We consider the problem of finding an informative path through a graph, given initial and terminal nodes and a given maximum path length. We assume that a linear noise corrupted measurement is taken at each node of an underlying unknown vector that we wish to estimate. The informativeness is measured by the reduction in uncertainty in our estimate, evaluated using several metrics. We present a convex relaxation for this informative path planning problem, which we can readily solve to obtain a bound on the possible performance. We develop an approximate sequential method where the path is constructed segment by segment through dynamic programming. This involves solving an orienteering problem, with the node reward acting as a surrogate for informativeness, taking the first step, and then repeating the process. The method scales to very large problem instances and achieves performance not too far from the bound produced by the convex relaxation. We also demonstrate our method's ability to handle adaptive objectives, multimodal sensing, and multi-agent variations of the informative path planning problem.

翻译：本文研究在给定初始节点与终止节点及最大路径长度约束下，通过图结构寻找一条信息路径的问题。我们假设在每个节点处对某个待估计的未知底层向量进行线性含噪测量，并采用多种指标评估估计不确定性的降低程度（即信息量）。针对该信息路径规划问题，我们提出一种凸松弛方法，可快速求解获得性能上界。进一步开发了一种近似序贯方法：通过动态规划逐段构建路径，每次求解一个导向性问题（其中节点奖励作为信息量的替代指标），完成单步行走后重复该过程。该方法可扩展至超大规模问题实例，所得性能与凸松弛上界相差不大。我们还展示了该方法在自适应目标、多模态感知及多智能体变体信息路径规划问题中的适用性。