arxiv: 2604.17679 · v1 · submitted 2026-04-20 · 💻 cs.RO

Recognition: unknown

A Hamilton-Jacobi Reachability-Guided Search Framework for Efficient and Safe Indoor Planar Robot Navigation

Hanyang Hu , Cameron Siu , Mo Chen

Authors on Pith no claims yet

Pith reviewed 2026-05-10 05:18 UTC · model grok-4.3

classification 💻 cs.RO

keywords robot navigationHamilton-Jacobi reachabilitygraph searchpath planningsafety constraintsheuristicsindoor environmentsdynamic obstacles

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The pith

Precomputed Hamilton-Jacobi reachability value functions guide online graph search to make robot navigation both faster and safer.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to improve autonomous indoor robot navigation so that paths can be found quickly while avoiding collisions even when the space contains moving people or unknown obstacles. It does so by computing Hamilton-Jacobi reachability value functions once offline and then feeding those values into a standard graph-search planner at runtime. The precomputed values act both as better-than-default heuristics that prune the search tree and as explicit safety constraints that keep candidate paths away from dangerous states. Because the search itself runs online, the method can react to new sensor data without needing a complete static map in advance. The result is a planner that runs faster than pure graph search yet remains safer than methods that ignore reachability.

Core claim

Precomputed HJ value functions, used as informative heuristics and proactive safety constraints, amortize online computation of the graph search process. At the same time, graph search enables reachability-based reasoning to be incorporated into online planning, overcoming the long-standing challenge of HJ reachability requiring full knowledge of the environment.

What carries the argument

Offline-computed Hamilton-Jacobi reachability value functions inserted into online graph search both to steer the search with admissible heuristics and to enforce proactive safety constraints on candidate paths.

If this is right

Online planning time decreases because the precomputed values prune large portions of the search space.
Safety improves because unsafe states are excluded before the robot commits to a path.
The planner works with only partial or incrementally revealed environment information.
Performance gains appear in both simulation and physical indoor experiments with and without humans.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same offline-online split could be tried with other reachability or optimal-control precomputations in 3D or non-planar robot models.
If the environment changes faster than the precomputation can be refreshed, an incremental update scheme for the value functions would be needed.
The approach might transfer to other graph-search domains such as motion planning for manipulators or multi-robot coordination where safety margins are critical.

Load-bearing premise

The precomputed reachability values remain accurate enough to guide search and enforce safety even when the real environment differs from the one used for precomputation or contains moving obstacles.

What would settle it

Deploy the planner in a controlled indoor testbed with moving human obstacles, measure wall-clock planning time and collision rate against standard A* and pure HJ baselines, and check whether the hybrid method loses its reported advantage in either metric.

Figures

Figures reproduced from arXiv: 2604.17679 by Cameron Siu, Hanyang Hu, Mo Chen.

**Figure 2.** Figure 2: Heuristic comparisons for the robot at two orientations: [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: , the volume of the BRT increases with the robot’s speed (positive z-axis direction), reflecting the reduced ability of the robot to avoid collisions at higher velocities. This pruning strategy is particularly effective for static obstacles. Since obstacle configurations remain unchanged over time, dangerous nodes can be identified and pruned as soon as their BRT values approach the safety threshold ϵmap,… view at source ↗

**Figure 4.** Figure 4: The influence of heading angle and relative distance [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Simulated navigation costmap with static obstacles. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: Left: ANA* w/ Dist created a trajectory requiring continuous backward movement (The heading angles represented by arrows are always pointing downwards). Right: ANA* w/ TTR generated a more reasonable trajectory where the robot reversed briefly and reoriented toward the goal. B. Pruning Strategies Comparison BRT pruner improves the search efficiency and trajectory safety by cutting off the nodes that will … view at source ↗

**Figure 7.** Figure 7: Left: ANA* w/ OBS pruner got too close to the obstacle to find the goal; Right: ANA* w/ BRT pruner eliminated dangerous nodes early and found the goal. As for ANA*-based planners, we compared the effects of two pruning strategies under the same long-distance setting with 12 initial groups. As shown in Table IV, ANA* equipped with the OBS pruner failed in 4 out of the 12 tasks, whereas the version with the … view at source ↗

