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arxiv: 2604.26626 · v1 · submitted 2026-04-29 · 💻 cs.RO

STAR-Filter: Efficient Convex Free-Space Approximation via Starshaped Set Filtering in Noisy Environments

Yuwei Wu , Yichen Zhao , Dexter Ong , Vijay Kumar This is my paper

Pith reviewed 2026-05-07 13:04 UTC · model grok-4.3

classification 💻 cs.RO
keywords starshaped setsconvex free-spacepolytope generationrobot motion planningsensor noisecollision avoidancesafe flight corridorsquadrotor planning
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The pith

The STAR-Filter uses starshaped sets to identify active obstacle constraints and generate convex free-space regions faster with less conservatism in noisy data.

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

The paper presents STAR-Filter, which builds starshaped sets from obstacle points detected by sensors to quickly filter which points serve as active boundaries before creating convex shapes such as polytopes. This step replaces slower iterative optimization loops that struggle with complex or noisy environments and often produce overly tight regions. The construction aims to keep the final convex areas feasible for robot motion while expanding their usable volume compared with prior methods. Applications include generating Safe Flight Corridors and planning trajectories for quadrotors under real sensor noise.

Core claim

STAR-Filter employs starshaped set construction as a lightweight pre-filter that marks obstacle points as active supporting constraints for convex polytope generation. The filter reduces redundant computations in inflation-based methods, yielding lower run times and larger feasible volumes while remaining robust to sensor noise. Theoretical properties of the starshaped sets guarantee that the resulting convex regions stay feasible across environments of different complexity, and simulations on noisy large-scale data confirm the gains for Safe Flight Corridor construction and agile quadrotor flight.

What carries the argument

starshaped set construction that selects active supporting constraints from obstacle points to precondition convex polytope inflation

Load-bearing premise

Constructing starshaped sets from obstacle points correctly isolates only the active constraints needed for feasible convex regions without missing points that would cause collisions or empty spaces.

What would settle it

A test case with known ground-truth obstacle geometry and added sensor noise where the STAR-Filter polytope intersects an obstacle or blocks all feasible paths that a full non-filtered optimizer finds.

Figures

Figures reproduced from arXiv: 2604.26626 by Dexter Ong, Vijay Kumar, Yichen Zhao, Yuwei Wu.

Figure 1
Figure 1. Figure 1: Generation of a collision-free starshaped set from point clouds and a query point. Blue points are the extreme points of the starshaped set. gets flipped outside of the sphere. Moreover, f −1 R (fR(x)) = Id(x) = x, where f −1 R = fR. We show that (1) yields a starshaped set that preserves visibility. Proposition 1 (Starshaped set from sphere flipping). Let X = {xi} N i=1 be a finite set of points, Let B¯(q… view at source ↗
Figure 2
Figure 2. Figure 2: Iterative refinement of the polytope, ellipsoid, and associated normals. A subset of obstacle points serves as supporting points that determine the active hyperplanes of the polytope, and this subset is contained in the starshaped set. As shown in view at source ↗
Figure 3
Figure 3. Figure 3: Starshaped construction. (a) Monotonic expansion of a 2D starshaped region as R increases; darker to lighter (yellow) indicates increasing R. (b) Increased boundary sampling reduces region loss (region in blue). (c) 3D starshaped meshes. The augmented set S + R remains starshaped with respect to the query point and typically provides a larger and more robust inner approximation of the free space, as can be… view at source ↗
Figure 4
Figure 4. Figure 4: Evaluation maps (left to right): real, obstacle, maze. We evaluate the proposed framework using the benchmark pipeline in [37] using diverse environments. As shown in view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of performance by different ellipsoid initialization. and segment-aligned initialization generates the smallest final ellipsoid volumes. It does not improve performance and consistently leads to poor local optima. As this elongated ellipsoid introduces overly restrictive geometric constraints, re￾sulting in conservative polytope growth and limited expansion of the free space. Even in scenarios w… view at source ↗
Figure 6
Figure 6. Figure 6: Pairwise comparison of polytope volumes in maze maps with FIRI-lite as the x-axis reference. To further illustrate the volume differences across each test, we plot the pairwise comparisons against FIRI-lite on maze maps in view at source ↗
Figure 7
Figure 7. Figure 7: Convex polytopes over increasing temporal windows. The top row uses event￾based data, and the bottom row uses ground-truth LiDAR. convex regions from event camera point clouds and evaluate collisions against the ground-truth point cloud. The average rate of volume in collision is 0.0226± 0.0257. The results demonstrate that the proposed method achieves low-latency computation and enables fast incremental u… view at source ↗
Figure 8
Figure 8. Figure 8: Piecewise polynomial trajectories (in magenta) optimized within SFC. 7 Conclusion and Future Work We propose a framework for superfast polytope inflation that leverages star￾shaped set as an efficient filtering to accelerate polytope extraction. By filtering obstacle points that are likely to become active supporting constraints, the pro￾posed approach reduces the number of candidates considered during sep… view at source ↗
read the original abstract

Approximating collision-free space is fundamental to robot planning in complex environments. Convex geometric representations, such as polytopes and ellipsoids, are widely employed due to their structural properties, which can be easily integrated with convex optimization. Iterative optimization-based inflation methods can generate large volume polytopes in cluttered environments, but their efficiency degrades as the obstacle set becomes more complex or when sensor data are noisy. These methods are also sensitive to initialization and often rely on accurate geometric models. In this paper, we propose the STAR-Filter, a lightweight framework that employs starshaped set construction as a fast filter for convex region generation in collision-free space. By identifying obstacle points as active supporting constraints, the proposed method significantly reduces redundant computation while preserving feasibility and robustness to sensor noise. We provide theoretical and numerical analyses that characterize the structural properties of the starshaped set and proposed pipeline in environments of varying complexity. Simulation results show that the proposed framework achieves the lowest computation time and reduces conservativeness in polytope generation for real-world noisy and large-scale data. We demonstrate the effectiveness of the framework for Safe Flight Corridor (SFC) generation and agile quadrotor planning in noisy environments.

