The research in this dissertation is concerned with developing a method to produce flocking behavior in a swarm of mobile robots. The dissertation itself is divided into three articles. The research in the first article is a proof-of-concept that demonstrates that one can create a swarm of mobile robots that engage in flocking behavior by the use of a position tracking controller in concert with a method for defining the desired trajectory for each object. The research in the second article develops a method for implementing both attractive and repulsive artificial potential functions with a position tracking controller. The research in the third article builds on that in the first two articles in order to construct a large swarm of mobile robots that engages in flocking behavior using a social potential function that is contructed from the attractive and repulsive functions of the second article. Each article contains both control-theoretic analysis of robot behavior and demonstrations of the behavior using Matlab simulations. The overall result is a successful, yet relatively simple, method for creating a swarm of mobile robots in which each robot has a degree of freedom of action.