**Figure 8.** Figure 8: A sequence from the Face-to-Face scenario with the [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗

**Figure 9.** Figure 9: Layout of the two static environments: Long Hallway [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗

**Figure 10.** Figure 10: Comparison of the OBS and BRT pruners across consecutive timesteps (from [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗

**Figure 11.** Figure 11: Layout of the dynamic environment. Dotted lines [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗

read the original abstract

Autonomous navigation requires planning to reach a goal safely and efficiently in complex and potentially dynamic environments. Graph search-based algorithms are widely adopted due to their generality and theoretical guarantees when equipped with admissible heuristics. However, the computational complexity of graph search grows rapidly with the dimensionality of the search space, often making real-time planning in dynamic environments intractable. In this paper, we combine offline Hamilton-Jacobi (HJ) reachability with online graph search to leverage the complementary strengths of both. Precomputed HJ value functions, used as informative heuristics and proactive safety constraints, amortize online computation of the graph search process. At the same time, graph search enables reachability-based reasoning to be incorporated into online planning, overcoming the long-standing challenge of HJ reachability requiring full knowledge of the environment. Extensive simulation studies and real-world experiments demonstrate that the proposed approach consistently outperforms baseline methods in terms of planning efficiency and navigation safety, in environments with and without human presence.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper combines precomputed HJ value functions as heuristics and safety constraints inside graph search for indoor planar robot navigation, which is a reasonable engineering step but does not fully escape the full-environment-model requirement.

read the letter

The punchline is that the authors precompute Hamilton-Jacobi reachability value functions offline and then feed them into an online graph search planner, using the values both to guide the search and to enforce safety margins. This hybrid lets them keep some formal safety properties while making the planner fast enough for real-time indoor use with a planar robot. They report that it beats baselines on planning time and collision avoidance in simulations and on a physical robot, including scenes with humans present. That integration is the actual new piece; it is not just another HJ paper or another A* variant. The work does a clean job of showing how the offline computation amortizes the expensive reachability solve and how the search step lets the system react to a goal without re-solving the full differential game every time. The real-robot experiments with human presence are a plus for relevance. The soft spot is exactly the one flagged in the stress-test note. Precomputing the value functions still requires a complete model of the workspace, obstacles, and robot dynamics. The abstract claims the method overcomes the “full knowledge” limitation of pure HJ reachability, but the precomputation step itself does not. If the indoor space contains unmodeled moving people or unknown static obstacles, the stored functions become either invalid or overly conservative; the paper would need to show explicitly how it bounds or updates those functions online to keep the safety claims intact. Without the quantitative tables or baseline descriptions in the abstract it is also hard to judge how large the reported gains actually are. The math and citations look standard for this subfield and do not raise obvious red flags. This is useful reading for anyone working on safe, real-time navigation in human-shared indoor spaces. A reader who already knows HJ reachability and graph search will pick up the practical integration tricks quickly. It is worth sending to peer review; the core idea is sound enough that referees can usefully pressure the dynamic-environment assumptions and the experimental evidence.

Referee Report

2 major / 2 minor

Summary. The paper proposes a hybrid navigation framework for planar indoor robots that precomputes Hamilton-Jacobi (HJ) reachability value functions offline and uses them online as informative heuristics and proactive safety constraints within a graph-search planner. This combination is claimed to amortize online computation while incorporating reachability-based safety reasoning, thereby overcoming HJ reachability's traditional requirement for full environment knowledge. The approach is evaluated in simulations and real-world experiments (with and without humans) and asserted to consistently outperform baseline methods in planning efficiency and navigation safety.

