Formation Control of Multi-Agent Systems

3Double‐Integrator Model

In this chapter, we re‐discuss the class of formation controllers presented in Chapter 2 in the context of a slightly more refined model, viz., the double‐integrator model. We will follow the same format as the previous chapter for ease of correlation.

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. Given a system of agents, the equations of motion for the double‐integrator model are

(3.1a)

(3.1b)

where represents the velocity of the th agent with respect to an Earth‐fixed coordinate frame, is the acceleration‐level control input, and is defined as in (2.1). Since the agent velocity is now a system state rather than the ...