Formation Control With Unknown Directions and General Coupling Coefficients

Generally, the normal displacement-based formation control of multiagent systems has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling coefficients. However, the direction may be unknown, and the coupling coefficients may also involve negative ones. In this article, these phenomena are introduced into a class of displacement-based formation control for multiagent system, which have nonconvexity that inevitably leads to difficulties of analysis. Then, a geometric approach has been employed to overcome the difficulties. The purpose of this approach is to construct some convex polytopes for containing the effects caused by the above-mentioned phenomena, and maintain the invariance of these polytopes in view of the contractive set method. It further means that the convergence of formation shape can be guaranteed. The considered formation control problem can admit the unknown direction and negative coupling coefficients in a certain range, which are a major improvement compared to the normal displacement-based formation control. Subsequently, the applicability of this formation control problem is examined through a simulation. This simulation indicates that the direction of agents and the negative coupling coefficients do not affect the convergency of the formation shape.