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Navigating in Uncertain Environments with Heterogeneous Visibility

Jongann Lee, Melkior Ornik

TL;DR

A novel heuristic algorithm is proposed that balances the cost of detouring to high-visibility locations against the gain in information by optimizing the sum of a custom observation reward and the cost of traversal.

Abstract

Navigating an environment with uncertain connectivity requires a strategic balance between minimizing the cost of traversal and seeking information to resolve map ambiguities. Unlike previous approaches that rely on local sensing, we utilize a framework where nodes possess varying visibility levels, allowing for observation of distant edges from certain vantage points. We propose a novel heuristic algorithm that balances the cost of detouring to high-visibility locations against the gain in information by optimizing the sum of a custom observation reward and the cost of traversal. We introduce a technique to sample the shortest path on numerous realizations of the environment, which we use to define an edge's utility for observation and to quickly estimate the path with the highest reward. Our approach can be easily adapted to a variety of scenarios by tuning a single hyperparameter that determines the importance of observation. We test our method on a variety of uncertain navigation tasks, including a map based on real-world topographical data. The method demonstrates lower mean cost of traversal compared to a shortest path baseline that does not consider observation and has exponentially lower computational overhead compared to an existing method for balancing observation with path cost minimization.

Navigating in Uncertain Environments with Heterogeneous Visibility

TL;DR

A novel heuristic algorithm is proposed that balances the cost of detouring to high-visibility locations against the gain in information by optimizing the sum of a custom observation reward and the cost of traversal.

Abstract

Navigating an environment with uncertain connectivity requires a strategic balance between minimizing the cost of traversal and seeking information to resolve map ambiguities. Unlike previous approaches that rely on local sensing, we utilize a framework where nodes possess varying visibility levels, allowing for observation of distant edges from certain vantage points. We propose a novel heuristic algorithm that balances the cost of detouring to high-visibility locations against the gain in information by optimizing the sum of a custom observation reward and the cost of traversal. We introduce a technique to sample the shortest path on numerous realizations of the environment, which we use to define an edge's utility for observation and to quickly estimate the path with the highest reward. Our approach can be easily adapted to a variety of scenarios by tuning a single hyperparameter that determines the importance of observation. We test our method on a variety of uncertain navigation tasks, including a map based on real-world topographical data. The method demonstrates lower mean cost of traversal compared to a shortest path baseline that does not consider observation and has exponentially lower computational overhead compared to an existing method for balancing observation with path cost minimization.
Paper Structure (13 sections, 4 equations, 4 figures, 4 tables, 1 algorithm)

This paper contains 13 sections, 4 equations, 4 figures, 4 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. PROBLEM FORMULATION
  3. RELATED WORKS
  4. METHOD
  5. Short Diverse Path Sampling
  6. Edge Utility and Observation Reward
  7. Path Reward Maximization
  8. EXPERIMENTS
  9. Plateau Environment
  10. Procedurally Generated Environments
  11. Natural Terrain Environment
  12. Ablation Study
  13. CONCLUSIONS

Figures (4)

  • Figure 1: Short Diverse Path Sampling: We generate a set of short diverse paths by repeatedly generating the shortest path, then placing an obstacle on the path to generate a blocked environment. The generated set of paths forms a rooted tree.
  • Figure 2: Plateau Environment: A grid environment with plateaus (high visibility, high entry cost). Chokepoint edges have an independent blockage probability $p$ (not used during planning).
  • Figure 3: Procedurally Generated Environment Test Results: The performance improvement $(\%)$ of our method with $\lambda=3$ compared to $\lambda=0$. The top pie charts show the fraction of maps where $\lambda=3$ is better, equal or worse. The bottom histograms show the distribution of non-zero improvements.
  • Figure 4: Natural Terrain Navigation: Result of navigation from the top right to the bottom left on a real topographical map, comparing the shortest path baseline (blue) and our proposed method (red). The dashed lines show the initial intended path and the solid lines shows the actual path used.