pith. sign in

arxiv: 2605.20566 · v1 · pith:KFLQX2FMnew · submitted 2026-05-19 · 💻 cs.RO

Conflict-Aware Active Perception and Control in 3D Gaussian Splatting Fields via Control Barrier Functions

Amirhossein Mollaei Khass , Athanasios Cosse , Vivek Pandey , Nader Motee This is my paper

Pith reviewed 2026-05-21 06:12 UTC · model grok-4.3

classification 💻 cs.RO
keywords 3D Gaussian splattingcontrol barrier functionsactive perceptioncollision riskquadratic programmingrobot navigationinformation gainsafety-critical control
0
0 comments X

The pith

A control barrier function built from average value-at-risk on 3D Gaussian splatting keeps robots safe while they choose informative viewpoints.

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 resolve the built-in conflict that arises when a robot must both avoid collisions and gather observations that reduce uncertainty in a partially known scene. It represents the environment with 3D Gaussian splatting and converts an average value-at-risk measure of collision probability into a control barrier function that is guaranteed to keep the robot inside a chosen safe set. Perception is handled by a risk-aware form of expected information gain together with auxiliary barrier functions that steer the camera toward directions of greatest uncertainty reduction. These competing goals are combined inside one quadratic program that treats the safety constraint as hard and relaxes the perception terms with slack variables. If the construction holds, robots could explore and map uncertain spaces more thoroughly without sacrificing the safety guarantees that standard planners often lose when they chase information.

Core claim

The authors establish that a Control Barrier Function derived from an Average Value-at-Risk collision-risk metric defined on a 3D Gaussian Splatting representation renders a prescribed safe set forward invariant. At the same time, a risk-aware Expected Information Gain criterion and perception barrier functions drive the robot toward viewpoints that reduce map uncertainty. These objectives are unified in a single quadratic program that enforces the safety barrier as a hard constraint while softening the perception objectives through slack variables.

What carries the argument

The unified safety-critical, perception-aware quadratic program, which enforces the CBF safety inequality as a hard constraint and relaxes perception objectives with slack variables.

If this is right

  • The robot maintains forward invariance of the safe set even while moving toward regions of high geometric uncertainty.
  • Risk-aware expected information gain selects next-best views that trade information against estimated collision probability.
  • Perception barrier functions actively align camera orientation with the local direction of steepest uncertainty reduction.
  • The quadratic program produces trajectories that improve both collision avoidance and map uncertainty reduction in simulation.

Where Pith is reading between the lines

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

  • The same barrier-function construction could be applied to other scene representations if an analogous uncertainty metric can be defined.
  • Real-world performance would require empirical validation that the average value-at-risk values track actual collision rates under sensor noise.
  • Extending the method to dynamic scenes would need an online update rule for the risk metric as new observations arrive.
  • The quadratic-program structure is compatible with receding-horizon planners that could add longer-term prediction.

Load-bearing premise

The average value-at-risk metric extracted from the 3D Gaussian splatting model is accurate enough to let the derived barrier function keep the robot inside the safe set even when real sensor noise and model mismatch are present.

What would settle it

Execute the controller on a robot whose 3D Gaussian splatting model is known to omit some obstacles; record whether any executed trajectory intersects the true geometry of those omitted obstacles.

Figures

Figures reproduced from arXiv: 2605.20566 by Amirhossein Mollaei Khass, Athanasios Cosse, Nader Motee, Vivek Pandey.

Figure 1
Figure 1. Figure 1: Comparison of navigation trajectories in Stonehenge [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Trajectory for Case Study II (q = 2) where the robot reduces map uncertainty while navigating. Green segments indicate active perception (hπ > 0) with no conflict. Red segments indicate perception relaxation (hπ ≤ 0), either due to safety constraints or low information gain in the trajectory relevant region. the unicycle dynamics, the safety barrier functions hs have relative degree one, and hence the corr… view at source ↗
Figure 6
Figure 6. Figure 6: Results follow the same simulation as Figure 2 as Case [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: Trajectories for Case Study III correspond to Figure 4. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

Active perception in uncertain environments requires robots to navigate safely while acquiring informative observations to reduce map uncertainty. These objectives inherently conflict, as informative viewpoints often lie near uncertain regions with higher collision risk. To address this challenge, we develop a conflict-aware active perception and control framework for robotic systems operating in environments represented by 3D Gaussian Splatting (3DGS). Safety is enforced using a Control Barrier Function (CBF) derived from an Average Value-at-Risk AV@R collision-risk metric that accounts for geometric uncertainty and guarantees forward invariance of a safe set. To improve perception, we propose a risk-aware Expected Information Gain (EIG) formulation for selecting the next-best-view and introduce perception barrier functions that align the camera orientation with the local information-ascent direction. To obtain a tractable formulation for these conflicting safety and perception objectives, we propose a unified safety-critical, perception-aware quadratic program that enforces safety as a hard constraint while relaxing perception constraints through slack variables. Simulation results demonstrate that the proposed method improves both safety and information acquisition compared to existing 3DGS-based approaches.

