Pith. sign in

REVIEW 5 major objections 5 minor 41 references

SHIELD: Safety on Humanoids via CBFs In Expectation on Learned Dynamics

T0 review · 5 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read Using a learned model of tracking error, SHIELD bounds the probability that a humanoid leaves its safe set without relying on the walking policy's internals.

desk verdict A useful, hardware-validated modular safety filter whose formal guarantee is not yet connected to the learned distribution actually used at runtime. read the letter →

arxiv 2505.11494 v3 pith:GH6WX6UJ submitted 2025-05-16 cs.RO

Lizhi Yang , Blake Werner , Ryan K. Cosner , David Fridovich-Keil , Preston Culbertson , Aaron D. Ames This is my paper · ORCID
classification cs.RO
keywords controlbarrierfunctionsstochasticsafetyhumanoidrobotsreinforcementlearninggenerativeresidualmodelconditionalvariationalautoencoderobstacleavoidancefilter
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

SHIELD is a safety layer that claims to give a humanoid robot a probabilistic collision-avoidance guarantee even when the walking controller is an opaque reinforcement-learned policy and no accurate dynamics model is available. The key is to model the robot's tracking error as a random disturbance learned from real trajectory data, and then to modulate the reference velocity command so that a stochastic discrete-time control barrier function holds in expectation. If the paper is right, safety constraints can be added or changed at runtime without retraining the underlying controller, the same way a reference governor reshapes commands. On a 23-degree-of-freedom humanoid with onboard LiDAR perception, the filtered commands avoid obstacles and pedestrians indoors and outdoors while improving tracking over the unfiltered commands.

What carries the argument

The load-bearing mechanism is the stochastic discrete-time control barrier function (S-DTCBF) condition $E[h(x_{k+1})\mid \mathcal{F}_k] \ge \alpha h(x_k)$, combined with the martingale concentration inequality of Theorem 1 to convert that one-step condition into a finite-horizon exit-probability bound. For online use, the paper replaces the intractable expectation with a generative-model lower bound: a conditional variational autoencoder (CVAE) learned from hardware rollouts supplies the mean and covariance of the disturbance $d_k$, and the concavity inequality of Proposition 1 converts $E[h(x_{k+1})]$ into $h(E[x_{k+1}]) - (\lambda_{\max}/2)\,\mathrm{tr}(\mathrm{cov}(d_k))$. The safety filter (Equation 14) then minimally perturbs the residual-compensated command subject to this tightened constraint, with $\alpha$ selected by root-finding from the desired risk level, covariance, horizon, and safety margin; for the concave single-obstacle barrier the paper proves a directional variance bound (Theorem 2) so the same filter works with covariance projected along the obstacle direction.

What would settle it

Run the SHIELD filter on hardware or in simulation for many $K$-step windows under a condition the residual model did not train on (heavier payload, slippery ground, an unseen obstacle type), count how often $h(x_k) < 0$, and compare with the claimed bound; if the empirical exit frequency exceeds the bound, the variance or surprise assumption is violated. A direct check is to log $E[h(x_{k+1})\mid \mathcal{F}_k]$ and $h(x_{k+1})$ during deployment and verify the conditional variance and surprise stay below $\sigma^2$ and $\delta$ used to choose $\alpha$.

Watch

Extended reading notes

Core claim

The paper's central claim is that enforcing the one-step conditional inequality $E[h(x_{k+1})\mid \mathcal{F}_k] \ge \alpha h(x_k)$, with $h$ the signed-distance-based safety function and $\alpha$ chosen from a desired risk level, yields a formal bound on the $K$-step exit probability via the martingale inequality of Theorem 1. The bound requires two assumptions: a conditional covariance bound and a bound on the one-step surprise $E[h(x_k)\mid \mathcal{F}_{k-1}] - h(x_k)$. SHIELD estimates the residual distribution $d_k$ with a conditional variational autoencoder trained on hardware rollouts, uses Proposition 1's concavity bound to turn the expectation constraint into a tractable deterministic constraint $h(F(x)+G(x)u + E[d]) - (\lambda_{\max}/2)\,\mathrm{tr}(\mathrm{cov}(d)) \ge \alpha h(x)$, and solves the resulting minimization every control tick at 100 Hz. In hardware experiments, the safety filter outperforms a conventional DTCBF filter that ignores the residual, which either collides because it is overconfident or is overly conservative, and the same layer works with more than one walking controller and in unstructured environments with people.

