Optimal motion planning using navigation measure
Optimal motion planning using navigation measure
复制标题
使用导航测量的最佳运动规划
DOI：
10.1080/00207179.2017.1300838
复制
发表时间：
2018
影响因子：
2.1
通讯作者：
U. Vaidya
中科院分区：
文献类型：
--
作者：
U. Vaidya
摘要本文引入导航测度作为一种新的工具来解决存在静态障碍物时的运动规划问题。导航措施的存在，保证碰撞无收敛在最终的目的地集开始，几乎每一个初始条件的勒贝格措施。导航测量可以被看作是导航功能的一个对偶。导航函数在最终目的地集合处最小，在障碍物集合处最大，导航测度在目的地集合处最大，在障碍物集合处为零。本文提出了一种线性规划的形式化方法来构造导航措施。面向集的数值方法被用来获得有限维近似的导航措施。所提出的导航测量为基础的理论和计算框架的应用证明了在一个复杂的流体流动的运动规划问题。
ABSTRACT We introduce navigation measure as a new tool to solve the motion planning problem in the presence of static obstacles. Existence of navigation measure guarantees collision-free convergence at the final destination set beginning with almost every initial condition with respect to the Lebesgue measure. Navigation measure can be viewed as a dual to the navigation function. While the navigation function has its minimum at the final destination set and peaks at the obstacle set, navigation measure takes the maximum value at the destination set and is zero at the obstacle set. A linear programming formalism is proposed for the construction of navigation measure. Set-oriented numerical methods are utilised to obtain finite dimensional approximation of this navigation measure. Application of the proposed navigation measure-based theoretical and computational framework is demonstrated for a motion planning problem in a complex fluid flow.