Pith. sign in

REVIEW 4 major objections 6 minor 82 references

One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environments

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read One observation-conditioned safety filter can protect many quadruped controllers across unseen environments and dynamics.

desk verdict Real step forward with honest experiments, but the disturbance-bound heuristic undercuts the formal safety claim and the 'one filter' promise has per-setting caveats. read the letter →

arxiv 2412.09989 v1 pith:H2XJOWSC submitted 2024-12-13 cs.RO cs.AIcs.LGcs.SYeess.SY

Albert Lin , Shuang Peng , Somil Bansal This is my paper · ORCID
classification cs.ROcs.AIcs.LGcs.SYeess.SY
keywords Hamilton-Jacobireachabilitysafetyfilterquadrupedalnavigationobservation-conditionedvaluenetworkdisturbanceestimationconformalpredictionLiDARsafety-criticalcontrol
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that safety can be made a transportable layer for legged navigation: one filter, trained once, can protect many different quadruped controllers in environments it has never seen. The claim is that a value network conditioned on a LiDAR scan and on an online estimate of dynamics uncertainty can reproduce the optimal reachability-based safety value function well enough to serve as a safety filter. If true, users would no longer need to re-derive safety certificates whenever they swap a locomotion policy or enter a new obstacle configuration. The paper supports the claim with simulation and hardware trials showing high success rates across learning-based and model-based controllers, including under slippery terrain and external pushes.

What carries the argument

The load-bearing object is the Observation-Conditioned Reachability Value Network (OCR-VN), a neural network that maps a reduced state $x_r=(p_x,p_y,p_\theta)$, a 100-ray LiDAR observation $o^e$, and a disturbance bound $\bar d^e_r$ to a predicted safety value $V_\psi(x_r,\bar d^e_r,o^e)$ and its spatial gradient. It is trained by supervised regression against ground-truth Hamilton-Jacobi reachability value functions on 1,000 randomly generated obstacle environments, using sinusoidal activations so that the gradients the filter needs are modeled accurately. The companion mechanism is the online disturbance estimator, which computes the difference between the actual state history and the disturbance-free reduced-order prediction over a sliding window of about two seconds and converts the spread of those residuals into position and heading disturbance bounds. A conformal-calibration shift $\delta$ is subtracted from the network output so that overestimation of safety is controlled to a chosen violation rate. Together these pieces turn the classical backward reachable tube computation, normally too heavy for online use, into a query that can be answered at control rate.

What would settle it

Run the filter on a quadruped that steps onto a low-friction patch that appears suddenly, such as an oil-soaked tarp placed just before a wall, and record whether the robot collides before the two-second disturbance window has registered the slip; if the robot enters the failure set while the estimated bound is still low, the central claim fails for that regime.

Watch

Extended reading notes

Core claim

The central claim is that the optimal control-theoretic safety value function for a quadruped — the function whose sign tells whether the robot can avoid a failure set under worst-case disturbance — can be predicted at deployment time from onboard sensing and recent experience, rather than recomputed for each new controller and environment. The authors model the robot as a reduced-order 3D Dubins car with additive adversarial disturbances, compute ground-truth Hamilton-Jacobi reachability value functions over 1,000 randomly generated obstacle fields and disturbance bounds, and train the OCR-VN to output both the value and its spatial gradients from a LiDAR observation, the reduced state, and the estimated disturbance bound. The predicted value function is wrapped in an adaptive least-restrictive safety filter: while the predicted value exceeds a calibrated threshold the nominal controller runs unmodified, and once the value drops to the threshold the filter solves a quadratic program to minimally adjust the twist command so that the value function's derivative constraint is satisfied. The paper reports that this single filter safeguards a range of high-level planners and low-level policies without retraining, and outperforms a policy-specific safety-critic method, especially when ground friction and payloads vary.

Load-bearing premise

The whole guarantee rests on the assumption that the disturbance bound computed from the last two seconds of state-action history really upper-bounds the disturbance the robot is about to experience, and that the estimate updates faster than the environment changes.

Editorial extensions

If this is right

  • A single trained OCR-VN can be attached in zero-shot fashion to a new hierarchical controller (high-level planner plus low-level locomotion policy) with no retraining or policy-specific tuning, provided the controller emits twist commands.
  • Because the filter only intervenes when the calibrated value function falls to the threshold, it preserves nominal agility and minimizes deviation; in cluttered settings it can be made less conservative by dropping calibration or limiting LiDAR to a front-facing cone.
  • Online disturbance estimation is what extends safety from nominal dynamics to real-world slips, payload changes, and tracking errors; without it, success rates drop sharply under hard dynamic conditions.
  • The hardware results on the quadruped show the same pattern as simulation: the filter raises success from zero for a naive goal-seeking controller to roughly nine out of ten trials, even on a slippery floor.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The two-second sliding-window disturbance estimate implicitly assumes disturbances change slowly; a terrain-aware estimator that predicts friction or slip from exteroception before the robot enters a patch could close the adaptation lag the authors acknowledge.
  • The same conditioning recipe — a reduced-order model plus a network that maps observations and uncertainty bounds to a reachability value function — should transfer to other twist-command robots, such as wheeled bases, drones, or manipulators with a low-level tracker.
  • The filter's conservatism in cluttered, walled environments suggests a testable extension: instead of discarding LiDAR readings outside a front cone, one could train with wall-like obstacles or learn an observation-conditioned calibration level to reduce stalling.
  • Because the filter operates at the twist level and only needs a backup low-level policy, it could serve as a generic safety wrapper for end-to-end RL locomotion policies that do not natively separate planning from control.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes an observation-conditioned reachability (OCR) safety-filter framework for quadrupedal navigation. A value network (OCR-VN) is trained offline, via supervised learning on Hamilton-Jacobi reachability value functions, to predict the safety value function from LiDAR observations, the reduced-order state, and an estimated disturbance bound. At deployment, an online disturbance estimator (Eq. 13-14) computes disturbance bounds from recent state-action history, and a quadratic-program-based filter (Eq. 15-16) overrides nominal high-level twist commands when the predicted value falls below a calibrated threshold. The authors evaluate the framework in Isaac Sim and on a Unitree Go1 quadruped across several nominal planners and locomotion policies, including model-based, learning-based, and teleoperated controllers, and compare against the ABS baseline and ablations without disturbance estimation or calibration. The central claim is that the filter provides reusable, policy-agnostic safety in unknown environments without a priori access to controllers or environments.