Load-bearing premise

The guarantee collapses if real-world disturbances turn out to be bigger or more variable than anything in the training data, because the two bounds that feed the probability calculation are estimated from data, not proven.

Editorial extensions

If this is right

  • A nominal black-box locomotion controller can be retrofitted with runtime obstacle-avoidance constraints without any retraining of the policy.
  • Because the learned residual also corrects the mean tracking error, the safety layer is less invasive than a filter that only considers the simplified model.
  • The $K$-step exit-probability guarantee can be extended to arbitrarily long runs by re-selecting $\alpha$ every $K$ steps and chaining the intervals with a union bound.
  • The filter runs online at 100 Hz on embedded hardware with 0.83 Hz model updates, so the guarantee is compatible with real-world onboard sensing.
  • The same S-DTCBF layer transfers across different walking controllers by retraining the residual model on data from the new controller.

Reading between the lines

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

  • If the training-data covariance is not a certified upper bound, the guarantee is really conditional on deployment matching the training distribution; a natural hardening would replace the variance estimate with a distribution-free confidence bound from the collected residuals.
  • The single-obstacle concave-barrier proof suggests an explicit testable extension: a multi-obstacle filter that retains rigor by treating each obstacle direction separately or by explicitly bounding the error introduced when the closest obstacle switches.
  • Because SHIELD acts on reference commands rather than joint torques, the same framework should apply to any command-tracking abstraction, such as footstep positions, whole-body velocities, or task-space poses, provided a residual model can be trained for it.
  • An adversarial evaluation would be to deploy the filter on terrain or with payloads outside the training distribution and measure the empirical $K$-step exit frequency against the claimed bound; this would reveal whether the variance and surprise assumptions are the dominant source of risk.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The paper proposes SHIELD, a layered safety architecture for humanoid robots that filters high-level velocity commands from a black-box locomotion controller. A conditional variational autoencoder (CVAE) is trained on hardware rollouts to model the distribution of the tracking residual between the robot's reduced-order dynamics and its actual closed-loop behavior. The filter enforces a stochastic discrete-time control barrier function (S-DTCBF) condition in expectation under the learned residual distribution, using Jensen's inequality to obtain a tractable constraint. The authors claim that this procedure yields a formal probabilistic safety guarantee, namely a bounded K-step exit probability from a user-defined safe set, via a Freedman-style inequality from prior work. The method is evaluated in simulation with a known disturbance distribution and on a Unitree G1 humanoid in indoor and outdoor obstacle-avoidance experiments, including multi-obstacle scenarios with onboard perception.

Significance. If the formal guarantees held as stated, this would be a valuable contribution: a minimally-invasive safety filter that can be layered on top of an unknown RL locomotion policy, requiring only data from nominal rollouts and providing runtime constraint specification. The use of a generative model to capture non-Gaussian, state-dependent residuals is timely, and the hardware demonstration on a humanoid is substantial. The paper also contributes a specialized Jensen-type bound for a smoothed single-obstacle signed-distance safety function (Theorem 2). The system is well engineered, with clear potential for practical impact. However, the central theoretical claim—that the deployed filter provides a formal exit-probability guarantee—is not actually established, because the gap between the learned distribution used in the filter and the true conditional distribution of the system is not addressed. If the authors can close this gap or appropriately scope the claims, the paper could be a strong candidate for publication.

