Optimal partitioning for multi-vehicle systems using quadratic performance criteria
Optimal partitioning for multi-vehicle systems using quadratic performance criteria
复制标题
使用二次性能标准对多车辆系统进行优化划分
DOI：
10.1016/j.automatica.2013.08.005
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发表时间：
2013
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
我们考虑的问题的特征的广义Voronoi图，这是相关的一类特殊的区域分配问题的多车辆系统。它被假定为每个车辆的运动描述的二阶机械系统随时间变化的线性或仿射动力学。所提出的广义Voronoi图编码的信息之间的车辆和任意目标点在平面上的邻近关系。这些邻近关系是由一个各向异性（广义）的距离函数，结合车辆动力学。特别地，广义距离被认为是车辆在固定的最终时间以小的终端速度过渡到任意目标点所需的最小控制努力。我们希望划分的空间对应于每个飞行器使用有限控制力所能达到的所有终端位置的并集。因此，分区空间具有比每个车辆的状态空间低的维度。我们表明，在一般情况下，建议的分区问题的解决方案可以与一组领域在一个五维欧氏空间中的计算，其中有效的技术存在于相关文献中所产生的功率Voronoi图。
We consider the problem of characterizing a generalized Voronoi diagram that is relevant to a special class of area assignment problems for multi-vehicle systems. It is assumed that the motion of each vehicle is described by a second order mechanical system with time-varying linear or affine dynamics. The proposed generalized Voronoi diagram encodes information regarding the proximity relations between the vehicles and arbitrary target points in the plane. These proximity relations are induced by an anisotropic (generalized) distance function that incorporates the vehicle dynamics. In particular, the generalized distance is taken to be the minimum control effort required for the transition of a vehicle to an arbitrary target point with a small terminal speed at a fixed final time. The space we wish to partition corresponds to the union of all the terminal positions that can be attained by each vehicle using finite control effort. Consequently, the partition space has lower dimension than the state space of each vehicle. We show that, in the general case, the solution to the proposed partitioning problem can be associated with a power Voronoi diagram generated by a set of spheres in a five-dimensional Euclidean space for the computation of which efficient techniques exist in the relevant literature.