Significance. If the empirical claims hold, this is a valuable step toward reusable safety layers for legged locomotion: the value function is policy-independent, the ground-truth data are computed by HJ reachability rather than derived from the safety outcomes, and the ablations give credible evidence that disturbance estimation and calibration each contribute to the observed success rates. The simulation study is reasonably large (100 trials per condition), the hardware experiments cover multiple controllers and a slippery-floor condition, and the paper is unusually candid about residual collision rates and known failure modes. However, the central robustness claim is stated more strongly than the guarantees support: the online disturbance bound is a heuristic location-scale summary rather than an upper bound, the filter uses a slack-softened constraint, and the calibration guarantee does not transfer to deployment. These issues do not invalidate the empirical contribution, but they require a re-framing of what is claimed and, ideally, additional analysis of the residual risk.

major comments (4)
  1. [Section V-B1, Eq. (14)] The online disturbance bound is not an upper bound on the actual disturbance. Equation (14) computes the trimmed mean plus/minus two standard deviations over only the middle 80% (c = 0.8) of a two-second sliding window; by construction it discards 20% of observed disturbances and has no distribution-free or worst-case coverage guarantee. The HJ reachability guarantee in Section IV-A (Eqs. 5-6) requires the disturbance set D to be a known, fixed bound on the true disturbance. When the true disturbance exceeds the estimated bound, the predicted value can exceed the true safety value, and the filter (Eq. 15) can classify an unsafe state as safe. The authors acknowledge this in Section VIII, but the acknowledgment is placed in the limitations rather than in the framing of the central claim, which states robustness to unmodeled dynamics. The observed nonzero collision rates in Tables III, IV, VI, and VII are consistent with this gap. I request a quantitative characterization: for the reported trials, report how often the true disturbance exceeded the estimated bound, the resulting time-to-collision during the latency window, or a conservative tail bound that can be used to restore a formal guarantee.
  2. [Section V-B2, Eqs. (15)-(16)] The deployed filter does not implement the smooth least-restrictive filter of Eqs. (8)-(9), so the reachability-based safety guarantee does not directly apply. Equation (16) replaces the hard constraint DtV + min_d ∇V·f = 0 with the softened constraint ... ≥ -s, and the slack variable s is only penalized with a finite weight λ = 10^3 (rather than enforced to zero). Even with a perfect value function and exact disturbance bounds, a positive slack allows the value function to decrease along the filtered trajectory, so the superlevel set is not invariant and the statement in Section V-B2 that the filter is 'grounded in reachability theory' is only approximate. The paper should either enforce s = 0 when feasible and characterize when slack is active, or explicitly describe the resulting behavior as a heuristic safety filter and provide an analysis of the residual risk from slack activation.
  3. [Section V-A4 and Section VIII] The conformal calibration guarantee in Theorem 1 is stated over the calibration distribution P on the validation dataset, and Section VIII correctly notes that the guarantees cannot be extrapolated to the real world because of distribution shift. This is a load-bearing caveat: the threshold δ = 0.49 m used in Eq. (15) is drawn from Table II, but the paper does not quantify how likely it is that the true deployment-time error exceeds this threshold. The result is that the 'safety margin' from calibration is not a safety margin in any formally guaranteed sense. I would like to see either an online calibration scheme, a sensitivity analysis of δ, or an explicit statement that the calibrated threshold is a heuristic tuning parameter rather than a probabilistic safety certificate during deployment.
  4. [Section VII-B5 and Section VI-E] The claim that a single filter is deployed across all settings is tempered by per-setting modifications. In Section VII-B5, the authors state that for highly cluttered indoor environments they discard LiDAR readings outside a front-facing cone of π/2 rad and use the uncalibrated output of the OCR-VN. Similarly, Section VI-E and Figure 7(b) report using OCR \ C in a hand-designed dead-end environment. These are not merely implementation details: they change the network input and the activation threshold, and they are motivated by a distribution shift from the training data. The 'one filter to deploy them all' framing should therefore be scoped to the settings in which the same configuration is used, or the paper should justify that the modifications are automatic and not environment-specific tuning.
minor comments (6)
  1. [Section I] There is a typo in 'cluttered anda priori unknown environments'; it should read 'cluttered and a priori unknown environments'.
  2. [Section V-B1] The disturbance estimation parameters (c = 0.8, b = 2, η·k = 2 s, η·φ = 2 s) are introduced without a sensitivity study. Since the central robustness claim depends on these values, a small ablation or a discussion of how the results change with c and b would be helpful.
  3. [Tables III, IV, VI, VII] The hardware results report only 10 trials per condition, and the simulation tables do not include confidence intervals or standard errors. Given that several comparisons (e.g., ABS-Agile in the slippery condition) involve small counts, reporting binomial confidence intervals would strengthen the empirical claims.
  4. [Figure 3 caption] The caption says 'Right top-row' and 'Right bottom-row' but it is clearer to label the panels directly, since the left panel shows the LiDAR observation and the right panels show ground truth and prediction.
  5. [Section VII-B5] The phrases 'We believe this is necessary' and 'We theorize that' are informal; they should be supported by a quantitative comparison or an explicit hypothesis test, otherwise the statements read as speculation.
  6. [Appendix A] The quantile definition in the proof of Theorem 1 uses N−k/N, while standard split conformal prediction often uses a slightly different finite-sample correction. The paper should either justify this choice or reconcile it with the cited reference [79].