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 manuscript develops a conflict-aware framework for active perception and control in 3D Gaussian Splatting (3DGS) environments. Safety is enforced via a Control Barrier Function (CBF) derived from an Average Value-at-Risk (AV@R) collision-risk metric that accounts for geometric uncertainty and is claimed to guarantee forward invariance of a safe set. Perception is improved via a risk-aware Expected Information Gain (EIG) formulation and perception barrier functions that align camera orientation with information ascent. These objectives are combined in a unified quadratic program (QP) that treats safety as a hard constraint while relaxing perception constraints with slack variables. Simulation results are presented to show improvements in safety and information acquisition over prior 3DGS-based methods.

Significance. If the forward-invariance guarantee holds under realistic sensor noise and map updates, the work would provide a concrete method for reconciling safety-critical control with active perception in uncertain 3D scenes. The use of AV@R within a CBF and the risk-aware EIG are technically interesting extensions, but the significance is tempered by the absence of detailed verification that the risk gradient remains well-defined and that the safe set remains invariant when 3DGS parameters are estimates rather than ground truth.

major comments (2)
  1. [Abstract, §3] Abstract and §3 (Safety Enforcement): The claim that the AV@R-derived CBF 'guarantees forward invariance of a safe set' is load-bearing for the central contribution, yet the manuscript provides no explicit derivation of the Lie derivative condition that accounts for how control inputs simultaneously affect state evolution and reduce map uncertainty through new viewpoints. The formulation appears to treat the 3DGS representation as a fixed probabilistic model whose risk gradient can be evaluated exactly; any non-differentiability arising from splat rendering or unmodeled sensor noise would violate the standard CBF decrease condition.
  2. [§4] §4 (Perception Barrier Functions and QP Formulation): The unified QP enforces safety as a hard constraint while relaxing perception constraints via slack variables, but the manuscript does not analyze how the choice of risk threshold or slack penalty affects the trade-off or whether the resulting closed-loop trajectories remain inside the claimed safe set when the AV@R metric is recomputed online.
minor comments (2)
  1. [§2] Notation for the AV@R risk metric and its gradient with respect to camera pose should be introduced earlier and used consistently across the safety and perception sections.
  2. [§5] Simulation figures would benefit from explicit reporting of the number of Monte Carlo trials, the distribution of initial map uncertainty, and quantitative metrics (e.g., collision rate, cumulative EIG) with error bars.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough and constructive review of our manuscript. We address each major comment point by point below, providing clarifications and indicating the revisions made to strengthen the presentation of the forward invariance guarantee and the QP analysis.

read point-by-point responses

  1. Referee: [Abstract, §3] Abstract and §3 (Safety Enforcement): The claim that the AV@R-derived CBF 'guarantees forward invariance of a safe set' is load-bearing for the central contribution, yet the manuscript provides no explicit derivation of the Lie derivative condition that accounts for how control inputs simultaneously affect state evolution and reduce map uncertainty through new viewpoints. The formulation appears to treat the 3DGS representation as a fixed probabilistic model whose risk gradient can be evaluated exactly; any non-differentiability arising from splat rendering or unmodeled sensor noise would violate the standard CBF decrease condition.

    Authors: We agree that an explicit derivation of the Lie derivative is necessary to rigorously support the forward invariance claim. In the original formulation, the AV@R-based barrier function is defined on the current 3DGS estimate and the CBF condition is enforced along the robot state dynamics, with the map treated as fixed over the continuous-time control interval (a standard assumption in CBF literature for environments with slowly evolving uncertainty). Map updates occur discretely via the perception module. To address the referee's concern, we have revised Section 3 to include a detailed derivation of the Lie derivative that accounts for the dependence of the risk metric on both the state trajectory and the probabilistic map parameters. Regarding differentiability, 3DGS is constructed to be differentiable, and the risk metric employs smooth approximations; we have added a discussion of the assumptions on sensor noise and potential edge cases in the revised manuscript. revision: yes

  2. Referee: [§4] §4 (Perception Barrier Functions and QP Formulation): The unified QP enforces safety as a hard constraint while relaxing perception constraints via slack variables, but the manuscript does not analyze how the choice of risk threshold or slack penalty affects the trade-off or whether the resulting closed-loop trajectories remain inside the claimed safe set when the AV@R metric is recomputed online.

