Formation Control of Multi-Agent Systems

4Robotic Vehicle Model

In this chapter we extend the graph rigidity‐based formation control framework to multi‐robotic vehicles. As opposed to the simple linear models of Chapters 2 and 3, the agent model here will include the nonlinear kinematics and dynamics of the vehicle. Specifically, we will consider a class of robotic vehicles moving in 2D which includes unicycle robots, marine (surface) vessels, underwater vehicles with constant depth, and aircraft with constant altitude.

In the first part of the chapter we will only account for the nonholonomic kinematics of the vehicles and design a velocity‐level control law based on the main result from Chapter 2. In the second part, we will include the holonomic vehicle dynamics in the control design. Since the resulting dynamic model will be a second‐order nonlinear differential equation, the backstepping methodology will again be utilized to embed the velocity‐level inputs from Chapter 2 in the torque/force‐level control law. Two controllers will be presented in this second part. First, we consider the case where the dynamics are completely known, leading to the design of a fully model‐based formation controller. We then assume the model is subject to parametric uncertainty. In this case, we use adaptive control tools to add parameter adaptation to the control law for the purpose of compensating for the unknown parameters.

The discussions in this chapter are limited to the static formation acquisition problem. Extensions to the ...