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the OCR-VN is supervised by independently computed HJ value functions, and the acknowledged disturbance-estimation gap is a robustness limitation, not a circular derivation.

full rationale

The paper's derivation chain is self-contained and non-circular. The OCR-VN is trained by supervised regression against ground-truth Hamilton-Jacobi value functions computed offline with the hj_reachability toolbox for randomly generated environments with known disturbance bounds; these ground-truth values are not derived from the network, the safety filter's collision outcomes, or any fitted parameter. The conformal calibration of Section V-A4 is a standard post-processing step whose Theorem 1 is proved in Appendix A from split conformal prediction [79], and the chosen calibration level is not fitted to the reported collision rates. The deployment-time disturbance bound (Eq. 14) is a heuristic estimate (trimmed mean plus/minus two standard deviations over a two-second window) and is explicitly acknowledged in Section VIII to be neither an absolute upper bound nor free of latency; this is a correctness and robustness limitation, not circularity, because the filter's conditional guarantee is stated in terms of the estimated bound and the paper reports nonzero collision rates consistent with that gap. Self-citations such as [68] and [80] point to peer-reviewed, externally published results and are not used to define the target quantities into existence; the core HJ reachability guarantee is standard theory also supported by independent references [75] and [76]. No step reduces by construction to its own inputs.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The safety guarantee depends on the reduced-order model, the validity of online disturbance bounds, the sufficiency of LiDAR observations, and the transferability of the calibration. These are stated assumptions, not independently verified beyond the empirical experiments.

free parameters (3)
  • Calibration level delta = 0.49 m (with epsilon = 1e-2); set to 0 (uncalibrated) in cluttered hardware settings
    Selected from conformal scores on the validation dataset to shift the network output conservatively. Directly affects the safety filter threshold in Eq. (15). In cluttered settings, the authors switch to uncalibrated output (Section VII-B5), effectively changing this parameter per environment.
  • Disturbance estimation parameters (coverage c, spread b, history eta*k, window eta*phi) = c=0.8, b=2, eta*k=2 s, eta*phi=2 s
    Hand-chosen in Section V-B1 to balance conservatism and adaptivity. These determine the disturbance bound that the safety value function is conditioned on, and thus the filter's intervention level.
  • Slack weight lambda in the safety QP = lambda = 1e3
    Sets the penalty for violating the safety constraint in Eq. (16). A larger lambda enforces safety more strictly at the cost of deviating from the nominal control.
assumptions (5)
  • domain assumption The quadruped plus locomotion policy can be abstracted as a 3D Dubins car with additive bounded disturbance (Eq. 10).
    This reduced-order model ignores higher-order dynamics, assuming that all modeling error is captured by disturbance bounds. Introduced in Section V-A1.
  • domain assumption The online disturbance estimation (Eq. 13-14) produces a valid bound on the true disturbance, which is low-frequency and approximately constant over the 2 s history window.
    If the disturbance changes faster (e.g., sudden slippery patch), the estimated bound is invalid and the safety value function may be incorrect. Stated in Section V-B1 and acknowledged as a failure mode in Section VIII.
  • domain assumption The LiDAR observation provides sufficient information to reconstruct the failure set and value function for novel environments.
    The OCR-VN is trained with LiDAR scans from randomly placed circular obstacles. Real environments with walls and narrow corridors cause a distribution shift, requiring manual LiDAR cone cropping in Section VII-B5.
  • domain assumption Conformal calibration bounds the OCR-VN's overestimation error on the deployment distribution (Theorem 1).
    The bound is probabilistic over the validation distribution, and the paper acknowledges distribution shift to the real world in Section VIII. In cluttered settings, they use uncalibrated output, effectively dropping this assumption.
  • standard math The value function converges within a 2 s horizon for the reduced-order model.
    Used to compute converged value functions for training data. Stated in Section V-A2.

how reviews work

0 comments
Cite this review

Pith. "Pith review of One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environments." pith.science (2026). https://pith.science/paper/H2XJOWSC

@misc{pith2026241209989,
  author       = {Pith},
  title        = {Pith review of: One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environments},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H2XJOWSC}},
  note         = {Machine review of arXiv:2412.09989}
}
read the original abstract

As learning-based methods for legged robots rapidly grow in popularity, it is important that we can provide safety assurances efficiently across different controllers and environments. Existing works either rely on a priori knowledge of the environment and safety constraints to ensure system safety or provide assurances for a specific locomotion policy. To address these limitations, we propose an observation-conditioned reachability-based (OCR) safety-filter framework. Our key idea is to use an OCR value network (OCR-VN) that predicts the optimal control-theoretic safety value function for new failure regions and dynamic uncertainty during deployment time. Specifically, the OCR-VN facilitates rapid safety adaptation through two key components: a LiDAR-based input that allows the dynamic construction of safe regions in light of new obstacles and a disturbance estimation module that accounts for dynamics uncertainty in the wild. The predicted safety value function is used to construct an adaptive safety filter that overrides the nominal quadruped controller when necessary to maintain safety. Through simulation studies and hardware experiments on a Unitree Go1 quadruped, we demonstrate that the proposed framework can automatically safeguard a wide range of hierarchical quadruped controllers, adapts to novel environments, and is robust to unmodeled dynamics without a priori access to the controllers or environments - hence, "One Filter to Deploy Them All". The experiment videos can be found on the project website.

Figures

Figures reproduced from arXiv: 2412.09989 by the authors.