    Authors: We appreciate this suggestion for deeper analysis of the QP parameters. The original manuscript demonstrates through simulations that the hard safety constraint is respected while perception objectives are pursued. In the revised Section 4, we have added a parameter sensitivity study that examines the effects of different risk thresholds and slack penalties on the safety-perception trade-off, including quantitative metrics and trajectory visualizations. We further show via additional closed-loop simulations that trajectories remain inside the safe set as the AV@R metric is recomputed online, since the QP is solved at each timestep with the latest map estimate, re-enforcing the CBF condition with the current risk gradient. revision: yes

Circularity Check

0 steps flagged

New risk-aware EIG and perception barrier functions; central CBF guarantee derived from AV@R metric without reduction to fitted inputs or self-citation chains

full rationale

The paper proposes a novel unified QP that treats safety as a hard CBF constraint derived from an AV@R collision-risk metric on the 3DGS representation and relaxes perception objectives via slack variables. No equations or claims in the provided abstract reduce the forward-invariance guarantee to a self-definition, a fitted parameter renamed as prediction, or a load-bearing self-citation. The derivation applies standard CBF Lie-derivative conditions to the newly defined risk metric, which remains an independent modeling choice rather than a tautology. Any self-citations present are peripheral and do not carry the core safety or perception claims.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that 3DGS provides a usable uncertainty model for both collision risk and information gain; no free parameters or invented entities are explicitly introduced in the abstract, but the AV@R metric and perception barrier functions are new constructs whose validity depends on domain assumptions about Gaussian representations.

axioms (2)
  • domain assumption 3D Gaussian Splatting representation accurately models both geometry and uncertainty for collision risk and information gain calculations
    Invoked in the safety and perception sections of the abstract
  • domain assumption The quadratic program with slack variables remains tractable and real-time solvable under the stated safety and perception constraints
    Stated as the method to obtain a tractable formulation

pith-pipeline@v0.9.0 · 5737 in / 1398 out tokens · 24770 ms · 2026-05-21T06:12:44.467446+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages

  1. [1]

    Efficient greedy algo- rithms for feature selection in robot visual localization,

    V . Pandey, A. Mollaei, and N. Motee, “Efficient greedy algo- rithms for feature selection in robot visual localization,”arXiv preprint arXiv:2511.20894, 2025

    work page arXiv 2025

  2. [2]

    AG-SLAM: Active gaussian splatting SLAM,

    W. Jiang, B. LEI, K. Ashton, and K. Daniilidis, “AG-SLAM: Active gaussian splatting SLAM,” 2024

    work page 2024

  3. [3]

    Vista: Open- vocabulary, task-relevant robot exploration with online semantic gaussian splatting,

    K. Nagami, T. Chen, J. Yu, O. Shorinwa, M. Adang, C. Dougherty, E. Cristofalo, and M. Schwager, “Vista: Open- vocabulary, task-relevant robot exploration with online semantic gaussian splatting,”IEEE Robotics and Automation Letters, 2026

    work page 2026

  4. [4]

    Biosignal-integrated robotic systems with emerging trends in visual interfaces: A systematic review,

    J. Lee, S. Miri, A. Bayro, M. Kim, H. Jeong, and W.-H. Yeo, “Biosignal-integrated robotic systems with emerging trends in visual interfaces: A systematic review,”Biophysics Reviews, vol. 5, no. 1, 2024

    work page 2024

  5. [5]

    Active next-best-view optimization for risk- averse path planning,

    A. M. Khass, G. Liu, V . Pandey, W. Jiang, B. Lei, K. Daniilidis, and N. Motee, “Active next-best-view optimization for risk- averse path planning,”arXiv preprint arXiv:2510.06481, 2025

    work page arXiv 2025

  6. [6]

    Rt-guide: Real-time gaussian splatting for information-driven exploration,

    Y . Tao, D. Ong, V . Murali, I. Spasojevic, P. Chaudhari, and V . Kumar, “Rt-guide: Real-time gaussian splatting for information-driven exploration,”IEEE Robotics and Automation Letters, 2025

    work page 2025

  7. [7]

    Risk-averse markov decision processes: Applications to electricity grid and reservoir management,

    A. Khojaste, J. Pearce, D. P. de Farias, G. Pritchard, and G. Zakeri, “Risk-averse markov decision processes: Applications to electricity grid and reservoir management,”arXiv preprint arXiv:2601.02207, 2026

    work page arXiv 2026

  8. [8]

