Connecting Gaits in Energetically Conservative Legged Systems

TL;DR

This paper introduces a nonlinear dynamics approach to generate and connect gaits in conservative legged systems, using numerical continuation to explore gait space and energy-preserving impacts, demonstrated on a one-legged hopper.

Contribution

It presents a novel framework for identifying connected families of gaits in conservative models using numerical methods and energy-preserving impact conditions.

Findings

Connected gait space forms a continuous 1D manifold parameterized by energy.

Numerical continuation effectively finds gait families and bifurcations.

Framework successfully applied to a one-legged hopper model.

Abstract

In this work, we present a nonlinear dynamics perspective on generating and connecting gaits for energetically conservative models of legged systems. In particular, we show that the set of conservative gaits constitutes a connected space of locally defined 1D submanifolds in the gait space. These manifolds are coordinate-free parameterized by energy level. We present algorithms for identifying such families of gaits through the use of numerical continuation methods, generating sets and bifurcation points. To this end, we also introduce several details for the numerical implementation. Most importantly, we establish the necessary condition for the Delassus' matrix to preserve energy across impacts. An important application of our work is with simple models of legged locomotion that are often able to capture the complexity of legged locomotion with just a few degrees of freedom and a small number of physical parameters. We demonstrate the efficacy of our framework on a one-legged hopper with four degrees of freedom.