Figure 1
Figure 1. Our proposed observation-conditioned reachability-based (OCR) safety-filter framework automatically safeguards [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. The OCR framework. (Left) During training, we generate environments with random obstacles and disturbance bounds. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. (Left) A LiDAR observation o e in a validation environ￾ment where ¯d e px,py = 0.82 m/s, ¯d e pθ = 0.56 rad/s. (Right top￾row) The ground-truth value function and its spatial gradients. (Right bottom-row) OCR-VN predictions using o e and ¯d e r . As shown above, the OCR-VN predictions for the value function and its spatial gradients are highly accurate. substantially increasing the computational effort, which is imp… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: The OCR framework (green/red : nominal/filtered) safeguards different nominal controllers navigating to a goal (cyan) in an environment with a payload of −0.6 kg and a friction of 0.7. By themselves (white), the (a) PS + WTW, (b) NVE + WTW, and (c) ABS-Agile controller…
Figure 5
Figure 5. Figure 5: (In color) Safety rates across settings (1,000 trials). [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: (a) visualizes the behavior of the OCR and ABS frameworks in an environment with high perturbations in dy￾namics (a payload of −0.9 kg and a friction of 0.5). The OCR framework estimates large disturbances online and accordingly intervenes to steer the system away from…
Figure 7
Figure 7. Figure 7: OCR (green/red : nominal/filtered) and ABS (white/black : nominal/filtered) frameworks in environments with hand￾designed obstacle configurations. In (b), the OCR framework is used without calibration due to the highly cluttered setting. to choose the most appropriate …
Figure 8
Figure 8. Figure 8: Hardware experiments with a slippery region outlined in white. (Left) The ABS baseline collides due to drifting caused [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

82 extracted references · 49 canonical work pages

  1. [1]

    Construction inspection and monitoring with quadruped robots in future human-robot teaming: A preliminary study,

    S. Halder, K. Afsari, E. Chiou, R. Patrick, and K. A. Hamed, “Construction inspection and monitoring with quadruped robots in future human-robot teaming: A preliminary study,” Journal of Building Engineering , vol. 65, p. 105814, 2023. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S2352710222018204

    2023

  2. [2]

    Anymal in the field: Solving industrial inspection of an offshore hvdc platform with a quadrupedal robot,

    C. Gehring, P. Fankhauser, L. Isler, R. Diethelm, S. Bachmann, M. Potz, L. Gerstenberg, and M. Hutter, “Anymal in the field: Solving industrial inspection of an offshore hvdc platform with a quadrupedal robot,” in Field and Service Robotics , G. Ishigami and K. Yoshida, Eds. Singapore: Springer Singapore, 2021, pp. 247–260

    2021

  3. [3]

    Fabrication and testing of the rescue quadruped robot for post-disaster search and rescue operations,

    N. Li, J. Cao, and Y . Huang, “Fabrication and testing of the rescue quadruped robot for post-disaster search and rescue operations,” in 2023 IEEE 3rd International Conference on Electronic Technology, Communication and Information (ICETCI) . IEEE, 2023, pp. 723–729

    work page 2023

  4. [4]

    Mixed-reality for quadruped-robotic guidance in sar tasks,

    C. Cruz Ulloa, J. del Cerro, and A. Barrientos, “Mixed-reality for quadruped-robotic guidance in sar tasks,” Journal of Computational Design and Engineering , vol. 10, no. 4, pp. 1479–1489, 2023

    work page 2023

  5. [5]

    Design and development of an intelligent pet-type quadruped robot,

    F. Gao, C. Lei, X. Long, J. Wang, and P. Song, “Design and development of an intelligent pet-type quadruped robot,” in 2021 IEEE 4th Interna- tional Conference on Multimedia Information Processing and Retrieval (MIPR). IEEE, 2021, pp. 366–371

    work page 2021

  6. [6]

    A human-robot interaction entertainment pet robot,

    H. Lee, “A human-robot interaction entertainment pet robot,” Journal of the Korean Institute of Intelligent Systems , vol. 24, no. 2, pp. 179–185, 2014

    work page 2014

  7. [7]

    Autonomous social distancing in urban environ- ments using a quadruped robot,

    Z. Chen, T. Fan, X. Zhao, J. Liang, C. Shen, H. Chen, D. Manocha, J. Pan, and W. Zhang, “Autonomous social distancing in urban environ- ments using a quadruped robot,” IEEE Access , vol. 9, pp. 8392–8403, 2021

    work page 2021

  8. [8]

    First steps toward formal controller synthesis for bipedal robots with experimental implementation,

    A. D. Ames, P. Tabuada, A. Jones, W.-L. Ma, M. Rungger, B. Sch ¨urmann, S. Kolathaya, and J. W. Grizzle, “First steps toward formal controller synthesis for bipedal robots with experimental implementation,” Nonlinear Analysis: Hybrid Systems, vol. 25, pp. 155– 173, 2017. [Online]. Available: http://ames.caltech.edu/ames2017first. pdf

    work page 2017

Show all 82 references
  1. [9]

    Multi-layered safety for legged robots via control barrier functions and model predic- tive control,

    R. Grandia, A. J. Taylor, A. D. Ames, and M. Hutter, “Multi-layered safety for legged robots via control barrier functions and model predic- tive control,” in 2021 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2021, pp. 8352–8358

    2021

  2. [10]

    A control barrier function-based motion planning scheme for a quadruped robot,

    H. U. Unlu, V . M. Gonc ¸alves, D. Chaikalis, A. Tzes, and F. Khor- rami, “A control barrier function-based motion planning scheme for a quadruped robot,” in 2024 IEEE International Conference on Robotics and Automation (ICRA) , 2024, pp. 12 172–12 178

    2024

  3. [11]

    Safe legged locomotion using collision cone control barrier functions (c3bfs),

    M. Tayal and S. Kolathaya, “Safe legged locomotion using collision cone control barrier functions (c3bfs),”arXiv preprint arXiv:2309.01898, 2023

    2023 arXiv

  4. [12]

    Safety-critical coordination for cooperative legged locomotion via control barrier functions,

    J. Kim, J. Lee, and A. D. Ames, “Safety-critical coordination for cooperative legged locomotion via control barrier functions,” in 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2023, pp. 2368–2375

    2023

  5. [13]

    Learning quadrupedal locomotion over challenging terrain,

    J. Lee, J. Hwangbo, L. Wellhausen, V . Koltun, and M. Hutter, “Learning quadrupedal locomotion over challenging terrain,” Science Robotics, vol. 5, no. 47, p. eabc5986, 2020. [Online]. Available: https://www.science.org/doi/abs/10.1126/scirobotics.abc5986