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 STAR-Filter, a lightweight framework that constructs starshaped sets from noisy obstacle points to identify active supporting constraints and filter them for subsequent convex polytope generation in free-space approximation. It claims this reduces redundant computation compared to iterative optimization-based inflation methods while preserving feasibility and robustness to sensor noise. Theoretical analyses characterize structural properties of the starshaped sets and pipeline; numerical analyses and simulations in environments of varying complexity show the lowest computation time and reduced conservativeness for real-world noisy/large-scale data. The framework is demonstrated on safe flight corridor (SFC) generation and agile quadrotor planning.

Significance. If the central claims hold, the work offers a practical advance for real-time convex optimization in robot motion planning under uncertainty, potentially enabling faster and less conservative free-space representations than existing methods without sacrificing safety. The combination of starshaped filtering with empirical validation on noisy data and planning tasks addresses a relevant gap in deploying convex techniques for cluttered, sensor-based environments.

major comments (2)
  1. [Theoretical Analysis] Theoretical Analysis section: the manuscript asserts that starshaped set construction identifies active supporting constraints while preserving feasibility and robustness to sensor noise, yet provides only characterization of starshaped properties rather than a formal theorem (e.g., proving the output convex region is always a subset of the true free space under bounded noise). This is load-bearing for the safety and reduced-conservativeness claims in planning applications.
  2. [Simulation Results] Simulation Results section: the claims of lowest computation time and reduced conservativeness rest on numerical comparisons, but the manuscript does not specify baseline implementations, exact error metrics, noise models, or data exclusion criteria; without these, the superiority for large-scale noisy data cannot be fully evaluated and risks overstatement.
minor comments (2)
  1. [Abstract] Abstract: include at least one key equation or quantitative metric (e.g., time reduction factor or volume ratio) to make the performance claims more concrete for readers.
  2. [Methods] Notation: ensure consistent definition of starshaped set parameters across the methods and theoretical sections to avoid ambiguity in the filtering step.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of the significance of our work. We address each major comment below and indicate the corresponding revisions to the manuscript.

read point-by-point responses

  1. Referee: [Theoretical Analysis] Theoretical Analysis section: the manuscript asserts that starshaped set construction identifies active supporting constraints while preserving feasibility and robustness to sensor noise, yet provides only characterization of starshaped properties rather than a formal theorem (e.g., proving the output convex region is always a subset of the true free space under bounded noise). This is load-bearing for the safety and reduced-conservativeness claims in planning applications.

    Authors: We acknowledge the referee's observation that the theoretical analysis provides characterizations of the structural properties of the starshaped sets and pipeline rather than an explicit formal theorem establishing that the output convex region is always a subset of the true free space under bounded noise. While the existing characterizations support the claims of feasibility preservation and robustness, we agree that a dedicated theorem would strengthen the safety guarantees for planning applications. In the revised manuscript, we will add a formal theorem proving the subset property based on the bounded noise assumption and the starshaped filtering mechanism, along with supporting corollaries on conservativeness. revision: yes

  2. Referee: [Simulation Results] Simulation Results section: the claims of lowest computation time and reduced conservativeness rest on numerical comparisons, but the manuscript does not specify baseline implementations, exact error metrics, noise models, or data exclusion criteria; without these, the superiority for large-scale noisy data cannot be fully evaluated and risks overstatement.

    Authors: We agree that the simulation results would be strengthened by explicit details on the experimental setup. In the revised manuscript, we will expand the Simulation Results section to specify: the exact baseline implementations (including the optimization-based inflation methods and their parameter settings); the precise error metrics (e.g., polytope volume ratios, computation times, and conservativeness measures); the noise models used (including distributions and variance parameters for sensor noise); and the data exclusion or preprocessing criteria applied to the real-world and large-scale datasets. These additions will improve reproducibility and allow fuller evaluation of the performance claims. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The paper introduces STAR-Filter as an independent lightweight framework that uses starshaped set construction to filter obstacle points as active supporting constraints before convex polytope generation. The abstract and provided context describe this as a new filtering step that reduces redundant computation while preserving feasibility and robustness to noise, followed by separate theoretical/numerical analyses of structural properties and simulation-based performance claims. No equations, fitted parameters, self-citations, or ansatzes are visible that would reduce any claimed prediction or result back to its own inputs by construction. The central claims rest on the proposed pipeline's design and empirical results rather than redefinitions or load-bearing self-references, making the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities beyond naming the STAR-Filter framework itself; no details on any fitted scales, geometric assumptions, or new postulated constructs.

pith-pipeline@v0.9.0 · 5512 in / 1001 out tokens · 69170 ms · 2026-05-07T13:04:05.146690+00:00 · methodology

discussion (0)

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