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REVIEW 3 major objections 4 minor 40 references

Learning Fault-Tolerant Locomotion with Adaptive Gait Timing

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A single policy keeps a 68 kg quadruped walking after sudden joint power loss.

desk verdict A competent fault-tolerant locomotion paper with a credible hardware demo, but the adaptive gait timing claim rests on a confounded ablation and needs a cleaner experiment. read the letter →

arxiv 2608.07328 v1 pith:33265Z4L submitted 2026-08-07 cs.RO cs.LG

Giovanbattista Gravina , Luca Rossini , Carlo Rizzardo , Arturo Laurenzi , Nikos Tsagarakis This is my paper · ORCID
classification cs.ROcs.LG
keywords fault-tolerantlocomotionquadrupedrobotsreinforcementlearningasymmetricactor-criticlatentalignmentgaitfrequencyadaptationpowerlossfaultsim-to-realtransfer
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 show that a single control policy, trained once in simulation, can keep a 68 kg quadruped walking after one of its actuators suddenly loses power, without being told which leg is damaged or how to alter the gait. The robot infers the fault from a short history of its own joint readings and copes by learning to change step timing through a gait-frequency action, rather than by adopting a predefined tripod or three-legged strategy. The authors argue that such adaptive timing is the right response for heavier robots, where the mass and actuation limits make the fast corrective movements used on smaller quadrupeds impractical. They back this with simulation results on uneven terrain, ablations showing the value of history and of the alignment loss, and a real-robot demonstration on flat ground after a knee joint fails. If the claim holds, it would mean that robust fault tolerance can be bought with a single learned controller rather than a library of failure-specific responses.

What carries the argument

The central machinery is an asymmetric actor-critic architecture reinforced by two additions on top of the standard PPO objective. First, a latent-alignment loss $\mathcal{L}_{\mathrm{MSE}} = \mathbb{E}[(\hat{r}_t - r_t)^2]$ forces the actor encoder's latent representation $\hat{r}_t$, computed from a history $h_t = \langle o_t,\ldots,o_{t-H+1}\rangle$ of proprioceptive observations, to match the critic encoder's latent $r_t$, which is computed from privileged observations including the joint fault mask $m_{J,t}$. Second, the action space is augmented with a scalar gait-frequency action $a^\nu_t$ that modulates the reference stepping frequency $\nu^{\mathrm{ref}}_t = \nu^{\mathrm{def}} + s_\nu a^\nu_t$, whose phase update $\phi_{t+1,\ell} = \mathrm{mod}(\phi_{t,\ell} + 2\pi\Delta t\,\nu^{\mathrm{ref}}_t + \pi, 2\pi) - \pi$ drives the reference contact schedule used in the reward. Power loss is encoded in training by scaling the PD torque output as $\tau_j \leftarrow k_{\tau,j}\tau_j$ with a curriculum over $k_{\tau,j}$, and faulty legs are excluded from the feet-phase reward so the policy is never pushed toward a specific compensation gait.

What would settle it

Compare the trained policy's survival time and command-tracking error on the physical robot under a partial torque collapse (for example $k_{\tau,j} = 0.5$) and a hip-joint fault during stair descent, against the simulation values reported in Fig. 5; if real-robot performance falls far below the simulated distribution, the zero-shot sim-to-real claim and the fault model are contradicted.

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Extended reading notes

Core claim

On its own terms, the paper's central claim is that an asymmetric actor-critic reinforcement learning setup, augmented with a latent-alignment loss and a learnable gait-frequency action, yields a single policy that maintains locomotion under sudden actuator power loss on a 68 kg quadruped, with no predefined faulty-leg strategy. The critic is trained with privileged information that explicitly includes a joint fault mask, while the deployed actor sees only a history of noisy proprioceptive observations plus terrain height; a mean-squared-error term forces the actor's latent code toward the critic's privileged code, and the phase-consistency reward is masked for faulty legs so the policy is free to discover contact schedules that work with a dead joint. Torque loss is modeled as scaling the commanded torque by a factor $k_{\tau,j} \in [0,1]$ on the failed joint, with a curriculum that gradually deepens the fault severity based on velocity-tracking performance. The result is a policy whose gait-frequency action rises during single support and falls during double support after a knee fault, effectively switching to a tripodal pattern with longer, more periodic stance phases, and which transfers zero-shot to the real Kyon robot for a rear-left knee-pitch power loss on flat ground.