    2020 doi

  6. [14]

    Anymal parkour: Learning agile navigation for quadrupedal robots,

    D. Hoeller, N. Rudin, D. Sako, and M. Hutter, “Anymal parkour: Learning agile navigation for quadrupedal robots,” Science Robotics , vol. 9, no. 88, p. eadi7566, 2024. [Online]. Available: https: //www.science.org/doi/abs/10.1126/scirobotics.adi7566

    2024 doi

  7. [15]

    Visual cpg-rl: Learning central pattern generators for visually-guided quadruped navigation,

    G. Bellegarda and A. Ijspeert, “Visual cpg-rl: Learning central pattern generators for visually-guided quadruped navigation,” arXiv preprint arXiv:2212.14400, 2022

    2022 arXiv

  8. [16]

    Sim-to-real: Learning agile locomotion for quadruped robots,

    J. Tan, T. Zhang, E. Coumans, A. Iscen, Y . Bai, D. Hafner, S. Bohez, and V . Vanhoucke, “Sim-to-real: Learning agile locomotion for quadruped robots,” arXiv preprint arXiv:1804.10332 , 2018

    2018 arXiv

  9. [17]

    Carl: controllable agent with reinforcement learning for quadruped locomotion,

    Y .-S. Luo, J. H. Soeseno, T. P.-C. Chen, and W.-C. Chen, “Carl: controllable agent with reinforcement learning for quadruped locomotion,” ACM Trans. Graph. , vol. 39, no. 4, Aug. 2020. [Online]. Available: https://doi.org/10.1145/3386569.3392433

    2020

  10. [18]

    Terrain-aware quadrupedal locomotion via reinforcement learning,

    H. Shi, Q. Zhu, L. Han, W. Chi, T. Li, and M. Q.-H. Meng, “Terrain-aware quadrupedal locomotion via reinforcement learning,” arXiv preprint arXiv:2310.04675 , 2023

    2023 arXiv

  11. [19]

    Learning risk-aware quadrupedal locomotion using distributional reinforcement learning,

    L. Schneider, J. Frey, T. Miki, and M. Hutter, “Learning risk-aware quadrupedal locomotion using distributional reinforcement learning,” in 2024 IEEE International Conference on Robotics and Automation (ICRA), 2024, pp. 11 451–11 458

    2024

  12. [20]

    Rma: Rapid motor adaptation for legged robots,

    A. Kumar, Z. Fu, D. Pathak, and J. Malik, “Rma: Rapid motor adaptation for legged robots,” 2021

    2021

  13. [21]

    Walk these ways: Tuning robot control for generalization with multiplicity of behavior,

    G. B. Margolis and P. Agrawal, “Walk these ways: Tuning robot control for generalization with multiplicity of behavior,” Conference on Robot Learning, 2022

    2022

  14. [22]

    Real-time trajectory adaptation for quadrupedal locomotion using deep reinforcement learning,

    S. Gangapurwala, M. Geisert, R. Orsolino, M. Fallon, and I. Havoutis, “Real-time trajectory adaptation for quadrupedal locomotion using deep reinforcement learning,” in 2021 IEEE International Conference on Robotics and Automation (ICRA) , 2021, pp. 5973–5979

    2021

  15. [23]

    Safe deep policy adaptation,

    W. Xiao, T. He, J. Dolan, and G. Shi, “Safe deep policy adaptation,” in 2024 IEEE International Conference on Robotics and Automation (ICRA), 2024, pp. 17 286–17 292

    2024

  16. [24]

    End-to-end safe reinforcement learning through barrier functions for safety-critical continuous control tasks,

    R. Cheng, G. Orosz, R. M. Murray, and J. W. Burdick, “End-to-end safe reinforcement learning through barrier functions for safety-critical continuous control tasks,” in Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence and Thirty-First Innovative Appli...

    2019 doi

  17. [25]

    Model-free safe control for zero-violation reinforcement learning,

    W. Zhao, T. He, and C. Liu, “Model-free safe control for zero-violation reinforcement learning,” in Proceedings of the 5th Conference on Robot Learning , ser. Proceedings of Machine Learning Research, A. Faust, D. Hsu, and G. Neumann, Eds., vol. 164. PMLR, 08–11 Nov 2022, pp. ...

    2022

  18. [26]

    Chance-constrained trajectory optimization for safe exploration and learning of nonlinear systems,

    Y . K. Nakka, A. Liu, G. Shi, A. Anandkumar, Y . Yue, and S.-J. Chung, “Chance-constrained trajectory optimization for safe exploration and learning of nonlinear systems,” IEEE Robotics and Automation Letters , vol. 6, no. 2, pp. 389–396, 2021. 14

    2021

  19. [27]

    Recovery rl: Safe reinforcement learning with learned recovery zones,

    B. Thananjeyan, A. Balakrishna, S. Nair, M. Luo, K. Srinivasan, M. Hwang, J. E. Gonzalez, J. Ibarz, C. Finn, and K. Goldberg, “Recovery rl: Safe reinforcement learning with learned recovery zones,” IEEE Robotics and Automation Letters , vol. 6, no. 3, pp. 4915–4922, 2021

    2021

  20. [28]

    Sim-to-lab-to-real: Safe reinforcement learning with shielding and generalization guarantees,

    K.-C. Hsu, A. Z. Ren, D. P. Nguyen, A. Majumdar, and J. F. Fisac, “Sim-to-lab-to-real: Safe reinforcement learning with shielding and generalization guarantees,” Artificial Intelligence , vol. 314, p. 103811, 2023. [Online]. Available: https://www.sciencedirect.com/ science/ar...

