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arXiv · 2403.02836

Forced Symmetric Formation Control

Daniel Zelazo·Shin-ichi Tanigawa·Bernd Schulze
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Abstract

This work considers the distance constrained formation control problem with an additional constraint requiring that the formation exhibits a specified spatial symmetry. We employ recent results from the theory of symmetry-forced rigidity to construct an appropriate potential function that leads to a gradient dynamical system driving the agents to the desired formation. We show that only $(1+1/|\Gamma|)n$ edges are sufficient to implement the control strategy when there are $n$ agents and the underlying symmetry group is $\Gamma$. This number is considerably smaller than what is typically required from classic rigidity-theory based strategies ($2n-3$ edges). We also provide an augmented control strategy that ensures the agents can converge to a formation with respect to an arbitrary centroid. Numerous numerical examples are provided to illustrate the main results.

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Daniel Zelazo, Shin-ichi Tanigawa, Bernd Schulze. 2024-03-05. Forced Symmetric Formation Control. https://doi.org/10.1109/tcns.2025.3525814

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