Agile asymmetric multi-legged locomotion contact planning via geometric mechanics and spin model duality

Title: Agile asymmetric multi-legged locomotion: contact planning via geometric mechanics and spin model duality
Authors: Jackson Habala, Gabriel B. Margolis, Tianyu Wang, Pratyush Bhatt, Juntao He, Naheel Naeem, Zhaochen Xu, Pulkit Agrawal, Daniel I. Goldman, Di Luo, Baxi Chong
arXiv: https://arxiv.org/abs/2602.09123

This paper asks a fundamental scaling question for legged robotics: if adding legs increases contact opportunities, why do we still mostly run controllers that look like biped or quadruped heuristics? The authors argue that the bottleneck is not hardware, but representation. As leg count grows, contact schedules become combinatorial, so hand-designed gaits collapse to a tiny low-dimensional subset of the behavior space.

Their core contribution is a physics-first reformulation. They use geometric mechanics to map contact-rich locomotion into a graph optimization view over shape changes and resulting body displacement, then import a spin-model duality perspective to reason about symmetry breaking in gait organization. Intuitively, the spin analogy provides a structured way to search asymmetric modes that would be unlikely under symmetric gait priors.

$$\underset{\pi \in \Pi }{\max }\Delta x(\pi )\text{s.t.}c(\pi )\in \mathcal{C},\pi \in \mathcal{G}$$

Here $\pi$ denotes a contact-and-shape cycle on the locomotion graph, $\Delta x(\pi )$ is net forward displacement per cycle, $c(\pi )$ encodes feasibility constraints (friction, actuator limits, contact consistency), and $\mathcal{G}$ is the reduced graph induced by geometric mechanics. The point is not this exact equation form, but the decomposition: optimize locomotion via structured cycle search instead of ad hoc gait scripting.

Empirically, the discovered asymmetric hexapod strategy reaches $0.61$ body lengths per cycle, about a $50\%$ gain over conventional baselines. The intriguing detail is that asymmetry appears simultaneously in control and morphology utilization: turning dynamics are phase-asymmetric, and two same-side legs can be left unactuated without major degradation.

For your research taste, this is a strong example of “use theory to cut search dimensionality” rather than just scaling data or policy capacity. The actionable takeaway is to treat contact planning as symmetry management: explicitly model when symmetry should be broken, then encode that bias into the optimization space before learning residual control.

Graph: Paper Node 2602.09123