Load-bearing premise

The method's real-world validity rests on the assumption that the torque-scaling model of power loss used in training, with its domain-randomization ranges, reproduces real actuator failures closely enough that a policy trained in simulation works zero-shot on the physical robot; the paper only tests this for one joint at one severity on flat ground.

Editorial extensions

If this is right

  • A single policy, trained once in simulation, can be deployed without any fault-detection or leg-status input; the fault is inferred from proprioceptive history alone.
  • Under knee-joint faults the policy spontaneously adopts a tripodal gait with longer, more periodic stance phases, and the learned gait-frequency action rises in single support and falls in double support.
  • The controller generalizes in simulation to novel terrain profiles (stairs with 10 cm steps and ramps up to 13 degrees) without retraining.
  • Increasing the proprioceptive history beyond two steps yields only marginal gains, indicating that one-step temporal differences carry most of the information needed to reconstruct the privileged fault state.
  • For heavier quadrupeds, adaptive step timing may be the scalable fault-response strategy, because the robot's mass and actuation limits preclude the aggressive high-frequency corrections used on smaller platforms.

Reading between the lines

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

  • Beyond the paper's experiments, the latent-alignment loss likely also transfers non-fault privileged information (terrain, dynamics); a healthy-only ablation would reveal whether alignment still helps when no fault is present, which the paper does not report.
  • Because the real-world validation uses flat ground with terrain observations zeroed, the claims about uneven-terrain deployment depend on the perception pipeline; testing on uneven real terrain with onboard terrain reconstruction is a direct next step the paper lists but does not take.
  • The gait-frequency action's periodic modulation suggests the policy learns an internal phase clock tied to contact state; one testable implication is that commanding a different nominal frequency $\nu^{\mathrm{def}}$ would preserve the ratio of single-to-double support durations, which the paper does not measure.
  • A sharper falsification would target hip-roll faults during stair descent, where the passively swinging leg's dynamics differ most from the tested knee-pitch case; the paper's survival-time plots already show hip-roll faults are among the harder cases in simulation.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes a reinforcement-learning controller for a 68 kg quadruped (Kyon) that maintains locomotion after a sudden actuator power-loss fault. The architecture is an asymmetric actor-critic in which the critic uses privileged fault information while the actor is trained with a latent-alignment loss to reconstruct that information from a history of proprioceptive observations. The action space is augmented with a scalar gait-frequency action aν that modulates the reference phase used by a feet-phase reward. Training is done with PPO in MJX on stepped-pyramid terrain with a torque-efficiency curriculum, and evaluation includes five-seed learning curves, simulation tests with random faults, a sim-to-sim MuJoCo/XBot2 study, and one real-hardware flat-ground experiment with a rear-left knee fault.

Significance. If the mechanism claims are supportable, the paper contributes a useful single-policy approach to fault-tolerant locomotion: the policy is fault-unaware at deployment, no predefined faulty-leg strategy is prescribed, and the hardware result on a 68 kg quadruped is a meaningful step beyond small-platform demonstrations. Strengths of the manuscript include five-run confidence intervals on the learning curves, detailed reporting of network sizes and PPO hyperparameters, a realistic sim-to-sim setup with asynchronous XBot2 communication, and an honest distinction between uneven-terrain simulation and flat-ground hardware validation. The main weakness is that the headline 'adaptive gait timing' benefit is not causally identified by the presented ablation, because the reference phase used in the reward is a function of the policy's own frequency action and because the ablation changes the reward function at the same time as the action space.

