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This paper presents a novel decentralized control scheme that achieves dynamic formation control and collision avoidance for a group of nonholonomic robots. First, we derive a feedback law using Lyapunov-type analysis that guarantees collision avoidance and tracking of a reference trajectory for a single robot. Then, we extend this result to the case of multiple nonholonomic robots, and show how different classes of multi-agent problems involving an interacting group of nonholonomic robots such as formation control can be addressed in this framework. Finally, we combine the above results to address the problem of driving a group of robots according to a given trajectory while maintaining a specific formation.