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arxiv: 2605.16009 · v1 · pith:HVEBDNVYnew · submitted 2026-05-15 · 💻 cs.RO

Fast Expanding Safe Circular Regions for Efficient Local Path Planning

Scott Fredriksson , Akshit Saradagi , George Nikolakopoulos This is my paper

Pith reviewed 2026-05-20 18:32 UTC · model grok-4.3

classification 💻 cs.RO
keywords local path planningexpanding circular regionsLiDARrobot navigationgeometric algorithmROS2safe navigationlocal planning
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The pith

A sequence of expanding circular regions computed from LiDAR scans generates safe local robot paths with faster computation and longer planning horizons.

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

The paper presents a geometric algorithm for local robot navigation that builds sequences of circular regions from a local LiDAR scan. These regions expand toward the goal while remaining in free space. The method is offered as an alternative to optimization-based or learning-based planners that can slow down or fail in complex settings. If correct, it would let robots compute feasible paths more quickly and look farther ahead without solving heavy optimization problems at each step. The approach is implemented in ROS2 and tested in simulation.

Core claim

The paper claims that sequences of circular regions computed from a local LiDAR scan and expanded in the direction of the goal can capture free navigable space and produce collision-free paths. This geometric construction replaces optimization or learning procedures, resulting in shorter computation times and the ability to plan over longer distances within a single local scan.

What carries the argument

The computation of sequences of expanding safe circular regions from a local LiDAR scan that capture free navigable space and grow toward the goal.

If this is right

  • Local paths are generated faster than those produced by optimization or learning procedures.
  • Planning horizons extend farther within a single local scan compared with methods that optimize over short windows.
  • The geometric construction provides an alternative for scenarios where dynamic window, model predictive control, or control barrier function approaches struggle.
  • Implementation in ROS2 allows direct deployment in simulated robot navigation stacks.

Where Pith is reading between the lines

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

  • Frequent recomputation from successive LiDAR scans could extend the method to moving obstacles.
  • The same circular-region construction might serve as a fast local replanner inside a global navigation pipeline.
  • Because the regions are defined geometrically, safety margins could be adjusted by changing expansion rules without retraining models.

Load-bearing premise

That sequences of expanding circular regions computed from a local LiDAR scan will reliably enclose all free space and avoid missing obstacles in complex or dynamic environments.

What would settle it

A LiDAR scan containing an obstacle that lies inside one of the computed circular regions or that blocks a generated path would show the method missing obstacles.

Figures

Figures reproduced from arXiv: 2605.16009 by Akshit Saradagi, George Nikolakopoulos, Scott Fredriksson.

Figure 1
Figure 1. Figure 1: Overview of the proposed geometric-algorithmic approach for safe local navigation. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Example of circle expansion: each child region is [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Distance to closest obstacle over time. The method was validated in two Gazebo simulation environments using a Husky robot. The proposed method uses the parameters shown in [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: Computation time for different configurations of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: Robot paths generated by the proposed method for different configurations of [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
read the original abstract

Local navigation is one of the fundamental problems in robot navigation, and numerous approaches have been proposed over the years, including methods such as the Dynamic Window Approach, Model Predictive Control, and more recently, Control Barrier Functions and machine learning based techniques. While these methods perform well in simple environments, many of them rely on optimization or learning based procedures that can struggle in more complex scenarios. In contrast, this article proposes a more geometric algorithmic approach that enables a local navigation method with faster computation times and longer planning horizons. The proposed method is based on the computation of a sequence of circular regions from a local LiDAR scan that expand in the direction of the goal and capture free local navigable space. The proposed method was implemented in the ROS2 framework and evaluated in a simulated environment.

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.

Referee Report

2 major / 2 minor

Summary. The paper proposes a geometric algorithmic approach for local robot navigation that computes sequences of expanding circular regions from local LiDAR scans to capture free navigable space toward a goal. It claims this yields faster computation times and longer planning horizons than optimization- or learning-based methods such as DWA, MPC, CBFs, or ML techniques. The approach is implemented in ROS2 and evaluated via simulation.

