Formation Control of Multiple Autonomous Vehicle Systems

2 Formation Dynamics of Motion Systems

The concept of formation in motion can be intuitively described as a group of vehicle systems staying in a fixed pattern (e.g. a geometric shape) while in motion. We can extend the concept to allow these vehicles to follow a certain dynamic pattern (e.g. spinning in a geometric fashion). With this context in mind, in this chapter we shall formulate the dynamics of vehicle systems for establishing a fixed formation, but may extend this to allow for a time‐varying, dynamic formation.

Technical descriptions of formation control can be categorized into three main approaches:

• the leader–follower approach
• the behavioural approach
• the virtual structure approach.

In this chapter, we will use similar categories to establish the dynamics formulations of the motion of multiple vehicle systems.

2.1 Virtual Structure

Imagine a group of multiple vehicles in a “fixed” formation, so that they move as if one entity. Intuitively, one would treat such a a group of vehicles as if they were a rigid body. In this way, the concept of a virtual structure is born.

Let us take a moment to consider the properties of a rigid body and its relationship with a group of vehicles in fixed formation. First of all, any infinitesimal mass point on the rigid body has a fixed position relative to the centre of mass (CM) of the body, and these relative positions remain fixed for any time instant in motion. Secondly, each element on the body has a fixed orientation ...