybrid dynamics of this model is formulated and numerical simulations under representative parameter values reveal several types of stable periodic solutions with stick-slip transitions. Remarkably, it is found that slippage due to low friction can sometimes increase average speed and improve energetic efficiency by significantly reducing the mechanical cost of transport.

Dynamic Walking on Slippery Surfaces : Demonstrating Stable Bipedal Gaits with Planned Ground Slippage

“…Recent theoretical work has incorporated slippage into classic simple planar models of legged locomotion both in passive dynamic and actuated walking -the rimless wheel [27], compass biped [27], [28] and SLIP [29]. The models use Coulomb's friction law and account for stickslip transitions and friction-bounded inelastic impacts, which add complexity to the system's multi-domain hybrid dynamics.…”

“…Nonetheless, stability can be recovered when adding simple PD control to track a reference trajectory. In addition, it has been found in [27], [28], [29] that periodic solutions with slipping impact showed a significant reduction in energetic cost of transport compared to their no-slip counterparts. Nonetheless, these promising theoretical results have never been tested and implemented experimentally on legged robots.…”