major comments (3)
  1. [III-B, III-C, Eq. (2)] The feet-phase reward is endogenous in a way that undermines the causal interpretation of the learnable gait-frequency action. In Section III-B the reference frequency is νref_t = ν_def + sν aν_t, and the same phase update is used to generate the reference contact schedule cref in Eq. (2) and Table II. Thus the policy can increase its feet-phase reward by moving aν_t so that cref shifts toward the contact pattern the policy already produces, rather than by coordinating to a fixed temporal reference. The paper's stated novelty depends on aν being beneficial as an adaptation mechanism, so this endogeneity weakens the support for that central claim.
  2. [IV-C.2, Fig. 9, Fig. 10] The learnable-gait-frequency ablation is confounded because it changes two variables at once. The text states that, 'For a fair comparison, we replace the feet-phase reward term ... with the widely used feet air-time reward.' The full method therefore differs from the 'free-gait' baseline both in the presence of aν and in the reward function, and any observed performance difference could come from the air-time reward alone rather than from the frequency action. A clean ablation should keep the reward fixed (for example, a feet-phase reward computed from the default frequency for both policies) and remove only the frequency action from the action space.
  3. [IV-B, Fig. 5] The main simulation performance metrics in Fig. 5 are reported without error bars or confidence intervals. The figure is the primary deployment-time evidence that the full method outperforms its ablations across fault locations, yet it appears to be based on one selected policy per training run without reporting variance over the five runs or over the 1024 test agents. The learning curves in Fig. 4 already use 95% confidence intervals, and the same standard should be applied to the evaluation metrics so that the comparison is statistically grounded.
minor comments (4)
  1. [IV-B.2] The real-hardware validation covers a single fault configuration (rear-left knee pitch joint) on flat ground with terrain observations set to zero. This is a useful proof of concept, but the text could state more prominently that hardware transfer to other joints, partial torque degradation, and uneven terrain remains untested.
  2. [III-D, Table V] The fault model is a scalar torque-efficiency scaling τ_j ← kτ,j τ_j applied to the PD output. The paper does not discuss how real failures involving partial torque collapse, increased joint friction, or communication latency would map to this model; a brief limitation sentence would clarify the intended scope of the sim-to-real claim.
  3. [Fig. 4 caption] The caption says the method 'outperforms the same architecture without proprioceptive history (green) and without latent-alignment loss (yellow),' but the comparison with the oracle is also shown; it would be clearer to state explicitly that the red curve is closest to the oracle among the non-privileged variants.
  4. [IV-B, Fig. 5] The relationship between the 25 s experiment duration and the reported maximum survival time of 20 s is confusing; since the fault occurs at t = 5 s, the maximum post-fault survival time is 20 s, and this should be stated in the text to avoid an apparent inconsistency.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the RL pipeline is self-contained and validated against external sim and real-robot benchmarks; the self-referential phase reward is a reward-design detail, not a derived prediction.

full rationale

The paper's central claims are empirical: a single policy, trained with asymmetric actor-critic and a latent-alignment loss, maintains locomotion under sudden actuator power loss. The training objective, the fault model (Section III-D), and the domain randomization (Table V) are stated independently of the results, and the main validation comes from external benchmarks: sim-to-sim generalization to unseen stair and ramp profiles (Section IV-B.1) and a zero-shot real-world fault experiment on the Kyon robot (Section IV-B.2). No fitted parameter is renamed as a prediction, and no load-bearing claim rests on a self-citation: citations to the authors' own Kyon platform [5] and XBot2 middleware [39] are infrastructural, not evidential for the method's effectiveness. The one self-referential element is the feet-phase reward (Table II), whose reference contact schedule c_ref is generated from the phase update phi_{t+1,ell} = mod(phi_{t,ell} + 2*pi*Delta_t*nu_ref + pi, 2*pi) - pi with nu_ref = nu_def + s_nu*a_nu, so the policy's own frequency action shifts the reward target. This is a training-objective design choice, not a derivation that makes a reported result equivalent to its inputs; it does not, by construction, force the fault-tolerance outcome. Similarly, the learnable-gait-frequency ablation (Section IV-C.2) changes both the action space and the reward term (replacing feet-phase reward with air-time reward), which is an experimental confound rather than a circularity: it weakens causal attribution but does not reduce the claim to an identity. The latent cosine-similarity analysis (Section IV-C.1) reports the training target itself, but the accompanying episodic-reward and command-tracking curves provide independent signal. Overall, the paper contains no equation-level reduction of a prediction to an input and no self-citation chain that forces its conclusions; the derivation chain is self-contained.

