Double‐Integrator Model

This chapter discusses the class of formation controllers in the context of a slightly more refined model, viz., the double-integrator model. The double-integrator model accounts for the agent acceleration by treating the agent as a point mass. Therefore, it can be considered a very simple dynamic model for omnidirectional robots. The chapter also discusses a complication in the stability analysis of the closed-loop system that arises from the double-integrator model. Specifically, the complication is related to the avoidance of flip ambiguities. Solving the target interception problem for the double-integrator model requires a more elaborate solution than the one presented in the chapter for the single-integrator model. Formation controllers based on the double-integrator model are not as prevalent as single-integrator-based ones, especially within the realm of inter-agent distance control. The chapter provides a discussion on results that explicitly or implicitly address the formation control problem.