Distance-based undirected formations of single-integrator and double-integrator modeled agents in n-dimensional space

We study the local asymptotic stability of undirected formations of single-integrator and double-integrator modeled agents based on interagent distance control. First, we show that n-dimensional undirected formations of single-integrator modeled agents are locally asymptotically stable under a gradient control law. The stability analysis in this paper reveals that the local asymptotic stability does not require the infinitesimal rigidity of the formations. Second, on the basis of the topological equivalence of a dissipative Hamiltonian system and a gradient system, we show that the local asymptotic stability of undirected formations of double-integrator modeled agents in n-dimensional space is achieved under a gradient-like control law. Simulation results support the validity of the stability analysis.