Coordination and collision avoidance for Lagrangian systems with disturbances.

*(English)*Zbl 1201.93008Summary: We address the problem of cooperation and collision avoidance for Lagrangian systems with input disturbances. We design control laws that guarantee cooperation as well as collision-free maneuvers. We show, using a two-step proof, that the avoidance part of the control laws guarantees safety of the agents independently of the coordinating part. Then, we establish an ultimate bound on the region to which all the agents converge to. The obtained theoretical results are illustrated through numerical examples.

##### MSC:

93A14 | Decentralized systems |

93C15 | Control/observation systems governed by ordinary differential equations |

34H05 | Control problems involving ordinary differential equations |

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\textit{P. F. Hokayem} et al., Appl. Math. Comput. 217, No. 3, 1085--1094 (2010; Zbl 1201.93008)

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