    2023

  21. [29]

    Agile but safe: Learning collision-free high-speed legged locomotion,

    T. He, C. Zhang, W. Xiao, G. He, C. Liu, and G. Shi, “Agile but safe: Learning collision-free high-speed legged locomotion,” in Robotics: Science and Systems (RSS) , 2024

    2024

  22. [30]

    Conservative safety critics for exploration,

    H. Bharadhwaj, A. Kumar, N. Rhinehart, S. Levine, F. Shkurti, and A. Garg, “Conservative safety critics for exploration,” in International Conference on Learning Representations , 2021. [Online]. Available: https://openreview.net/forum?id=iaO86DUuKi

    2021

  23. [31]

    Vision aided dynamic exploration of unstructured terrain with a small-scale quadruped robot,

    D. Kim, D. Carballo, J. Di Carlo, B. Katz, G. Bledt, B. Lim, and S. Kim, “Vision aided dynamic exploration of unstructured terrain with a small-scale quadruped robot,” in 2020 IEEE International Conference on Robotics and Automation (ICRA) , 2020, pp. 2464–2470

    2020

  24. [32]

    Robust autonomous navigation of a small-scale quadruped robot in real-world environments,

    T. Dudzik, M. Chignoli, G. Bledt, B. Lim, A. Miller, D. Kim, and S. Kim, “Robust autonomous navigation of a small-scale quadruped robot in real-world environments,” in 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , 2020, pp. 3664– 3671

    2020

  25. [33]

    Perceptive whole-body planning for multilegged robots in confined spaces,

    R. Buchanan, L. Wellhausen, M. Bjelonic, T. Bandyopadhyay, N. Kottege, and M. Hutter, “Perceptive whole-body planning for multilegged robots in confined spaces,” Journal of Field Robotics, vol. 38, no. 1, pp. 68–84, 2021. [Online]. Available: https://onlinelibrary.wiley.com/do...

    2021 doi

  26. [34]

    Collision-free mpc for legged robots in static and dynamic scenes,

    M. Gaertner, M. Bjelonic, F. Farshidian, and M. Hutter, “Collision-free mpc for legged robots in static and dynamic scenes,” in 2021 IEEE International Conference on Robotics and Automation (ICRA) , 2021, pp. 8266–8272

    2021

  27. [35]

    A collision-free mpc for whole-body dynamic locomotion and manipula- tion,

    J.-R. Chiu, J.-P. Sleiman, M. Mittal, F. Farshidian, and M. Hutter, “A collision-free mpc for whole-body dynamic locomotion and manipula- tion,” in 2022 International Conference on Robotics and Automation (ICRA), 2022, pp. 4686–4693

    2022

  28. [36]

    An efficient locally reactive controller for safe navigation in visual teach and repeat missions,

    M. Mattamala, N. Chebrolu, and M. Fallon, “An efficient locally reactive controller for safe navigation in visual teach and repeat missions,” IEEE Robotics and Automation Letters , vol. 7, no. 2, pp. 2353–2360, 2022

    2022

  29. [37]

    Walking in narrow spaces: Safety-critical locomotion control for quadrupedal robots with duality-based optimization,

    Q. Liao, Z. Li, A. Thirugnanam, J. Zeng, and K. Sreenath, “Walking in narrow spaces: Safety-critical locomotion control for quadrupedal robots with duality-based optimization,” in 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , 2023, pp. 2723– 2730

    2023

  30. [38]

    Artplanner: Robust legged robot naviga- tion in the field,

    L. Wellhausen and M. Hutter, “Artplanner: Robust legged robot naviga- tion in the field,” Field Robotics, vol. 3, pp. 413–434, 2023

    2023

  31. [39]

    Toward safety-aware informative motion planning for legged robots,

    S. Teng, Y . Gong, J. W. Grizzle, and M. Ghaffari, “Toward safety-aware informative motion planning for legged robots,” 2021. [Online]. Available: https://arxiv.org/abs/2103.14252

    2021 arXiv

  32. [40]

    Dynamic locomotion on slippery ground,

    F. Jenelten, J. Hwangbo, F. Tresoldi, C. D. Bellicoso, and M. Hutter, “Dynamic locomotion on slippery ground,” IEEE Robotics and Automa- tion Letters, vol. 4, no. 4, pp. 4170–4176, 2019

    2019

  33. [41]

    Isaac gym: High performance gpu-based physics simulation for robot learning,

    V . Makoviychuk, L. Wawrzyniak, Y . Guo, M. Lu, K. Storey, M. Macklin, D. Hoeller, N. Rudin, A. Allshire, A. Handa, and G. State, “Isaac gym: High performance gpu-based physics simulation for robot learning,” 2021

    2021

  34. [42]

    Learning to walk in minutes using massively parallel deep reinforcement learning,

    N. Rudin, D. Hoeller, P. Reist, and M. Hutter, “Learning to walk in minutes using massively parallel deep reinforcement learning,” in 5th Annual Conference on Robot Learning , 2021. [Online]. Available: https://openreview.net/forum?id=wK2fDDJ5VcF

    2021

  35. [43]

    Reinforcement learning in robotics: A survey,

    J. Kober, J. Bagnell, and J. Peters, “Reinforcement learning in robotics: A survey,” The International Journal of Robotics Research , vol. 32, pp. 1238–1274, 09 2013

    2013

  36. [44]

    Rapid locomotion via reinforcement learning,

    G. B. Margolis, G. Yang, K. Paigwar, T. Chen, and P. Agrawal, “Rapid locomotion via reinforcement learning,” The International Journal of Robotics Research , vol. 43, no. 4, pp. 572–587, 2024. [Online]. Available: https://doi.org/10.1177/02783649231224053

    2024 doi

  37. [45]

    Learning agile and dynamic motor skills for legged robots,

    J. Hwangbo, J. Lee, A. Dosovitskiy, D. Bellicoso, V . Tsounis, V . Koltun, and M. Hutter, “Learning agile and dynamic motor skills for legged robots,” Science Robotics , vol. 4, no. 26, p. eaau5872, 2019. [Online]. Available: https://www.science.org/doi/abs/10.1126/scirobotics.aau5872

    2019 doi

  38. [46]

    Rloc: Terrain-aware legged locomotion using reinforcement learning and optimal control,

