球面上异构机器人群的鲁棒同步
Robust synchronization of heterogeneous robot swarms on the sphere
摘要：
在群体机器人的某些控制应用中，球体上的同步是很重要的。最近感兴趣的是Lohe模型，它将仓本模型从圆形推广到球体。Lohe模型主要作为量子同步的玩具模型在数学物理中进行研究。该模型几乎没有假设，因此它非常适合代表一个群体。以前的工作集中在这个模型的情况下，完全和无环网络或均匀的情况下，所有的振荡器频率是相等的。本文研究了由非平凡网络连接的异质振子的情形。我们表明，任何不需要的平衡是指数不稳定的，如果频率满足给定的界限。这个属性也可以被解释为一个鲁棒性的结果，小模型扰动的均匀情况下，零频率。因此，Lohe模型是群体机器人控制应用的一个很好的选择。
英文摘要：
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.
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