    Control barrier functions: Theory and applications,

    A. D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K. Sreenath, and P. Tabuada, “Control barrier functions: Theory and applications,” in2019 18th European control conference (ECC). Ieee, 2019, pp. 3420–3431

    work page 2019

  9. [9]

    Control barrier function based quadratic programs for safety critical systems,

    A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,”IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3861–3876, 2017

    work page 2017

  10. [10]

    Control barrier functions for systems with high relative degree,

    W. Xiao and C. Belta, “Control barrier functions for systems with high relative degree,” in2019 IEEE 58th Conference on Decision and Control (CDC), 2019, pp. 474–479

    work page 2019

  11. [11]

    3d gaussian splatting for real-time radiance field rendering,

    B. Kerbl, G. Kopanas, T. Leimk ¨uhler, and G. Drettakis, “3d gaussian splatting for real-time radiance field rendering,”ACM Transactions on Graphics, vol. 42, no. 4, July 2023

    work page 2023

  12. [12]

    Fisherrf: Active view selection and uncertainty quantification for radiance fields using fisher information,

    W. Jiang, B. Lei, and K. Daniilidis, “Fisherrf: Active view selection and uncertainty quantification for radiance fields using fisher information,”arXiv, 2023

    work page 2023

  13. [13]

    Splat-nav: Safe real- time robot navigation in gaussian splatting maps,

    T. Chen, O. Shorinwa, J. Bruno, A. Swann, J. Yu, W. Zeng, K. Nagami, P. Dames, and M. Schwager, “Splat-nav: Safe real- time robot navigation in gaussian splatting maps,” 2024

    work page 2024

  14. [14]

    A control barrier function for safe navigation with online gaussian splatting maps,

    T. Chen, A. Swann, J. Yu, O. Shorinwa, R. Murai, M. Kennedy, and M. Schwager, “A control barrier function for safe navigation with online gaussian splatting maps,” in2025 IEEE International Conference on Robotics and Automation (ICRA), 2025

    work page 2025

  15. [15]

    Perception-integrated safety critical control via analytic collision cone barrier functions on 3d gaussian splatting,

    D. Tscholl, Y . Nakka, and B. Gunter, “Perception-integrated safety critical control via analytic collision cone barrier functions on 3d gaussian splatting,”arXiv preprint arXiv:2509.14421, 2025

    work page arXiv 2025

  16. [16]

    Unifying approaches in active learning and active sampling via fisher information and information- theoretic quantities,

    A. Kirsch and Y . Gal, “Unifying approaches in active learning and active sampling via fisher information and information- theoretic quantities,”Transactions on Machine Learning Re- search, 2022

    work page 2022

  17. [17]

    Beyond uncertainty: Risk-aware active view acquisition for safe robot navigation and 3d scene understanding with fisherrf,

    G. Liu, W. Jiang, B. Lei, V . Pandey, K. Daniilidis, and N. Motee, “Beyond uncertainty: Risk-aware active view acquisition for safe robot navigation and 3d scene understanding with fisherrf,”arXiv preprint arXiv:2403.11396, 2024

    work page arXiv 2024

  18. [18]

    Conditional value-at-risk for general loss distributions,

    R. T. Rockafellar and S. Uryasev, “Conditional value-at-risk for general loss distributions,”Journal of Banking & Finance, vol. 26, no. 7, pp. 1443–1471, 2002

    work page 2002

  19. [19]

    Soft-minimum barrier functions for safety-critical control subject to actuation constraints,

    P. Rabiee and J. B. Hoagg, “Soft-minimum barrier functions for safety-critical control subject to actuation constraints,” in2023 American Control Conference (ACC), 2023, pp. 2646–2651

    work page 2023

  20. [20]

    Boyd and L

    S. Boyd and L. Vandenberghe,Convex Optimization. Cambridge University Press, 2004

    work page 2004

  21. [21]

    Splatfacto-w: A nerfstudio implementation of gaussian splatting for unconstrained photo collections,

    C. Xu, J. Kerr, and A. Kanazawa, “Splatfacto-w: A nerfstudio implementation of gaussian splatting for unconstrained photo collections,”ArXiv, vol. abs/2407.12306, 2024

    work page arXiv 2024

  22. [22]

    Point cloud-based control barrier function regression for safe and efficient vision-based control,

    M. De Sa, P. Kotaru, and K. Sreenath, “Point cloud-based control barrier function regression for safe and efficient vision-based control,” in2024 IEEE International Conference on Robotics and Automation (ICRA), 2024, pp. 366–372

    work page 2024