    S. Gangapurwala, M. Geisert, R. Orsolino, M. Fallon, and I. Havoutis, “Rloc: Terrain-aware legged locomotion using reinforcement learning and optimal control,” IEEE Transactions on Robotics , vol. 38, no. 5, pp. 2908–2927, 2022

    2022

  39. [47]

    Multi-expert learning of adaptive legged locomotion,

    C. Yang, K. Yuan, Q. Zhu, W. Yu, and Z. Li, “Multi-expert learning of adaptive legged locomotion,” Science Robotics , vol. 5, no. 49, p. eabb2174, 2020. [Online]. Available: https://www.science.org/doi/abs/ 10.1126/scirobotics.abb2174

    2020 doi

  40. [49]

    Robot parkour learning,

    Z. Zhuang, Z. Fu, J. Wang, C. Atkeson, S. Schwertfeger, C. Finn, and H. Zhao, “Robot parkour learning,” in Conference on Robot Learning (CoRL), 2023

    2023

  41. [51]

    Dtc: Deep tracking control,

    F. Jenelten, J. He, F. Farshidian, and M. Hutter, “Dtc: Deep tracking control,” Science Robotics, vol. 9, no. 86, p. eadh5401, 2024. [Online]. Available: https://www.science.org/doi/abs/10.1126/scirobotics.adh5401

    2024 doi

  42. [52]

    Extreme parkour with legged robots,

    X. Cheng, K. Shi, A. Agarwal, and D. Pathak, “Extreme parkour with legged robots,” arXiv preprint arXiv:2309.14341 , 2023

    2023 arXiv

  43. [53]

    Learning robust perceptive locomotion for quadrupedal robots in the wild,

    T. Miki, J. Lee, J. Hwangbo, L. Wellhausen, V . Koltun, and M. Hutter, “Learning robust perceptive locomotion for quadrupedal robots in the wild,” Science Robotics, vol. 7, no. 62, Jan. 2022. [Online]. Available: http://dx.doi.org/10.1126/scirobotics.abk2822

    2022 doi

  44. [54]

    Learning robust, agile, natural legged locomotion skills in the wild,

    Y . Wang, Z. Jiang, and J. Chen, “Learning robust, agile, natural legged locomotion skills in the wild,” in RoboLetics: Workshop on Robot Learning in Athletics @CoRL 2023 , 2023. [Online]. Available: https://openreview.net/forum?id=b5hiuuX1sm

    2023

  45. [55]

    Legged locomotion in challenging terrains using egocentric vision,

    A. Agarwal, A. Kumar, J. Malik, and D. Pathak, “Legged locomotion in challenging terrains using egocentric vision,” in Conference on robot learning. PMLR, 2023, pp. 403–415

    2023

  46. [56]

    Artplanner: Robust legged robot navigation in the field,

    L. Wellhausen and M. Hutter, “Artplanner: Robust legged robot navigation in the field,” Field Robotics, vol. 3, no. 1, p. 413–434, Jan

  47. [57]

    Resilient legged local navigation: Learning to traverse with compromised perception end-to-end,

    C. Zhang, J. Jin, J. Frey, N. Rudin, M. Mattamala, C. Cadena, and M. Hutter, “Resilient legged local navigation: Learning to traverse with compromised perception end-to-end,” in 2024 IEEE International Conference on Robotics and Automation (ICRA) , 2024, pp. 34–41

    2024

  48. [58]

    Safe and robust motion planning for autonomous navigation of quadruped robots in cluttered environments,

    H. Liu and Q. Yuan, “Safe and robust motion planning for autonomous navigation of quadruped robots in cluttered environments,” IEEE Access, vol. 12, pp. 69 728–69 737, 2024

    2024

  49. [59]

    Learning a state representation and navigation in cluttered and dynamic environ- ments,

    D. Hoeller, L. Wellhausen, F. Farshidian, and M. Hutter, “Learning a state representation and navigation in cluttered and dynamic environ- ments,” IEEE Robotics and Automation Letters , vol. 6, no. 3, pp. 5081– 5088, 2021

    2021

  50. [60]

    Learning vision- guided quadrupedal locomotion end-to-end with cross-modal transform- ers,

    R. Yang, M. Zhang, N. Hansen, H. Xu, and X. Wang, “Learning vision- guided quadrupedal locomotion end-to-end with cross-modal transform- ers,” in International Conference on Learning Representations , 2022. [Online]. Available: https://openreview.net/forum?id=nhnJ3oo6AB

    2022

  51. [61]

    Advanced skills by learning locomotion and local navigation end-to-end,

    N. Rudin, D. Hoeller, M. Bjelonic, and M. Hutter, “Advanced skills by learning locomotion and local navigation end-to-end,” in 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , 2022, pp. 2497–2503

    2022

  52. [62]

    Learning agile locomotion on risky terrains,

    C. Zhang, N. Rudin, D. Hoeller, and M. Hutter, “Learning agile locomotion on risky terrains,” 2024. [Online]. Available: https://arxiv.org/abs/2311.10484

    2024 arXiv

  53. [63]

    Learning to walk by steering: Perceptive quadrupedal locomotion in dynamic environments,

    M. Seo, R. Gupta, Y . Zhu, A. Skoutnev, L. Sentis, and Y . Zhu, “Learning to walk by steering: Perceptive quadrupedal locomotion in dynamic environments,” in 2023 IEEE International Conference on Robotics and Automation (ICRA), 2023, pp. 5099–5105

    2023

  54. [64]

    Vinl: Visual navigation and locomotion over obstacles,

    S. Kareer, N. Yokoyama, D. Batra, S. Ha, and J. Truong, “Vinl: Visual navigation and locomotion over obstacles,” in 2023 IEEE International Conference on Robotics and Automation (ICRA) . IEEE, 2023, pp. 2018–2024

    2023

  55. [65]

    Rethinking sim2real: Lower fidelity simulation leads to higher sim2real transfer in navigation,

    J. Truong, M. Rudolph, N. H. Yokoyama, S. Chernova, D. Batra, and A. Rai, “Rethinking sim2real: Lower fidelity simulation leads to higher sim2real transfer in navigation,” in 6th Annual Conference on Robot Learning, 2022. [Online]. Available: https://openreview.net/forum?id= B...

