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This paper introduces a distributed leaderless swarm formation control framework to address the problem of collectively driving a swarm of robots to track a time-varying formation. The swarm&#x0027;s formation is captured by the trajectory of an abstract shape that circumscribes the convex hull of robots&#x0027; positions and is independent of the number of robots and their ordering in the swarm. For each robot in the swarm, given global specifications in terms of the trajectory of the abstract shape parameters, the proposed framework synthesizes a control law that steers the swarm to track the desired formation using the information available at the robot&#x0027;s local neighbors. For this purpose, we generate a suitable local reference trajectory that the robot controller tracks by solving the input-output linearization problem. Here, we select the swarm output to be the parameters of the abstract shape. For this purpose, we design a dynamic average consensus estimator to estimate the abstract shape parameters. The abstract shape parameters are used as the swarm state feedback to generate a suitable robot trajectory. We demonstrate the effectiveness and robustness of the proposed control framework by providing the simulation of coordinated collective navigation of a group of car-like robots in the presence of robots and communication link failures.

Leaderless Swarm Formation Control: From Global Specifications to Local Control Laws