Modified gradient control for acyclic minimally persistent formations to escape from collinear position

In this paper, we consider formation shape control of moving agents in the plane, which has been examined for several years. We use distance-based control approach to achieve desired formations by controlling the relative distances between agents. Although there are various control schemes in the literature to control the moving agents, gradient control shows us a quite systematic way. However, one of the main problems in the gradient control happens when the agents are in an invariant subset under the collinearity, namely the agents cannot escape from the invariant subset under the gradient control. We propose a modification of the gradient control to solve the problem faced in the preliminary literature. Using the proposed control laws, we examine the convergence of distance errors to confirm that we are able to achieve the desired formations. Simulations supporting our results are provided.