Approximate Sequential Optimization for Informative Path Planning

TL;DR

The paper tackles IPP on graphs under a budget by formulating a mixed-integer convex program and introducing a convex relaxation that provides a lower bound. It then develops Approximate Sequential Path Optimization (ASPO), a dynamic-programming–based method that builds paths segment-by-segment by solving orienteering subproblems with information-guided rewards, achieving scalable performance and a bounded optimality gap. The authors extend the framework to adaptive objectives, multimodal sensing, and multi-agent IPP, and demonstrate competitive or superior results compared with exact MICP, MCTS, and neural-network–based approaches on large graphs, with an open-source implementation. These contributions enable robust, scalable planning for informative sensing in dynamic and heterogeneous environments while supporting extensions to complex sensing modalities and multiple agents. The work has practical impact for real-world exploration, environmental monitoring, and search missions where information gain must be maximized within resource constraints.

Abstract

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.

Figures (13)

• Figure 1: Comparative analysis of computational runtime (left) and the objective function $\textbf{tr}(\Sigma)$ (right) as functions of the graph size. Three methods are compared: the mixed integer program formulation dutta2022informative, the exact formulation from \ref{['eq:exact_ipp']}, and the exact method using the B-IPP $\textbf{tr}(\Sigma^{-1})$ objective. Each curve shows the average runtime and objective value respectively with the standard error reported over 25 different simulations. The dashed line on the left indicates the 120 second runtime constraint imposed on all methods.
• Figure 2: Runtime and A-IPP objective as a function of graph size for the six methods considered. Each curve shows the average runtime and objective value respectively with the standard error reported over 25 different simulations. The dashed line on the left indicates the $120$ second runtime constraint imposed on all methods.
• Figure 3: Runtime and D-IPP objective as a function of graph size for the six methods considered. Each curve shows the average runtime and objective value respectively with the standard error reported over 25 different simulations. The dashed line on the left indicates the $120$ second runtime constraint imposed on all methods.
• Figure 4: Examples of trajectories produced by each of the six methods considered. For demonstration purposes, we have also included the multimodal sensing aspect discussed in \ref{['ss:multimodal']}. The magenta line indicates the trajectory of the agent through a graph of size $n=625$. The $m=20$ prediction locations are shown in white. The yellow points indicate where more accurate sensing locations were chosen. For visualization purposes, the variance is displayed across the entire grid rather than at the prediction locations only.
• Figure 5: Comparison of the convex multimodal sensor selection against MCTS multimodal sensor selection. These comparisons were done with $k=3$ high-quality sensors. We can see that the convex multimodal sensor selection tends to select more informative distributions of the high-quality sensors for both the A and D-IPP objectives.