Assumptions & free parameters 9 free parameters · 6 assumptions · 0 invented entities

The central claim rests on a large set of hand-chosen hyperparameters and reward weights, plus the assumption that the simulation fault model and randomization transfer to hardware. No physically invented entities are introduced; the privileged fault mask and terrain features are simulation inputs, not new conserved quantities or forces. Most parameters were not swept or sensitivity-analyzed, which raises reproducibility risk.

free parameters (9)
  • lambda_3 latent alignment weight = 1
    Set by hand to balance PPO loss and latent MSE in Section III-C; the paper does not sweep this value.
  • observation history length H = 3
    Chosen after H in {1,2,3,5,7} ablation in Section IV-C1 as a trade-off; not used elsewhere.
  • initial torque efficiency k_init = 0.25
    Curriculum start in Section III-D; hand-chosen so the policy first experiences partial faults.
  • curriculum step delta_k = 0.0125
    Severity increments in Section III-D; hand-chosen, no sensitivity analysis.
  • curriculum tracking thresholds r_th_vxy, r_th_omegaz = 0.7, 0.8
    Used to decide when to increase fault severity in Section III-D.
  • default gait frequency nu_def = 1.25 Hz
    Nominal stepping frequency in Section IV-A; hand-chosen.
  • action scaling s_q, s_nu = 0.5, 1.25
    Scaling factors in Section III-B; hand-chosen without reported tuning.
  • PD gains Kp, Kd = 300I, 10I
    Low-level tracking gains in Section IV-A; standard for Kyon but not derived.
  • reward weights in Table II = see Table II
    Hand-designed weights following MuJoCo Playground [36]; central to shaping the learned behavior.
assumptions (6)
  • domain assumption MuJoCo MJX/MJWarp simulation with the Kyon model faithfully reproduces the robot's dynamics and power-loss behavior
    All training and most evaluation rely on this model; the sim-to-real transfer is only tested once.
  • domain assumption Scaling commanded torque by k_tau captures actuator power loss
    Section III-D defines the fault model; no hardware measurement of the real torque-efficiency curve is provided.
  • domain assumption A proprioceptive history of H=3 steps suffices to infer the joint fault mask
    Supported by the H ablation in Fig. 8, but the cosine similarity and reward are still training metrics, not a guarantee on hardware.
  • domain assumption Domain randomization ranges in Table V cover the real sim-to-real gap on the test terrain
    The real experiment is limited to flat ground, so uneven-terrain transfer is not validated.
  • domain assumption Terrain height observation o_z is available at deployment through a perception pipeline
    Section III-B states this assumption and notes integration of perception is future work; real experiments bypass it by zeroing terrain input on flat ground.
  • ad hoc to paper Excluding faulty legs from the feet-phase reward and the standing-posture reward is necessary and does not bias the learned behavior
    This design choice in Section III-C is hand-made for this paper and is not derived from an external principle.

