Distributed Shortest-Distance Formation for Multi-agent Systems

This paper studies distributed shortest distance formation optimization problems for multi-agent systems, where the agents cooperatively minimize the total quadratic distance functions to the given convex regions while realizing the predefined formation. Each agent only has knowledge on its associated convex region and its local objective function. First, a time-invariant shortest-distance formation problem is introduced and a distributed protocol is proposed. Then, sufficient conditions are given, under which the multi-agent system converge to the optimal solution. Furthermore, a time-varying distributed shortest-distance formation optimization problem is studied and a dynamic protocol is provided. Moreover, a numerical simulation example is given to demonstrate the effectiveness of the theoretical results.