Deployment of an Arbitrary Distribution of a Multi-Agent System With Finite Size on a Desired Formation

This paper considers the problem of deploying an arbitrary multi-agent system in a desired formation over an n-dimensional motion space. Each agent is considered to be a ball and collision avoidance is addressed. System evolution in ℝⁿ is decomposed into n one dimensional motion problems, where evolution of the agents q^th (q = 1, 2, 3) components are independently guided by two q-leaders. The remaining agents are considered q-followers, updating the q^th component of their positions by local interactions with two neighboring q-agents. Communications among the q-agents are weighted by values consistent with the q^th position components of agents in the desired configuration. This paper shows how specifying certain constraints on q-leader motion can address the problem of inter-agent collision avoidance when followers acquire their desired positions only by local communication.