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Pith. "Pith review of Learning Fault-Tolerant Locomotion with Adaptive Gait Timing." pith.science (2026). https://pith.science/paper/33265Z4L

@misc{pith2026260807328,
  author       = {Pith},
  title        = {Pith review of: Learning Fault-Tolerant Locomotion with Adaptive Gait Timing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/33265Z4L}},
  note         = {Machine review of arXiv:2608.07328}
}
read the original abstract

Hardware failures require legged robots to rapidly reorganize coordination and gait timing to maintain stability and mobility. This is particularly challenging for larger quadrupeds, where increased mass and tighter actuation limits reduce the feasibility of aggressive, high-frequency compensation strategies often observed on smaller platforms. In this work, we propose a deep reinforcement learning approach for fault-tolerant locomotion under actuator power loss. The method employs an asymmetric actor-critic architecture in which the critic has access to privileged information during training, while the actor learns to reconstruct a corresponding latent representation from proprioceptive observations. We introduce a latent-alignment loss that encourages consistency between actor and critic representations. Additionally, we augment the action space with a learnable gait frequency parameter, enabling adaptive gait timing in response to terrain variations and actuator degradation without predefined faulty-leg strategies. The approach is validated in high-fidelity simulation on uneven terrain and real-world experiments on flat ground using a 68 kg quadruped robot.

Figures

Figures reproduced from arXiv: 2608.07328 by the authors.

Figure 1
Figure 1. Fault-tolerant locomotion under sudden actuator power loss. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Overview of the proposed training approach based on asymmetric [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Hundreds of quadrupeds locomoting across the terrain used for [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Episodic total reward averaged over five training runs. Shaded [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 6
Figure 6. Figure 6: Snapshots from experiments in the MuJoCo simulator with XBot2 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: Real-world experimental validation of the proposed control policy conducted on the Kyon quadruped robot. The sequence of snapshots shows [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 10
Figure 10. Figure 10: Comparison between our gait-adaptive policy and a free-gait [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]
Figure 9
Figure 9. Figure 9: Analysis of the learnable gait frequency. Shaded red regions [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]

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Works this paper leans on

40 extracted references · 26 canonical work pages

  1. [1]

    Anymal - a highly mobile and dynamic quadrupedal robot,

    M. Hutter, C. Gehring, D. Jud, A. Lauber, C. D. Bellicoso, V . Tsounis, J. Hwangbo, K. Bodie, P. Fankhauser, M. Bloesch, R. Diethelm, S. Bachmann, A. Melzer, and M. Hoepflinger, “Anymal - a highly mobile and dynamic quadrupedal robot,” in2016 IEEE/RSJ Interna- tional Conference on Intelligent Robots and Systems (IROS), 2016, pp. 38–44

    work page 2016

  2. [2]

    Design of kaist hound, a quadruped robot platform for fast and efficient locomotion with mixed- integer nonlinear optimization of a gear train,

    Y .-H. Shin, S. Hong, S. Woo, J. Choe, H. Son, G. Kim, J.-H. Kim, K. Lee, J. Hwangbo, and H.-W. Park, “Design of kaist hound, a quadruped robot platform for fast and efficient locomotion with mixed- integer nonlinear optimization of a gear train,” in2022 International Conference on Robotics and Automation (ICRA), 2022, pp. 6614– 6620

    2022

  3. [3]

    Centauro: A hybrid locomotion and high power resilient manipulation platform,

    N. Kashiri, L. Baccelliere, L. Muratore, A. Laurenzi, Z. Ren, E. M. Hoffman, M. Kamedula, G. F. Rigano, J. Malzahn, S. Cordasco, P. Guria, A. Margan, and N. G. Tsagarakis, “Centauro: A hybrid locomotion and high power resilient manipulation platform,”IEEE Robotics and Automation Letters, vol. 4, no. 2, pp. 1595–1602, 2019

    work page 2019

  4. [4]

    Barry: A high-payload and agile quadruped robot,

    G. Valsecchi, N. Rudin, L. Nachtigall, K. Mayer, F. Tischhauser, and M. Hutter, “Barry: A high-payload and agile quadruped robot,”IEEE Robotics and Automation Letters, vol. 8, no. 11, pp. 6939–6946, 2023

    work page 2023

  5. [5]

