Formation Control via Orientation Alignment

Abstract

Based on gradient control laws, the global stabilization is assured for some specific formations in Chap. 3, and the local stabilization has been assured for general graphs in Chap. 4. It is noticeable that the traditional gradient control laws, or modified gradient control laws, only rely upon error signals measured at local coordinate frames. Thus, it is purely based on sensing information without any communications with neighboring agents. However, as commented in Chap. 1 and as shown in Fig. 4.5, although the gradient control law that does not use any communication is computationally light, it may not ensure a global convergence for general graphs. In this chapter, we assume that the neighboring agents could communicate with each other. The agents can sense each other relatively; then, the sensing variables and/or computational variables may be exchanged between neighboring agents. For example, it may be assumed that bearing measurements in misaligned coordinate frames can be exchanged between neighboring agents. With the help of communications, it can then be shown that a (quasi-) global convergence under more generalized initial conditions could be assured. Here, the key problem we would like to treat for a global convergence is to align the directions of agents, which also may be a key issue in collective behaviors in nature [2, 3].