Towards Abstraction and Control for Large Groups of Robots
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This paper addresses the problem of controlling a large number of robots required to accomplish a task as a group. We propose an abstraction based on the definition of a map from the configuration space of the robots to a lower dimensional manifold, whose dimension does not scale with the number of robots. The task to be accomplished by the team suggests a natural feedback control system on the group manifold. We show that, if mean and covariance matrix are chosen as group variables for fully actuated robots, it is possible to design decoupling control laws, i.e., the feedback control for a robot is only dependent on the state of the robot and the state of the group, therefore the communication necessary to accomplish the task is kept to a minimum.
KeywordsGroup Manifold Lower Dimensional Manifold Motion Planning Problem Virtual Leader Local Asymptotic Stability
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