    KYON: Semi-Modular Wheel-Legged Quadruped With Agile Bimanual Capability

    L. Rossini, A. Laurenzi, F. Ruscelli, Y . Zhang, G. Gravina, L. Baccelliere, C. Burchielli, S. Cordasco, and N. Tsagarakis, “Kyon: Semi-modular wheel-legged quadruped with agile bimanual capability,” 2026. [Online]. Available: https://arxiv.org/abs/2606.30243

    work page Pith review arXiv 2026

  6. [6]

    Robust robotic search and rescue in harsh environments: An example and open challenges,

    S. Solmaz, P. Innerwinkler, M. W ´ojcik, K. Tong, E. Politi, G. Dimi- trakopoulos, P. Purucker, A. H¨oß, B. W. Schuller, and R. John, “Robust robotic search and rescue in harsh environments: An example and open challenges,” in2024 IEEE International Symposium on Robotic and Sensors Environments (ROSE), 2024, pp. 1–8

    work page 2024

  7. [7]

    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,” inField and Service Robotics, G. Ishigami and K. Yoshida, Eds. Singapore: Springer Singapore, 2021, pp. 247–260

    work page 2021

  8. [8]

    Door-to-door parcel delivery from supply point to user’s home with heterogeneous robot team: The eurobin first-year robotics hackathon,

    A. Suarez, R. Kartmann, D. Leidneret al., “Door-to-door parcel delivery from supply point to user’s home with heterogeneous robot team: The eurobin first-year robotics hackathon,”IEEE Robotics & Automation Magazine, vol. 32, no. 3, pp. 8–25, 2025

    work page 2025

Show all 40 references
  1. [9]

    Alphred: A multi-modal operations quadruped robot for package delivery applications,

    J. Hooks, M. S. Ahn, J. Yu, X. Zhang, T. Zhu, H. Chae, and D. Hong, “Alphred: A multi-modal operations quadruped robot for package delivery applications,”IEEE Robotics and Automation Letters, vol. 5, no. 4, pp. 5409–5416, 2020

    2020

  2. [10]

    Fault-tolerant gaits of quadruped robots for locked joint failures,

    J.-M. Yang, “Fault-tolerant gaits of quadruped robots for locked joint failures,”IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), vol. 32, no. 4, pp. 507–516, 2002

    2002

  3. [11]

    Fault tolerance for kinematically re- dundant manipulators: anticipating free-swinging joint failures,

    J. English and A. Maciejewski, “Fault tolerance for kinematically re- dundant manipulators: anticipating free-swinging joint failures,”IEEE Transactions on Robotics and Automation, vol. 14, no. 4, pp. 566–575, 1998

    1998

  4. [12]

    Fault-tolerant control of a compliant legged quadruped robot for free swinging failure,

    M. M. Gor, P. Pathak, A. Samantaray, J. M. Yang, and S. Kwak, “Fault-tolerant control of a compliant legged quadruped robot for free swinging failure,”Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 232, no. 2, p...

    2018 doi

  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]

    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,

  7. [15]

    Learning quadrupedal locomotion on deformable terrain,

    S. Choi, G. Ji, J. Park, H. Kim, J. Mun, J. H. Lee, and J. Hwangbo, “Learning quadrupedal locomotion on deformable terrain,”Science Robotics, vol. 8, no. 74, p. eade2256, 2023. [Online]. Available: https://www.science.org/doi/abs/10.1126/scirobotics.ade2256

    2023 doi

  8. [16]

    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

  9. [17]

    Extreme parkour with legged robots,

    X. Cheng, K. Shi, A. Agarwal, and D. Pathak, “Extreme parkour with legged robots,” in2024 IEEE International Conference on Robotics and Automation (ICRA), 2024, pp. 11 443–11 450

    2024

  10. [18]

    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

  11. [19]