major comments (5)
  1. [§III, Eq. (16) and Algorithm 1] The S-DTCBF constraint is enforced using the learned distribution pθ, but Theorem 1 (Eq. (10)) and its assumptions (8)–(9) are stated in terms of the true conditional distribution D. The constraint actually implemented in Eq. (16) and Algorithm 1 substitutes E_{pθ}[d_k|·] and cov_{pθ}(d_k|·) into a Jensen lower bound that holds for pθ, with no argument that E_{pθ}[h(x_{k+1})] ≤ E_D[h(x_{k+1})] or that the moments of pθ dominate those of D. Consequently, the executed filter may violate the true S-DTCBF condition even when Eq. (16) is satisfied, and the K-step exit probability bound of Theorem 1 is not formally connected to the deployed system. This is load-bearing for the paper's central claim of a formal guarantee. Please provide a certified high-probability bound on the model error (e.g., via conformal prediction or distributionally robust optimization), or explicitly weaken the claim to a heuristic safety filter with empirical validation.
  2. [§III, Eq. (13) and §V, Simulation] Assumption (9) requires a deterministic bound δ on E[h(x_k)|F_{k-1}] - h(x_k). The paper asserts δ = 2(h(x_footstep k) - h(x_footstep k+1)) in Eq. (13) without a derivation linking the footstep-level safety change to the conditional expectation in (9). In the simulation, δ is simply set to 1, and the hardware experiments do not report how δ is computed from (13). Since δ appears explicitly in the exponential bound (10), an unvalidated δ means the claimed numerical probability bound is not established. Please provide a rigorous derivation of a valid δ, or present δ as a tunable hyperparameter and avoid claiming that Eq. (10) yields a quantified safety probability.
  3. [§IV and §V, Multi-obstacle experiments] Theorem 2 is proved only for the single-obstacle case N=1, and the text states that a rigorous analysis of the nonconcave rh with multiple obstacles is left for future work. Nevertheless, multi-obstacle avoidance is presented as a key hardware result (Fig. 6) and the abstract claims probabilistic safety guarantees without this caveat. The formal theory presented in the paper does not cover the multi-obstacle experiments, so the claim of a formal guarantee for the demonstrated scenarios is unsupported. Please either extend the theory (e.g., by showing that the minimum over obstacle-specific rh functions preserves the required martingale inequality) or clearly restrict the formal claims to single-obstacle settings and mark multi-obstacle results as empirical.
  4. [Appendix A, Proof of Theorem 2] There appears to be a sign error in the Hessian computation. For b_h(x) = λ(1 - e^{-γ((p-ρ_1)^T e_1 - R_1)}), the Hessian with respect to p is -λγ^2 e^{-γ(·)} e_1 e_1^T, which is negative semidefinite, not positive as stated in Eq. (27). The proof then claims ∇^2rh(x) is positive semidefinite, which is inconsistent with concavity of b_h. The inequality (28) may still be true because the Hessian of η = -rh is bounded above along e_1, but the written justification is incorrect. Additionally, the definition of rh in the 'else' branch of Eq. (22) is dimensionally inconsistent: ∇_x b_h(x) is a vector, while rh must be a scalar. Please correct the sign in the proof and clarify the definition of rh.
  5. [Algorithm 1, lines 7–14] Line 7 computes Σ as a covariance matrix from the CVAE, but line 8 calls L(K, h_k, P, δ, Σ) where L in Eq. (12) expects a scalar variance bound σ; the text says σ is set to the maximum value experienced in the data, which is not how Σ is used in the algorithm. Line 12 reuses λ for both the safety-function scale in Eq. (20) and the Hessian bound λ_max, making the pseudocode ambiguous. These inconsistencies hinder reproducibility of the algorithm and should be fixed.
minor comments (5)
  1. [Throughout] The symbol λ is overloaded: it denotes the safety-function amplitude in Eq. (20), the exponent in Theorem 1, and the Hessian bound in Algorithm 1. Please use distinct symbols for these quantities.
  2. [Eq. (13)] Please define x_footstep k and x_footstep k+1 precisely, and specify how the maximum step distance is measured in practice.
  3. [§V, Simulation] The statement that δ is set to 1 as 'the upper bound on the assumption of bounded difference of (9)' is disconnected from Eq. (13); clarify the relationship or state that δ is a design hyperparameter.
  4. [References] When introducing the CVAE, please cite the original VAE paper (Kingma and Welling, 2014) as well as the conditional VAE reference [30].
  5. [Eq. (22)] The 'else' branch should be written with clear parentheses, e.g., rh(x) = ∇b_h(x)^T (p - ρ_i) + λ(1 - e^{γ R_i}), to avoid dimensional inconsistency.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the probabilistic safety claim rests on externally stated theorems and the learned/fitted quantities enter as assumptions rather than as the predicted quantity.