Significance. If the integration is sound and the experimental claims hold, the work would be significant for bridging offline safety analysis with online adaptability in robot motion planning. It directly targets the computational intractability of high-dimensional graph search and the full-knowledge limitation of HJ methods, offering a practical path toward safer real-time navigation in dynamic indoor spaces. The use of precomputed value functions to guide search while retaining graph-search generality is a conceptually clean contribution.

major comments (2)

[Abstract and §1] Abstract and §1 (Introduction): The central claim that graph search 'overcomes the long-standing challenge of HJ reachability requiring full knowledge of the environment' requires clarification. Precomputing the HJ value functions still demands a complete differential-game model (workspace, obstacles, robot dynamics) at offline time. The manuscript must explicitly address how the method remains safe and effective when the online environment deviates from this model (e.g., unmodeled moving humans, partial observability, or layout changes), and whether the safety constraints remain valid or become conservative over-approximations.
[§4] §4 (Experimental Evaluation) and associated tables/figures: The abstract states that the method 'consistently outperforms baseline methods' in efficiency and safety, yet no quantitative metrics, baseline descriptions, success rates, timing distributions, or statistical significance tests are referenced. Without these details it is impossible to evaluate whether the hybrid approach delivers practically meaningful gains or merely marginal improvements under the tested conditions.

minor comments (2)

[§3] Notation for the HJ value function and its embedding into the graph-search heuristic should be defined more explicitly (e.g., how the value function is discretized and queried during A* or similar search).
[§2] The manuscript should include a clear statement of the assumptions on environment dynamics (static vs. moving obstacles) and whether the precomputed HJ functions are recomputed or adapted online.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and insightful comments on our manuscript. We have carefully considered each point and provide point-by-point responses below. Where appropriate, we have made revisions to clarify our contributions and strengthen the experimental presentation.

read point-by-point responses

Referee: [Abstract and §1] Abstract and §1 (Introduction): The central claim that graph search 'overcomes the long-standing challenge of HJ reachability requiring full knowledge of the environment' requires clarification. Precomputing the HJ value functions still demands a complete differential-game model (workspace, obstacles, robot dynamics) at offline time. The manuscript must explicitly address how the method remains safe and effective when the online environment deviates from this model (e.g., unmodeled moving humans, partial observability, or layout changes), and whether the safety constraints remain valid or become conservative over-approximations.

Authors: We thank the referee for highlighting this important clarification. The precomputation indeed requires a complete nominal model offline. However, the integration with graph search allows the planner to use online sensor information to update the search graph and replan in real time, thereby handling deviations from the nominal model such as moving humans or layout changes without needing full knowledge at runtime. The safety constraints from the HJ value functions are used as conservative over-approximations in the online phase; they ensure collision avoidance with respect to the modeled obstacles but may result in more conservative paths when unmodeled elements are present. We have revised §1 to include an explicit discussion of these points, the assumptions made, and the conditions under which the safety guarantees hold or become conservative. This addresses the central claim more precisely. revision: yes
Referee: [§4] §4 (Experimental Evaluation) and associated tables/figures: The abstract states that the method 'consistently outperforms baseline methods' in efficiency and safety, yet no quantitative metrics, baseline descriptions, success rates, timing distributions, or statistical significance tests are referenced. Without these details it is impossible to evaluate whether the hybrid approach delivers practically meaningful gains or merely marginal improvements under the tested conditions.

Authors: We agree that the abstract does not reference the specific quantitative results. In §4, we provide detailed experimental results including baseline descriptions (A* with different heuristics, sampling-based methods), success rates across multiple trials, timing distributions shown in figures, path efficiency metrics, and safety statistics (e.g., minimum distances). Statistical significance is evaluated using paired t-tests. To improve clarity, we have revised the abstract to briefly mention key performance improvements and added references to the relevant tables and figures in the introduction. We have also ensured all quantitative details are prominently presented in §4. These changes allow readers to better assess the practical significance of the gains. revision: yes

Circularity Check

0 steps flagged

No circularity: algorithmic hybrid with independent components

full rationale

The paper describes a practical combination of offline precomputed HJ value functions (as heuristics and safety constraints) with online graph search. No derivation chain, equations, or theorems are presented that reduce by construction to their own inputs. The central claim is an engineering integration that amortizes computation and relaxes full-environment requirements at runtime; this is supported by simulations and experiments rather than self-referential logic. No self-citations, ansatzes, or renamings function as load-bearing steps in any mathematical sense.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper is an algorithmic proposal that builds on established HJ reachability and graph-search methods; the abstract introduces no new free parameters, mathematical axioms, or invented entities.

pith-pipeline@v0.9.0 · 5466 in / 1144 out tokens · 54954 ms · 2026-05-10T05:18:01.206739+00:00 · methodology

discussion (0)

Reference graph

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