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.
Highlights
Legged locomotion is ubiquitous in the motion of living creatures throughout a wide range of scales, from small insects to rodents, mammals and humans [16]
In all types of periodic solutions under different values of μ, four out of the seven numerically computed eigenvalues of D Π ( x *) were very small, in the order of 10−3 − 10−5. The reason for this is the presence of hidden constraints on the hybrid dynamics, which are more evident if one chooses different Poincaré sections along the periodic solutions
We analysed a generalized version of the spring-loaded inverted pendulum (SLIP) model that incorporates the effects of Coulomb friction and Yizhar Or and Moti Moravia: 11 Analysis of Foot Slippage Effects on an Actuated Spring-mass Model of Dynamic Legged Locomotion foot slippage by adding a foot mass, linear damping and controlled torque actuation
Summary
Legged locomotion is ubiquitous in the motion of living creatures throughout a wide range of scales, from small insects to rodents, mammals and humans [16]. One type of legged locomotion that is typical to robotics is quasistatic motion, where the body and limbs slowly move while continuously maintaining static balance with external loads [38, 46]. Natural walking and running typically involve dynamic motion, where the body is constantly falling as an unstable inverted pendulum until a free foot reaches contact [8]. Models of robotic legged locomotion often include a chain of rigid links, as in the well-known examples of passive dynamic walking [33, 34] and compass biped [24]. Never‐ theless, in biological legged locomotion, elastic energy storage often plays an important role in dynamic behav‐ iour. A classic and simple model of DLL that captures this mθyxgk,lo (a)
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