    Asymmetric actor critic for image-based robot learning,

    L. Pinto, M. Andrychowicz, P. Welinder, W. Zaremba, and P. Abbeel, “Asymmetric actor critic for image-based robot learning,” 2017. [Online]. Available: https://arxiv.org/abs/1710.06542

    2017 arXiv

  12. [20]

    Cts: Concurrent teacher- student reinforcement learning for legged locomotion,

    H. Wang, H. Luo, W. Zhang, and H. Chen, “Cts: Concurrent teacher- student reinforcement learning for legged locomotion,”IEEE Robotics and Automation Letters, vol. 9, no. 11, pp. 9191–9198, 2024

    2024

  13. [21]

    Gait-adaptive perceptive humanoid locomotion with real-time under- base terrain reconstruction,

    H. Song, H. Zhu, T. Yu, Y . Liu, M. Yuan, W. Zhou, H. Chen, and H. Li, “Gait-adaptive perceptive humanoid locomotion with real-time under- base terrain reconstruction,”IEEE Robotics and Automation Letters, pp. 1–8, 2026

    2026

  14. [22]

    Fault-tolerant motion planning and generation of quadruped robots synthesised by posture optimization and whole body control,

    J. Cui, Z. Li, J. Qiu, and T. Li, “Fault-tolerant motion planning and generation of quadruped robots synthesised by posture optimization and whole body control,”Complex & Intelligent Systems, vol. 8, no. 4, pp. 2991–3003, 2022

    2022

  15. [23]

    Fault-tolerant gait design for quadruped robots with one locked leg using the gf set theory,

    Z. Chen, Q. Xi, F. Gao, and Y . Zhao, “Fault-tolerant gait design for quadruped robots with one locked leg using the gf set theory,” Mechanism and Machine Theory, vol. 178, p. 105069, 2022. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S0094114X22003160

    2022

  16. [24]

    Fault-aware robust control via adversarial reinforcement learning,

    F. Yang, C. Yang, D. Guo, H. Liu, and F. Sun, “Fault-aware robust control via adversarial reinforcement learning,” in2021 IEEE 11th An- nual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER), 2021, pp. 109–115

    2021

  17. [25]

    Meta-learning for fast adaptive locomotion with uncertainties in environments and robot dynamics,

    T. Anne, J. Wilkinson, and Z. Li, “Meta-learning for fast adaptive locomotion with uncertainties in environments and robot dynamics,” in2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2021, pp. 4568–4575

    2021

  18. [26]

    Reinforcement learning with adaptive curriculum dynamics randomization for fault-tolerant robot control,

    W. Okamoto, H. Kera, and K. Kawamoto, “Reinforcement learning with adaptive curriculum dynamics randomization for fault-tolerant robot control,” 2021. [Online]. Available: https://arxiv.org/abs/2111. 10005

    2021

  19. [27]

    Towards fault-tolerant quadruped loco- motion with reinforcement learning,

    D. Liu, J. Yin, and S. See, “Towards fault-tolerant quadruped loco- motion with reinforcement learning,” in2024 IEEE Conference on Artificial Intelligence (CAI), 2024, pp. 1438–1441

    2024

  20. [28]

    Ft-net: Learning failure recovery and fault-tolerant locomotion for quadruped robots,

    Z. Luo, E. Xiao, and P. Lu, “Ft-net: Learning failure recovery and fault-tolerant locomotion for quadruped robots,”IEEE Robotics and Automation Letters, vol. 8, no. 12, pp. 8414–8421, 2023

    2023

  21. [29]

    Learning quadrupedal locomotion with impaired joints using random joint masking,

    M. Kim, U. Shin, and J.-Y . Kim, “Learning quadrupedal locomotion with impaired joints using random joint masking,” in2024 IEEE International Conference on Robotics and Automation (ICRA), 2024, pp. 9751–9757

    2024

  22. [30]

