Distance-based directed formation control in three-dimensional space

This paper concentrates on the distance-based formation control problem in three-dimensional space. The objective is to achieve and maintain the formation of overall group of a multi-agent system, whose interaction graph is acyclic minimally persistent. The gradient-based control law derived from a class of potential functions is considered to address this problem. The trajectories of agents converge to a set of equilibria under the proposed control law. Every desired equilibrium, where all inter-agent distance constraints are satisfied, is locally exponentially stable and the undesired equilibrium set is repulsive.