Moving Formation

Abstract

In the previous chapters, we have studied formation control of multi-agents ignoring the ambiguity of translations. That is, if the goal of the formation control is to achieve a desired formation configuration that can be determined by desired distances $\Vert p_i^*- p_j^*\Vert$ or desired bearing vectors $g_{ji}^*= \frac{ p_j^*- p_i^*}{\Vert p_j^*- p_i^*\Vert }$, we can ignore a translation motion of a group of agents as far as the formation shape does not diverge. However, depending upon applications, it may be important to put a constraint on the motions or on the movements of the agents. For example, in a surveillance application, it will be important to consider not only the formation configuration but also the movement of the formation of the agents. First, this chapter considers the movement of agents under distance-based formation control setup. Each agent measures relative displacements in its own coordinate frame. Then, using the measured displacements, each agent estimates the velocity of leader agents. Then, using this estimated velocity, the agent controls the relative displacements as well as the velocity. It is supposed that there is one leader agent and the leader agent is moving with a constant velocity; so, the follower agents need to match their velocities to the velocity of leader agents. For a simplicity, we consider the AMP structure in 2-D. Sections 11.1 and 11.2 are dedicated to this problem. Second, we also consider double integrator dynamics for formulating the velocity matching among agents. Then, under the velocity consensus, agents can achieve the desired formation configuration under the moving formation. Section 11.3 is dedicated to the double integrator dynamics.