full rationale

SHIELD's central derivation chain is not circular. Theorem 1, cited as [29, Thm. 3], is a general Freedman-inequality bound whose assumptions (8) and (9) concern the true conditional variance and martingale difference of the safety function; these assumptions are not defined in terms of the CVAE's p_theta, and the theorem is not parameterized by SHIELD's implementation. Proposition 1, cited as [22, Lem. 1], is a standard Jensen-inequality lower bound for twice-differentiable concave functions; it is an independent, parameter-free mathematical statement. The actual filter in Eq. (16) enforces the S-DTCBF condition using the learned distribution p_theta in place of the true conditional distribution D, and the paper explicitly says it 'approximate[s] E[d_k|F_k] and cov(d_k|F_k) using the learned dynamics residual distribution p_theta'. If p_theta is miscalibrated, the hypothesis of Theorem 1 may fail, but this is a modeling/robustness gap rather than a reduction of the guarantee to its input. Similarly, the variance bound sigma^2 is 'approximated from the sampled dataset D' and delta is set by Eq. (13) to twice a footstep-level safety change, but these enter as assumed bounds in Eqs. (8)-(9), not as a fitted prediction of the exit probability; alpha is solved from a user-chosen risk level P via Eq. (12) and Fig. 3, not tuned to reproduce observed failures. The paper also explicitly defers a rigorous multi-obstacle treatment ('we leave a rigorous theoretical analysis of the nonconcave h with multiple obstacles for future work'), which is a stated limitation, not a circular step. The self-citations to [22] and [29] are load-bearing in the sense of supplying the theoretical backbone, but they are prior published theorems with proofs, not unpublished assertions by the same authors, and they do not assume the SHIELD implementation as an input. Overall the derivation is self-contained modulo standard external theorems, and none of the claimed predictions reduce by construction to fitted parameters or self-citations.

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

The central safety guarantee inherits several axioms from the architecture: the additive residual model is faithful, the learned CVAE distribution matches the true conditional residual, and the two Freedman bounds (variance and surprise) are valid. The first two are domain assumptions validated only by a six-minute training set and qualitative hardware success; the variance bound is a data-derived estimate and the surprise bound is asserted without derivation. The single-obstacle concavity result is proven, but the multi-obstacle extension is an unproven approximation.

