Partitioning algorithms for homogeneous multi-vehicle systems with planar rigid body dynamics
Partitioning algorithms for homogeneous multi-vehicle systems with planar rigid body dynamics
复制标题
具有平面刚体动力学的同质多车辆系统的分区算法
DOI：
10.1109/cdc.2014.7040232
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
E. Bakolas
中科院分区：
文献类型：
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作者：
E. Bakolas
我们考虑了一组具有平面刚体动力学的车辆的广义Voronoi分割问题。接近度量，即确定车辆与配置空间中任意点之间的接近关系的广义度量，对应于在每个车辆向其目标配置的转移期间发生的广义能量度量的减小。特别是，所采用的接近度由相应的稳定化问题的准李雅普诺夫函数诱导。选择这种接近度量的主要动机之一是获得一类空间分区，其计算成本显着低于空间分区的接近度量是相应的最优控制问题的成本去函数，这在我们以前的工作中进行了研究。特别是，在这项工作中使用的广义邻近度的结构，使我们能够开发简单，易于实现的分区算法，适用于涉及车辆的非线性动力学的问题。更重要的是，在一些温和的假设下，所提出的划分算法可以以分散的方式实现，允许每个车辆独立于其队友计算自己的单元。数值模拟，说明了理论的发展。
We consider a generalized Voronoi partitioning problem for a team of vehicles with planar rigid body dynamics. The proximity metric, that is, the generalized metric that determines the proximity relations between the vehicles and arbitrary points in the configuration space, corresponds to the decrease of a generalized energy metric that takes place during the transfer of each vehicle to its goal configuration. In particular, the employed proximity metric is induced by a quasi-Lyapunov function of a corresponding stabilization problem. One of the main motivations for the choice of this proximity metric is to obtain a class of spatial partitions whose computational cost is significantly lower than the one of spatial partitions whose proximity metric is the cost-to-go function of a corresponding optimal control problem, which were studied in our previous work. In particular, the structure of the generalized proximity metric utilized in this work allows us to develop simple and easily implementable partitioning algorithms that are applicable to problems involving vehicles with nonlinear dynamics. More importantly, the proposed partitioning algorithms can be implemented, under some mild assumptions, in a decentralized fashion that allows each vehicle to compute its own cell independently from its teammates. Numerical simulations that illustrate the theoretical developments are also presented.