ABSTRACT
It is possible to represent autonomous dynamic agents (e.g., robots, satellites, unmanned ground or air vehicles) using various mathematical models. One common representation is based on Newton’s second law of motion of point mass particles, which sometimes is also called the double integrator model and is given by
x˙i = vi , v˙i = ui (9.1)
where xi ∈ Rn is the position of agent i, vi ∈ Rn its velocity, and ui ∈ Rn its control (force) input. The index i is used to denote that the corresponding dynamics belong to agent i. We assume that there are N identical agents in the swarm. In the above model, without loss of generality, it has been assumed that the mass of all agents is mi = 1. This is because it can be easily compensated for by appropriately scaling the control inputs of the agents.
