This study presents a dynamic compound shape control for a swarm of robots. A new definition of dynamic potential energy associated with the desired compound shape, which is the union of various basic shapes, is presented. Each basic shape is specified by the corresponding inequality functions. With this new definition, a variety of interesting compound shapes, which are difficult to form by the existing methods, can be easily formed. The swarm can also change their shape and size during the course of movement with the aid of a time-varying transformation matrix. A Lyapunov-like function is presented for stability analysis of the swarm systems. Simulation results are presented to illustrate the performance of the proposed method.
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Hou et al. (2012) studied this question.
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