论文标题
在球体上的异质机器人群的强大同步
Robust synchronization of heterogeneous robot swarms on the sphere
论文作者
论文摘要
球体上的同步对于群体机器人技术中的某些控制应用很重要。最近感兴趣的是Lohe模型，该模型将库拉莫托模型从圆向球体推广。 LOHE模型主要在数学物理学中作为量子同步的玩具模型进行研究。该模型几乎没有假设，因此它非常适合代表群。该模型的先前工作集中在完整和无环网络的情况下，或所有振荡器频率均等的均质情况。本文涉及非平凡网络连接的异质振荡器的情况。我们表明，如果频率满足给定的结合，则任何不希望的平衡都是指数不稳定的。该属性也可以解释为具有零频率的同质情况的小型模型扰动的鲁棒性结果。因此，LOHE模型是控制群机器人技术中应用程序的好选择。
Synchronization on the sphere is important to certain control applications in swarm robotics. Of recent interest is the Lohe model, which generalizes the Kuramoto model from the circle to the sphere. The Lohe model is mainly studied in mathematical physics as a toy model of quantum synchronization. The model makes few assumptions, wherefore it is well-suited to represent a swarm. Previous work on this model has focused on the cases of complete and acyclic networks or the homogeneous case where all oscillator frequencies are equal. This paper concerns the case of heterogeneous oscillators connected by a non-trivial network. We show that any undesired equilibrium is exponentially unstable if the frequencies satisfy a given bound. This property can also be interpreted as a robustness result for small model perturbations of the homogeneous case with zero frequencies. As such, the Lohe model is a good choice for control applications in swarm robotics.