free parameters (5)
  • lambda (safety function scale) = 10 (simulation)
    Hand-chosen scale in Eq. (20) controlling the maximum value of the smoothed safety function; affects conservatism.
  • gamma (safety function smoothness) = 0.5 (simulation)
    Hand-chosen smoothing parameter in Eq. (20).
  • K (horizon) = 10
    Horizon for the exit-probability bound; alpha is recomputed every K steps.
  • sigma (variance bound for assumption (8)) = maximum covariance in training data
    Used to apply Freedman's inequality; it is an estimate, not a certified upper bound, so the formal guarantee is conditional.
  • delta (surprise bound for assumption (9)) = 2(h(footstep_k)-h(footstep_{k+1}))
    Approximation from maximum step distance, asserted without derivation.
assumptions (5)
  • domain assumption The additive residual model (4) with disturbance d_k sampled from a learned conditional distribution accurately represents the closed-loop reduced-order behavior of the robot.
    The CVAE is trained on 6 minutes of obstacle-free data; no certification that it holds during obstacle avoidance or on new commands.
  • domain assumption The conditional variance bound in assumption (8), Var(h(x_{k+1})|F_k) <= sigma^2, holds with sigma set to the maximum observed covariance in the training data.
    This is necessary for Theorem 1 but is not verified online; the deployed guarantee depends on this estimate.
  • domain assumption The surprise bound in assumption (9), E[h(x_k)|F_{k-1}] - h(x_k) <= delta, holds with delta from Eq. (13).
    The most fragile premise; Eq. (13) is asserted without derivation and must hold for the Freedman bound to apply.
  • ad hoc to paper The closest-obstacle concave approximation tilde(h) (Eqs. 21-22) is a valid safety characterization for multiple obstacles.
    The authors state that rigorous multi-obstacle analysis is future work; the deployed filter uses this non-rigorous approximation.
  • standard math Jensen's inequality applies to the chosen safety function (concave, twice differentiable, bounded Hessian).
    Used in Prop. 1 (from ref [22]) and Theorem 2 to lower-bound the expectation of h; standard but requires the concavity and bounded-curvature conditions.

how reviews work

0 comments
Cite this review

Pith. "Pith review of SHIELD: Safety on Humanoids via CBFs In Expectation on Learned Dynamics." pith.science (2026). https://pith.science/paper/GH6WX6UJ

@misc{pith2026250511494,
  author       = {Pith},
  title        = {Pith review of: SHIELD: Safety on Humanoids via CBFs In Expectation on Learned Dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GH6WX6UJ}},
  note         = {Machine review of arXiv:2505.11494}
}
read the original abstract

Robot learning has produced remarkably effective ``black-box'' controllers for complex tasks such as dynamic locomotion on humanoids. Yet ensuring dynamic safety, i.e., constraint satisfaction, remains challenging for such policies. Reinforcement learning (RL) embeds constraints heuristically through reward engineering, and adding or modifying constraints requires retraining. Model-based approaches, like control barrier functions (CBFs), enable runtime constraint specification with formal guarantees but require accurate dynamics models. This paper presents SHIELD, a layered safety framework that bridges this gap by: (1) training a generative, stochastic dynamics residual model using real-world data from hardware rollouts of the nominal controller, capturing system behavior and uncertainties; and (2) adding a safety layer on top of the nominal (learned locomotion) controller that leverages this model via a stochastic discrete-time CBF formulation enforcing safety constraints in probability. The result is a minimally-invasive safety layer that can be added to the existing autonomy stack to give probabilistic guarantees of safety that balance risk and performance. In hardware experiments on an Unitree G1 humanoid, SHIELD enables safe navigation (obstacle avoidance) through varied indoor and outdoor environments using a nominal (unknown) RL controller and onboard perception.

Figures

Figures reproduced from arXiv: 2505.11494 by the authors.

