Forced Symmetric Formation Control

Zelazo, Daniel and Tanigawa, Shin-ichi and Schulze, Bernd (2025) Forced Symmetric Formation Control. IEEE Transactions on Control of Network Systems, 12 (2). pp. 1415-1426. ISSN 2325-5870

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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/|Γ|)n edges are sufficient to implement the control strategy when there are n agents and the underlying symmetry group is Γ. 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 that the agents can converge to a formation with respect to an arbitrary centroid. Numerous numerical examples are provided to illustrate the main results.