Forced Symmetric Formation Control
arxiv(2024)
摘要
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 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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