Forced Symmetric Formation Control

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.

Submitted to the IEEE Transactions on Control of Network Systems

References in corpus (1)

• Infinitesimal Rigidity of Symmetric Frameworks