Figure 1
Figure 1. A humanoid robot implementing the SHIELD architecture au￾tonomously avoids collision with a human using onboard sensing. SHIELD combines a performant underlying controller (e.g., an RL-trained locomotion policy) with a safety layer, which modulates high-level reference signals through a generative model of tracking error trained using real-world trajectory data. This architecture allows safety constraints (like coll… view at source ↗
Figure 2
Figure 2. SHIELD enables real-world pedestrian avoidance with a humanoid robot, using a “general-purpose” RL policy. Top: Our robot safely walks among pedestrians using SHIELD’s stochastic safety framework. Bottom: The robot relies solely on onboard perception to detect and avoid obstacles. Experimental video of this experiment can be found at: https://vimeo.com/1061676063. barrier functions (CBFs) [15], [16]. This method tak… view at source ↗
Figure 3
Figure 3. Higher α = L(P, K = 10, h(x0) = 10, δ = 0.01, σ) values correspond to more conservative behavior. This increased conservatism is a consequence of a lower K-step exit probability or a higher variance. invertibility of G(xk), the optimal u is2 : u ∗ k = G† (xk)(−F(xk) + xk+1 − E[dk|Fk]). (11) However, since we do not have access to the true expectation E[dk|Fk], we approximate this with the learned expectation compute… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: SHIELD improves tracking performance by correcting learned disturbances. After applying the SHIELD correction as shown by the blue dashed lines, the robot’s tracking of the user’s intended velocities (shown as a black dashed lines) improves. In addition to meeting assu…
Figure 5
Figure 5. Figure 5: The trade-off between performance and safety. As the probability of K-step exit increases, we achieve better performance at cost of an increasing amount of safety violation under the proposed metric. (13), and the covariance σ is set to the maximum value experienced in…
Figure 6
Figure 6. Figure 6: SHIELD enforces safety in collision avoidance with adaptive conservatism. The A* planner path is not necessarily safe even though it does not cross the obstacle, thus naively following the path would result in collisions or scrapes. Nominal CBF, due to not accounting f…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

41 extracted references · 17 canonical work pages

  1. [29]

    Bounding stochastic safety: Leveraging freedman’s inequality with discrete-time control barrier functions,

    R. K. Cosner, P. Culbertson, and A. D. Ames, “Bounding stochastic safety: Leveraging freedman’s inequality with discrete-time control barrier functions,” IEEE Control Systems Letters , 2024

    work page 2024

  2. [1]

    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, Jan. 2019

    work page 2019

  3. [2]

    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

    2020

  4. [3]

    Genloco: Generalized locomotion controllers for quadrupedal robots,

    G. Feng, H. Zhang, Z. Li, X. B. Peng, B. Basireddy, L. Yue, Z. Song, L. Yang, Y . Liu, K. Sreenath,et al., “Genloco: Generalized locomotion controllers for quadrupedal robots,” in Conference on Robot Learning. PMLR, 2023, pp. 1893–1903

    work page 2023

  5. [4]

    Berkeley humanoid: A research platform for learning-based control,

    Q. Liao, B. Zhang, X. Huang, X. Huang, Z. Li, and K. Sreenath, “Berkeley humanoid: A research platform for learning-based control,” arXiv preprint arXiv:2407.21781 , 2024

    arXiv 2024

  6. [5]

    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, p. eabk2822, 2022

    2022

  7. [6]

    Real-world humanoid locomotion with reinforcement learning,

    I. Radosavovic, T. Xiao, B. Zhang, T. Darrell, J. Malik, and K. Sreenath, “Real-world humanoid locomotion with reinforcement learning,” Science Robotics, vol. 9, no. 89, p. eadi9579, 2024

    2024

  8. [7]

    Mujoco playground,

    K. Zakka, B. Tabanpour, Q. Liao, M. Haiderbhai, S. Holt, J. Y . Luo, A. Allshire, E. Frey, K. Sreenath, L. A. Kahrs, et al. , “Mujoco playground,” arXiv preprint arXiv:2502.08844 , 2025

    arXiv 2025

Show all 41 references
  1. [8]

    Humanoid parkour learning,

    Z. Zhuang, S. Yao, and H. Zhao, “Humanoid parkour learning,” arXiv preprint arXiv:2406.10759, 2024

    2024 arXiv

  2. [9]

    Safe planning in dynamic environments using conformal prediction,

    L. Lindemann, M. Cleaveland, G. Shim, and G. J. Pappas, “Safe planning in dynamic environments using conformal prediction,” IEEE Robotics and Automation Letters , 2023

    2023

  3. [10]

    Sample-based bounds for coherent risk measures: Applications to policy synthesis and verification,

    P. Akella, A. Dixit, M. Ahmadi, J. W. Burdick, and A. D. Ames, “Sample-based bounds for coherent risk measures: Applications to policy synthesis and verification,” Artificial Intelligence , vol. 336, p. 104195, 2024

