Geometry of contact: contact planning for multi-legged robots via spin models duality

TL;DR

This paper introduces a novel geometric mechanics approach for multi-legged robot contact planning, transforming it into a graph optimization problem solvable via spin models, enabling efficient discovery of optimal locomotion sequences.

Contribution

It develops a new geometric mechanics framework that simplifies contact planning to graph optimization and applies spin model duality for polynomial-time solutions in multi-legged robots.

Findings

Successfully generated new forward and sidewinding behaviors in hexapod and centipede robots.

Validated the approach with numerical simulations and robophysical experiments.

Achieved effective locomotion behaviors with optimal contact sequences.

Abstract

Contact planning is crucial in locomoting systems.Specifically, appropriate contact planning can enable versatile behaviors (e.g., sidewinding in limbless locomotors) and facilitate speed-dependent gait transitions (e.g., walk-trot-gallop in quadrupedal locomotors). The challenges of contact planning include determining not only the sequence by which contact is made and broken between the locomotor and the environments, but also the sequence of internal shape changes (e.g., body bending and limb shoulder joint oscillation). Most state-of-art contact planning algorithms focused on conventional robots (e.g.biped and quadruped) and conventional tasks (e.g. forward locomotion), and there is a lack of study on general contact planning in multi-legged robots. In this paper, we show that using geometric mechanics framework, we can obtain the global optimal contact sequence given the internal shape changes sequence. Therefore, we simplify the contact planning problem to a graph optimization problem to identify the internal shape changes. Taking advantages of the spatio-temporal symmetry in locomotion, we map the graph optimization problem to special cases of spin models, which allows us to obtain the global optima in polynomial time. We apply our approach to develop new forward and sidewinding behaviors in a hexapod and a 12-legged centipede. We verify our predictions using numerical and robophysical models, and obtain novel and effective locomotion behaviors.