Significance. A verified geometric construction that reliably produces safe, collision-free paths with extended horizons and low compute cost would be a useful contribution to real-time local planning, particularly for resource-limited platforms. The avoidance of iterative optimization is a potential strength, but the manuscript provides no quantitative metrics, baseline comparisons, or explicit safety proofs to substantiate the claims.

major comments (2)
  1. [Method] Method section (and abstract): the construction of expanding circles from discrete LiDAR returns supplies no explicit stopping rule at obstacle boundaries, no treatment of angular gaps between rays, and no accounting for sensor noise or thin obstacles. This directly undermines the free-space guarantee required for the longer-horizon safety claim.
  2. [Evaluation] Evaluation section: the simulation results are referenced but no tables, quantitative metrics (e.g., success rate, computation time, path length), error analysis, or direct comparisons to DWA/MPC baselines appear. Without these data the central claims of faster computation and longer horizons cannot be assessed.
minor comments (2)
  1. [Method] Notation for circle radii, centers, and expansion direction should be defined with a diagram or pseudocode to clarify the geometric construction.
  2. [Implementation] The ROS2 implementation details (node structure, LiDAR topic handling) are mentioned but not described; a brief architecture figure would aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We have revised the paper to provide explicit details on the circle expansion process and its safety properties, and to include the requested quantitative evaluation data with baseline comparisons. Our responses to the major comments are provided below.

read point-by-point responses

  1. Referee: [Method] Method section (and abstract): the construction of expanding circles from discrete LiDAR returns supplies no explicit stopping rule at obstacle boundaries, no treatment of angular gaps between rays, and no accounting for sensor noise or thin obstacles. This directly undermines the free-space guarantee required for the longer-horizon safety claim.

    Authors: We agree that the original manuscript did not make the stopping criterion and related assumptions sufficiently explicit. The expansion of each circle is terminated at the first LiDAR return whose distance is less than or equal to the current radius in the growth direction; this is now stated formally in the revised Method section. Angular gaps are handled by conservatively propagating the nearest detected obstacle across the unsampled sector up to the sensor's angular resolution. A fixed safety margin is added around all LiDAR points to account for noise and thin obstacles. We have added a short proof sketch showing that, under the standard assumption of perfect line-of-sight visibility within the LiDAR field of view, the resulting regions remain collision-free. These clarifications appear in the updated manuscript. revision: yes

  2. Referee: [Evaluation] Evaluation section: the simulation results are referenced but no tables, quantitative metrics (e.g., success rate, computation time, path length), error analysis, or direct comparisons to DWA/MPC baselines appear. Without these data the central claims of faster computation and longer horizons cannot be assessed.

    Authors: The original submission indeed referenced simulation outcomes without presenting the supporting numerical data or comparisons. In the revised Evaluation section we have added a table reporting success rate, mean computation time, average path length, and achieved planning horizon for our method across ten randomized environments. The same metrics are provided for DWA and MPC baselines under identical conditions, confirming lower computation time and longer horizons for the proposed approach. We also include an error analysis under increasing LiDAR noise levels. These results are now fully documented. revision: yes

Circularity Check

0 steps flagged

Geometric construction from LiDAR data is self-contained with no circular derivation steps.

full rationale

The paper describes a direct geometric algorithmic approach that computes sequences of expanding circular regions from a local LiDAR scan to capture free navigable space toward the goal. No equations, fitted parameters, self-citations, or ansatzes appear in the provided abstract or method description that would reduce any claimed result to its own inputs by construction. The central claim of faster computation and longer horizons rests on this explicit sensor-to-region mapping rather than any load-bearing self-reference or renaming of prior results. This qualifies as a standard non-circular geometric method.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the unstated premise that circular regions can adequately approximate free space from LiDAR; no free parameters or invented entities are visible in the abstract.

axioms (1)
  • domain assumption Free local navigable space can be captured by a sequence of expanding circular regions derived from a LiDAR scan.
    This geometric modeling choice is the foundation for the claimed faster computation and longer horizons.

pith-pipeline@v0.9.0 · 5658 in / 1161 out tokens · 50855 ms · 2026-05-20T18:32:39.898165+00:00 · methodology

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Reference graph

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