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Hierarchical Informative Path Planning via Graph Guidance and Trajectory Optimization

Avraiem Iskandar, Shamak Dutta, Kevin Murrant, Yash Vardhan Pant, Stephen L. Smith

TL;DR

The paper tackles informative path planning under a travel budget in cluttered environments by proposing a hierarchical pipeline that couples graph-based global guidance with edge-wise budget allocation and local spline-based trajectory refinement. It models the latent field with a Gaussian process and aims to minimize the posterior uncertainty over a test set, using a budget-constrained objective. The key contributions are the three-stage framework, geometric and kernel-informed bounds for budget allocation, and obstacle-aware trajectory refinement that yields faster runtimes while improving information gain over graph-only and fully continuous baselines. The approach is validated on synthetic obstacle scenarios and Arctic sea-ice datasets, showing up to 9× speedups over gradient-based solvers and 20× over black-box optimizers, with consistent reductions in posterior uncertainty. This framework has practical impact for efficient environmental monitoring and autonomous exploration in complex domains where both global structure and local sensing are critical.

Abstract

We study informative path planning (IPP) with travel budgets in cluttered environments, where an agent collects measurements of a latent field modeled as a Gaussian process (GP) to reduce uncertainty at target locations. Graph-based solvers provide global guarantees but assume pre-selected measurement locations, while continuous trajectory optimization supports path-based sensing but is computationally intensive and sensitive to initialization in obstacle-dense settings. We propose a hierarchical framework with three stages: (i) graph-based global planning, (ii) segment-wise budget allocation using geometric and kernel bounds, and (iii) spline-based refinement of each segment with hard constraints and obstacle pruning. By combining global guidance with local refinement, our method achieves lower posterior uncertainty than graph-only and continuous baselines, while running faster than continuous-space solvers (up to 9x faster than gradient-based methods and 20x faster than black-box optimizers) across synthetic cluttered environments and Arctic datasets.

Hierarchical Informative Path Planning via Graph Guidance and Trajectory Optimization

TL;DR

The paper tackles informative path planning under a travel budget in cluttered environments by proposing a hierarchical pipeline that couples graph-based global guidance with edge-wise budget allocation and local spline-based trajectory refinement. It models the latent field with a Gaussian process and aims to minimize the posterior uncertainty over a test set, using a budget-constrained objective. The key contributions are the three-stage framework, geometric and kernel-informed bounds for budget allocation, and obstacle-aware trajectory refinement that yields faster runtimes while improving information gain over graph-only and fully continuous baselines. The approach is validated on synthetic obstacle scenarios and Arctic sea-ice datasets, showing up to 9× speedups over gradient-based solvers and 20× over black-box optimizers, with consistent reductions in posterior uncertainty. This framework has practical impact for efficient environmental monitoring and autonomous exploration in complex domains where both global structure and local sensing are critical.

Abstract

We study informative path planning (IPP) with travel budgets in cluttered environments, where an agent collects measurements of a latent field modeled as a Gaussian process (GP) to reduce uncertainty at target locations. Graph-based solvers provide global guarantees but assume pre-selected measurement locations, while continuous trajectory optimization supports path-based sensing but is computationally intensive and sensitive to initialization in obstacle-dense settings. We propose a hierarchical framework with three stages: (i) graph-based global planning, (ii) segment-wise budget allocation using geometric and kernel bounds, and (iii) spline-based refinement of each segment with hard constraints and obstacle pruning. By combining global guidance with local refinement, our method achieves lower posterior uncertainty than graph-only and continuous baselines, while running faster than continuous-space solvers (up to 9x faster than gradient-based methods and 20x faster than black-box optimizers) across synthetic cluttered environments and Arctic datasets.
Paper Structure (29 sections, 3 theorems, 34 equations, 9 figures, 1 table)

This paper contains 29 sections, 3 theorems, 34 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Work
  4. Graph-based
  5. Continuous-space
  6. Problem Formulation and Approach
  7. Problem Formulation
  8. Hierarchical Approach Outline
  9. Graph-based stage
  10. Budget allocation stage
  11. Trajectory refinement stage
  12. Graph-Based Planning Stage
  13. Budget Allocation Stage
  14. Geometric Region Bounding
  15. Informative Region Bounding
  16. ...and 14 more sections

Key Result

Lemma 1

Let $\gamma: [0, 1] \to \mathbb{R}^d$ be a piecewise continuously differentiable curve. We define the arc length from $a$ to $b$ as $\operatorname{Length}(a \to b) := \int_a^b \|\gamma'(t)\| \, dt.$ In particular, $\operatorname{Length}(\gamma) := \operatorname{Length}(0 \to 1)$. Then:

Figures (9)

  • Figure 1: Illustration of the setting: a ship (yellow) navigates in the Arctic to collect measurements at target locations (orange), while planning a trajectory (black) to reach the goal region (green) under a strict travel budget.
  • Figure 2: An instance of informative path planning in $\mathcal{M}_{\text{free}}$. The robot moves from start $s$ (green circle) to goal $g$ (orange circle) along two trajectories $\gamma$: a higher-budget (purple) and a shorter-budget (dark green) trajectory, each collecting $n = 8$ measurements (dots). Test points $T$ (blue crosses) are locations of interest, and obstacles (light red) must be avoided. The longer path is able to take measurements closer to test points, while the shorter path is limited by its budget.
  • Figure 3: Illustration of the hierarchical IPP framework. A collision-free graph path provides global guidance. The path budget is then allocated across segments by maximizing coverage of test points using geometric and kernel-influence bounds. Finally, each segment is refined into a smooth spline trajectory that enforces obstacle and length constraints while pruning irrelevant obstacles, resulting in a continuous collision-free informative trajectory.
  • Figure 4: Left: Any trajectory starting at point $u$ and ending at $v$ with total length at most $L$ is fully contained within the ellipse $\mathcal{E}(u, v, L)$, defined by foci $u$, $v$ and major axis length $L$. Right: The converse does not hold, a trajectory that remains entirely within the ellipse can still exceed length $L$ if it contains loops.
  • Figure 5: The Minkowski sum of the ellipse $\mathcal{E}(u, v, L)$ and a ball of radius $r_{\mathrm{kernel}}$. The resulting region represents all points within distance $r_{\mathrm{kernel}}$ from some point on the ellipse.
  • ...and 4 more figures

Theorems & Definitions (12)

  • Lemma 1: Arc Length Bounds via Triangle Inequality
  • proof
  • Definition 1: Elliptical Region
  • Lemma 2: Elliptical Containment of Length-Bounded Trajectories
  • proof
  • Remark 1
  • Definition 2: Minkowski Sum
  • Lemma 3: Kernel Influence Radius via Minkowski Sum
  • proof
  • Remark 2: Negligible Effect of Distant Test Points
  • ...and 2 more