    2024

  4. [11]

    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,” arXiv preprint arXiv:2401.17583, 2024

    2024 arXiv

  5. [12]

    A time-dependent hamilton-jacobi formulation of reachable sets for continuous dynamic games,

    “A time-dependent hamilton-jacobi formulation of reachable sets for continuous dynamic games,” IEEE Transactions on automatic control, vol. 50, no. 7, pp. 947–957, 2005

    2005

  6. [13]

    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 2017 IEEE 56th Annual Conference on Decision and Control (CDC) , 2017, pp. 2242–2253

    2017

  7. [14]

    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. Tom- lin, 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

  8. [15]

    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

    2017

  9. [16]

    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,” in 2019 18th European Control Conference (ECC) , 2019, pp. 3420– 3431

    2019

  10. [17]

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

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

    2021

  11. [18]

    Episodic learning for safe bipedal locomotion with control barrier functions and projection-to-state safety,

    N. Csomay-Shanklin, R. K. Cosner, M. Dai, A. J. Taylor, and A. D. Ames, “Episodic learning for safe bipedal locomotion with control barrier functions and projection-to-state safety,” in Learning for dy- namics and control . PMLR, 2021, pp. 1041–1053

    2021

  12. [19]

    Model-free safety-critical control for robotic systems,

    T. G. Molnar, R. K. Cosner, A. W. Singletary, W. Ubellacker, and A. D. Ames, “Model-free safety-critical control for robotic systems,” IEEE robotics and automation letters , vol. 7, no. 2, pp. 944–951, 2021

    2021

  13. [20]

    Safety-critical control for autonomous systems: Control barrier functions via reduced-order models,

    M. H. Cohen, T. G. Molnar, and A. D. Ames, “Safety-critical control for autonomous systems: Control barrier functions via reduced-order models,” Annual Reviews in Control , vol. 57, p. 100947, 2024

    2024

  14. [21]

    Control barrier functions for complete and incomplete information stochastic systems,

    A. Clark, “Control barrier functions for complete and incomplete information stochastic systems,” in 2019 American Control Conference (ACC), 2019, pp. 2928–2935

    2019

  15. [22]

    Robust safety under stochastic uncertainty with discrete-time control barrier functions,

    R. K. Cosner, P. Culbertson, A. J. Taylor, and A. D. Ames, “Robust safety under stochastic uncertainty with discrete-time control barrier functions,” Robotics: Science and Systems , 2023

    2023

  16. [23]

    Generative modeling of residuals for real-time risk-sensitive safety with discrete-time control barrier functions,

    R. K. Cosner, I. Sadalski, J. K. Woo, P. Culbertson, and A. D. Ames, “Generative modeling of residuals for real-time risk-sensitive safety with discrete-time control barrier functions,” in 2024 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2024, pp. i–viii

    2024

  17. [24]

    Input- to-state stability in probability,

    P. Culbertson, R. K. Cosner, M. Tucker, and A. D. Ames, “Input- to-state stability in probability,” in 2023 62nd IEEE Conference on Decision and Control (CDC) . IEEE, 2023, pp. 5796–5803

    2023

  18. [25]

    A barrier function approach to finite-time stochastic system verification and control,

    C. Santoyo, M. Dutreix, and S. Coogan, “A barrier function approach to finite-time stochastic system verification and control,” Automatica, vol. 125, p. 109439, 2021

    2021

  19. [26]

    Finite-time regional verification of stochastic non-linear systems,

    J. Steinhardt and R. Tedrake, “Finite-time regional verification of stochastic non-linear systems,” The International Journal of Robotics Research, vol. 31, no. 7, pp. 901–923, 2012

    2012

  20. [27]

    Control barrier functions in sampled-data systems,

    J. Breeden, K. Garg, and D. Panagou, “Control barrier functions in sampled-data systems,” IEEE Control Systems Letters, vol. 6, pp. 367– 372, 2022

