Formation Control of Multi-Agent Systems

2Single‐Integrator Model

This chapter will set the foundation for the formation control designs presented in the book. We use here a very simple model for the motion of the agents known as the single‐integrator model, which only includes two variables: position and velocity. This is a simplified kinematic model for omnidirectional robots (e.g., mobile robots with Swedish wheels 41). Specifically, we consider a system of agents governed by the first‐order differential equation

(2.1)

where is the position and is the velocity‐level control input of the th agent with respect to an Earth‐fixed coordinate frame. The name “single integrator” originates from the fact that the transfer function matrix of (2.1) is

(2.2)

where is the Laplace variable, i.e., the inputs and outputs are separated by ...