    2022

  56. [66]

    Asc: Adaptive skill coordination for robotic mobile manipulation,

    N. Yokoyama, A. Clegg, J. Truong, E. Undersander, T.-Y . Yang, S. Ar- naud, S. Ha, D. Batra, and A. Rai, “Asc: Adaptive skill coordination for robotic mobile manipulation,” IEEE Robotics and Automation Letters , vol. 9, no. 1, pp. 779–786, 2024

    2024

  57. [67]

    Safe reinforce- ment learning for legged locomotion,

    T.-Y . Yang, T. Zhang, L. Luu, S. Ha, J. Tan, and W. Yu, “Safe reinforce- ment learning for legged locomotion,” in 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , 2022, pp. 2454– 2461. 15

    2022

  58. [68]

    On safety and liveness filtering using hamilton–jacobi reachability analysis,

    J. Borquez, K. Chakraborty, H. Wang, and S. Bansal, “On safety and liveness filtering using hamilton–jacobi reachability analysis,” IEEE Transactions on Robotics , vol. 40, pp. 4235–4251, 2024

    2024

  59. [69]

    Data-driven safety filters: Hamilton- jacobi reachability, control barrier functions, and predictive methods for uncertain systems,

    K. P. Wabersich, A. J. Taylor, J. J. Choi, K. Sreenath, C. J. Tomlin, A. D. Ames, and M. N. Zeilinger, “Data-driven safety filters: Hamilton- jacobi reachability, control barrier functions, and predictive methods for uncertain systems,” IEEE Control Systems Magazine , vol. 43,...

    2023

  60. [70]

    The safety filter: A unified view of safety-critical control in autonomous systems,

    K.-C. Hsu, H. Hu, and J. F. Fisac, “The safety filter: A unified view of safety-critical control in autonomous systems,” Annual Review of Control, Robotics, and Autonomous Systems , vol. 7, 2023

    2023

  61. [71]

    Hamilton-Jacobi Reachability: A brief overview and recent advances,

    S. Bansal, M. Chen, S. Herbert, and C. J. Tomlin, “Hamilton-Jacobi Reachability: A brief overview and recent advances,” in IEEE Confer- ence on Decision and Control (CDC) , 2017

    2017

  62. [72]

    Combining op- timal control and learning for visual navigation in novel environments,

    S. Bansal, V . Tolani, S. Gupta, J. Malik, and C. Tomlin, “Combining op- timal control and learning for visual navigation in novel environments,” in Conference on Robot Learning (CoRL) , 2019

    2019

  63. [73]

    Parameter-conditioned reach- able sets for updating safety assurances online,

    J. Borquez, K. Nakamura, and S. Bansal, “Parameter-conditioned reach- able sets for updating safety assurances online,” in 2023 IEEE Inter- national Conference on Robotics and Automation (ICRA) , 2023, pp. 10 553–10 559

    2023

  64. [74]

    unitree ros

    Unitree Robotics. unitree ros. [Online]. Available: https://github.com/ unitreerobotics/unitree ros

  65. [75]

    On reachability and minimum cost optimal control,

    J. Lygeros, “On reachability and minimum cost optimal control,” Auto- matica, vol. 40, no. 6, pp. 917–927, 2004

    2004

  66. [76]

    A time-dependent Hamilton- Jacobi formulation of reachable sets for continuous dynamic games,

    I. Mitchell, A. Bayen, and C. J. Tomlin, “A time-dependent Hamilton- Jacobi formulation of reachable sets for continuous dynamic games,” IEEE Transactions on Automatic Control (TAC), vol. 50, no. 7, pp. 947– 957, 2005

    2005

  67. [77]

    hj reachability: Hamilton-jacobi reachability analysis in jax

    Edward Schmerling. hj reachability: Hamilton-jacobi reachability analysis in jax. [Online]. Available: https://github.com/StanfordASL/hj reachability

  68. [78]

    DeepReach: A deep learning approach to high-dimensional reachability,

    S. Bansal and C. J. Tomlin, “DeepReach: A deep learning approach to high-dimensional reachability,” in IEEE International Conference on Robotics and Automation (ICRA) , 2021

    2021

  69. [79]

    Conformal prediction: A gentle introduction,

    A. N. Angelopoulos and S. Bates, “Conformal prediction: A gentle introduction,” Foundations and Trends® in Machine Learning , vol. 16, no. 4, pp. 494–591, 2023. [Online]. Available: http: //dx.doi.org/10.1561/2200000101

    2023 doi

  70. [80]

    Verification of neural reachable tubes via scenario optimization and conformal prediction,

    A. Lin and S. Bansal, “Verification of neural reachable tubes via scenario optimization and conformal prediction,” in Proceedings of the 6th Annual Learning for Dynamics and Control Conference, ser. Proceedings of Machine Learning Research, A. Abate, M. Cannon, K. Margellos, a...

    2024

  71. [81]

    tinyslam: A slam algorithm in less than 200 lines c-language program,

    B. Steux and O. E. Hamzaoui, “tinyslam: A slam algorithm in less than 200 lines c-language program,” in 2010 11th International Conference on Control Automation Robotics and Vision , 2010, pp. 1975–1979

    2010

  72. [82]

    NIST Digital Library of Mathematical Functions ,

    “ NIST Digital Library of Mathematical Functions ,” https://dlmf.nist. gov/, Release 1.1.11 of 2023-09-15, 2023, f. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V . Saunders, H. S. Cohl, and M. A. McClain, eds. ...

    2023

  73. [731]

    Available: https://proceedings.mlr.press/v242/lin24a.html

    [Online]. Available: https://proceedings.mlr.press/v242/lin24a.html

  74. [2023]

    Available: http://dx.doi.org/10.55417/fr.2023013

    [Online]. Available: http://dx.doi.org/10.55417/fr.2023013

    doi

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.