    Acl: Action learner for fault-tolerant quadruped locomotion control,

    T. Xu, Y . Cheng, P. Shen, and L. Zhao, “Acl: Action learner for fault-tolerant quadruped locomotion control,” 2025. [Online]. Available: https://arxiv.org/abs/2503.21401

    2025 arXiv

  23. [31]

    Contrastive forward prediction reinforcement learning for adaptive fault-tolerant legged robots,

    Y . Fu, Y . Zhang, Q. Yang, L. Yan, Z. Cao, and Y . Gao, “Contrastive forward prediction reinforcement learning for adaptive fault-tolerant legged robots,” inProceedings of The 9th Conference on Robot Learning, ser. Proceedings of Machine Learning Research, J. Lim, S. Song, an...

    2025

  24. [32]

    Dreamflex: Learning fault-aware quadrupedal locomotion controller for anomaly situation in rough terrains,

    S. Lee, I. M. A. Nahrendra, D. Lee, B. Yu, M. Oh, H. Lee, and H. Myung, “Dreamflex: Learning fault-aware quadrupedal locomotion controller for anomaly situation in rough terrains,” in2025 IEEE International Conference on Robotics and Automation (ICRA), 2025, pp. 16 001–16 007

    2025

  25. [33]

    Multi-task learning of active fault-tolerant controller for leg failures in quadruped robots,

    T. Hou, J. Tu, X. Gao, Z. Dong, P. Zhai, and L. Zhang, “Multi-task learning of active fault-tolerant controller for leg failures in quadruped robots,” in2024 IEEE International Conference on Robotics and Automation (ICRA), 2024, pp. 9758–9764

    2024

  26. [34]

    Ft-cpg: Learning central pat- tern generators for fault-tolerant quadruped locomotion under multi- joint failures,

    P. Zhang, Z. Hua, Q. Qiu, and J. Ding, “Ft-cpg: Learning central pat- tern generators for fault-tolerant quadruped locomotion under multi- joint failures,”IEEE Robotics and Automation Letters, vol. 10, no. 7, pp. 6936–6943, 2025

    2025

  27. [35]

    Proximal policy optimization algorithms,

    J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, “Proximal policy optimization algorithms,” 2017. [Online]. Available: https://arxiv.org/abs/1707.06347

    2017 arXiv

  28. [36]

    Mujoco playground: An open-source framework for gpu-accelerated robot learning and sim-to-real transfer

    K. Zakka, B. Tabanpour, Q. Liao, M. Haiderbhai, S. Holt, J. Y . Luo, A. Allshire, E. Frey, K. Sreenath, L. A. Kahrs, C. Sferrazza, Y . Tassa, and P. Abbeel, “Mujoco playground: An open-source framework for gpu-accelerated robot learning and sim-to-real transfer.” 2025. [Online...

    2025

  29. [37]

    Brax – a differentiable physics engine for large scale rigid body simulation,

    C. D. Freeman, E. Frey, A. Raichuk, S. Girgin, I. Mordatch, and O. Bachem, “Brax – a differentiable physics engine for large scale rigid body simulation,” 2021. [Online]. Available: https://arxiv.org/abs/2106.13281

    2021 arXiv

  30. [38]

    Mujoco: A physics engine for model-based control,

    E. Todorov, T. Erez, and Y . Tassa, “Mujoco: A physics engine for model-based control,” in2012 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, 2012, pp. 5026–5033

    2012

  31. [39]

    The xbot2 real-time middleware for robotics,

    A. Laurenzi, D. Antonucci, N. G. Tsagarakis, and L. Muratore, “The xbot2 real-time middleware for robotics,”Robotics and Autonomous Systems, vol. 163, p. 104379, 2023. [Online]. Available: https: //www.sciencedirect.com/science/article/pii/S0921889023000180

    2023

  32. [2022]

    Available: https://www.science.org/doi/abs/10.1126/ scirobotics.abk2822

    [Online]. Available: https://www.science.org/doi/abs/10.1126/ scirobotics.abk2822

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.