    2022

  21. [28]

    Discrete control barrier functions for safety-critical control of discrete systems with application to bipedal robot navigation,

    A. Agrawal and K. Sreenath, “Discrete control barrier functions for safety-critical control of discrete systems with application to bipedal robot navigation,” in Proceedings of Robotics: Science and Systems , Cambridge, Massachusetts, July 2017

    2017

  22. [30]

    Learning structured output representa- tion using deep conditional generative models,

    K. Sohn, H. Lee, and X. Yan, “Learning structured output representa- tion using deep conditional generative models,” in Advances in Neural Information Processing Systems , C. Cortes, N. Lawrence, D. Lee, M. Sugiyama, and R. Garnett, Eds., vol. 28. Curran Associates, Inc., 2015

    2015

  23. [31]

    Denoising diffusion probabilistic models,

    J. Ho, A. Jain, and P. Abbeel, “Denoising diffusion probabilistic models,” in Advances in Neural Information Processing Systems , H. Larochelle, M. Ranzato, R. Hadsell, M. Balcan, and H. Lin, Eds., vol. 33. Curran Associates, Inc., 2020, pp. 6840–6851

    2020

  24. [32]

    Flow matching for generative modeling,

    Y . Lipman, R. T. Q. Chen, H. Ben-Hamu, M. Nickel, and M. Le, “Flow matching for generative modeling,” 2023

    2023

  25. [33]

    Control barrier function based quadratic programs with application to adaptive cruise control,

    A. D. Ames, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs with application to adaptive cruise control,” in 53rd IEEE Conference on Decision and Control , 2014, pp. 6271– 6278

    2014

  26. [34]

    Reference and command governors for systems with constraints: A survey on theory and applications,

    E. Garone, S. Di Cairano, and I. Kolmanovsky, “Reference and command governors for systems with constraints: A survey on theory and applications,” Automatica, vol. 75, pp. 306–328, 2017

    2017

  27. [35]

    R. P. Brent, Algorithms for minimization without derivatives . Courier Corporation, 2013

    2013

  28. [36]

    3D is here: Point Cloud Library (PCL),

    R. B. Rusu and S. Cousins, “3D is here: Point Cloud Library (PCL),” in IEEE International Conference on Robotics and Automation (ICRA) . Shanghai, China: IEEE, May 9-13 2011

    2011

  29. [37]

    Unitree sdk2,

    U. Robotics, “Unitree sdk2,” 2024, accessed: 2025-03-01. [Online]. Available: https://github.com/unitreerobotics/unitree sdk2

    2024

  30. [38]

    Orbit: A unified simulation framework for interactive robot learning environments,

    M. Mittal, C. Yu, Q. Yu, J. Liu, N. Rudin, D. Hoeller, J. L. Yuan, R. Singh, Y . Guo, H. Mazhar, A. Mandlekar, B. Babich, G. State, M. Hutter, and A. Garg, “Orbit: A unified simulation framework for interactive robot learning environments,” IEEE Robotics and Automa- tion Lette...

    2023

  31. [39]

    Ad- vancing humanoid locomotion: Mastering challenging terrains with denoising world model learning,

    X. Gu, Y .-J. Wang, X. Zhu, C. Shi, Y . Guo, Y . Liu, and J. Chen, “Ad- vancing humanoid locomotion: Mastering challenging terrains with denoising world model learning,” in Robotics: Science and Systems , 2024

    2024

  32. [40]

    A formal basis for the heuristic determination of minimum cost paths,

    P. Hart, N. Nilsson, and B. Raphael, “A formal basis for the heuristic determination of minimum cost paths,” IEEE Transactions on Systems Science and Cybernetics , vol. 4, no. 2, pp. 100–107, 1968

    1968

  33. [41]

    Experimental video

    “Experimental video.” [Online]. Available: https://youtu.be/ -Qv1wR4jfj4

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.