{"kagg_id":"KAGG:2609.00009","slug":"2609.00009","title":"Adaptive Safety Margins for Quadruped Navigation with Calibrated Velocity Interfaces","authors":[{"name":"Junho Kang","affiliation":"Legged Locomotion and Control Lab, KAIST, Daejeon, South Korea"},{"name":"Hyesun Bae","affiliation":"Legged Locomotion and Control Lab, KAIST, Daejeon, South Korea"},{"name":"Daewon Ryu","affiliation":"Legged Locomotion and Control Lab, KAIST, Daejeon, South Korea"},{"name":"Minju Seo","affiliation":"Legged Locomotion and Control Lab, KAIST, Daejeon, South Korea"}],"affiliation":null,"abstract":"Fixed safety margins for legged navigation are tuned once, so they ignore both how well the robot's velocity interface is currently calibrated and how much free space the robot is about to enter. This paper presents an adaptive safety margin for quadruped navigation that combines the two signals. A calibrated interface model obtained with GAUGE supplies a high-confidence upper bound on the lateral deviation caused by command lag, and the control-aligned future-range predictor FutureRay supplies a lower confidence bound on the free range along the directions the controller can actually execute. The margin is the sum of a kinematic term and a lag-error term, each blended between its model-based value and its worst-case value by an explicit confidence weight. We prove that the margin is monotone nondecreasing in both uncertainty sources, that it never falls below the model-based bounds, and that it reduces exactly to the worst-case fixed margin when both confidences vanish. On a Unitree Go2 evaluated on 12 obstacle-adjacent segments at speeds from 1.0 to 4.0 m/s, with matching Isaac Lab simulation, the adaptive margin raises the collision-free speed from 3.10 m/s for the worst-case fixed margin to 3.40 m/s and task success from 78.4 to 90.8 percent, while lowering the 95th-percentile margin from 42.0 to 38.2 cm. When the interface model becomes stale after a payload change, the margin inflates toward the worst-case value without manual intervention.","publication_date":"2026-09-28","registered_at":"2026-10-01T13:00:00Z","updated_at":"2026-10-03T16:57:00Z","status":"published","html_path":null,"pdf_path":"articles/2609.00009/paper.pdf","source_type":"preprint","source_label":"Kaggleyes Academy Preprint","license":"CC BY 4.0","has_doi":false,"external_doi":null,"references":[{"text":"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, 2019. arXiv:1901.08652.","identifier":"arXiv:1901.08652","url":"https://arxiv.org/abs/1901.08652"},{"text":"J. Lee, J. Hwangbo, L. Wellhausen, V. Koltun, and M. Hutter. Learning Quadrupedal Locomotion over Challenging Terrain. Science Robotics, 2020. arXiv:2010.11251.","identifier":"arXiv:2010.11251","url":"https://arxiv.org/abs/2010.11251"},{"text":"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, 2022. arXiv:2201.08117.","identifier":"arXiv:2201.08117","url":"https://arxiv.org/abs/2201.08117"},{"text":"A. Kumar, Z. Fu, D. Pathak, and J. Malik. RMA: Rapid Motor Adaptation for Legged Robots. Robotics: Science and Systems, 2021. arXiv:2107.04034.","identifier":"arXiv:2107.04034","url":"https://arxiv.org/abs/2107.04034"},{"text":"N. Rudin, D. Hoeller, P. Reist, and M. Hutter. Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning. Conference on Robot Learning, 2021. arXiv:2109.11978.","identifier":"arXiv:2109.11978","url":"https://arxiv.org/abs/2109.11978"},{"text":"G. B. Margolis, G. Yang, K. Paigwar, T. Chen, and P. Agrawal. Rapid Locomotion via Reinforcement Learning. Robotics: Science and Systems, 2022. arXiv:2205.02824.","identifier":"arXiv:2205.02824","url":"https://arxiv.org/abs/2205.02824"},{"text":"G. B. Margolis and P. Agrawal. Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behavior. Conference on Robot Learning, 2022. arXiv:2212.03238.","identifier":"arXiv:2212.03238","url":"https://arxiv.org/abs/2212.03238"},{"text":"I. M. A. Nahrendra, B. Yu, and H. Myung. DreamWaQ: Learning Robust Quadrupedal Locomotion with Implicit Terrain Imagination via Deep Reinforcement Learning. IEEE International Conference on Robotics and Automation, 2023. arXiv:2301.10602.","identifier":"arXiv:2301.10602","url":"https://arxiv.org/abs/2301.10602"},{"text":"D. Hoeller, L. Wellhausen, F. Farshidian, and M. Hutter. Learning a State Representation and Navigation in Cluttered and Dynamic Environments. IEEE Robotics and Automation Letters, 2021. arXiv:2103.04351.","identifier":"arXiv:2103.04351","url":"https://arxiv.org/abs/2103.04351"},{"text":"L. Wellhausen and M. Hutter. ArtPlanner: Robust Legged Robot Navigation in the Field. Field Robotics, 2023. arXiv:2303.01420.","identifier":"arXiv:2303.01420","url":"https://arxiv.org/abs/2303.01420"},{"text":"M. Gaertner, M. Bjelonic, F. Farshidian, and M. Hutter. Collision-Free MPC for Legged Robots in Static and Dynamic Scenes. IEEE International Conference on Robotics and Automation, 2021. arXiv:2103.13987.","identifier":"arXiv:2103.13987","url":"https://arxiv.org/abs/2103.13987"},{"text":"J. Hu, S. Yuan, G. C. R. Bethala, A. Tzes, and Y. Fang. Learning Adaptive Safety Margins for Visual Navigation. arXiv:2607.18200, 2026.","identifier":"arXiv:2607.18200","url":"https://arxiv.org/abs/2607.18200"},{"text":"T. Zang, H. Huang, S. Cheng, and W. Zhang. GAUGE: Planner-Conditioned Active Calibration of Opaque Quadruped Velocity Interfaces. arXiv:2607.02841, 2026.","identifier":"arXiv:2607.02841","url":"https://arxiv.org/abs/2607.02841"},{"text":"T. Zang, S. Wang, H. Huang, and S. Cheng. FutureRay: Control-Aligned Future Range for Agile Quadruped Navigation. arXiv:2608.01197, 2026.","identifier":"arXiv:2608.01197","url":"https://arxiv.org/abs/2608.01197"},{"text":"T. Miki, L. Wellhausen, R. Grandia, F. Jenelten, T. Homberger, and M. Hutter. Elevation Mapping for Locomotion and Navigation using GPU. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2022. arXiv:2204.12876.","identifier":"arXiv:2204.12876","url":"https://arxiv.org/abs/2204.12876"},{"text":"W. Xu, Y. Cai, D. He, J. Lin, and F. Zhang. FAST-LIO2: Fast Direct LiDAR-Inertial Odometry. IEEE Transactions on Robotics, 2022. arXiv:2107.06829.","identifier":"arXiv:2107.06829","url":"https://arxiv.org/abs/2107.06829"},{"text":"N. Rudin, D. Hoeller, M. Bjelonic, and M. Hutter. Advanced Skills by Learning Locomotion and Local Navigation End-to-End. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2022. arXiv:2209.12827.","identifier":"arXiv:2209.12827","url":"https://arxiv.org/abs/2209.12827"},{"text":"F. Yang, C. Wang, C. Cadena, and M. Hutter. iPlanner: Imperative Path Planning. Robotics: Science and Systems, 2023. arXiv:2302.11434.","identifier":"arXiv:2302.11434","url":"https://arxiv.org/abs/2302.11434"},{"text":"P. Roth, J. Nubert, F. Yang, M. Mittal, and M. Hutter. ViPlanner: Visual Semantic Imperative Learning for Local Navigation. IEEE International Conference on Robotics and Automation, 2024. arXiv:2310.00982.","identifier":"arXiv:2310.00982","url":"https://arxiv.org/abs/2310.00982"},{"text":"Z. Fu, A. Kumar, A. Agarwal, H. Qi, J. Malik, and D. Pathak. Coupling Vision and Proprioception for Navigation of Legged Robots. IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022. arXiv:2112.02094.","identifier":"arXiv:2112.02094","url":"https://arxiv.org/abs/2112.02094"},{"text":"J. Frey, M. Mattamala, N. Chebrolu, C. Cadena, M. Fallon, and M. Hutter. Fast Traversability Estimation for Wild Visual Navigation. Robotics: Science and Systems, 2023. arXiv:2305.08510.","identifier":"arXiv:2305.08510","url":"https://arxiv.org/abs/2305.08510"},{"text":"T. Miki, J. Lee, L. Wellhausen, and M. Hutter. Learning to Walk in Confined Spaces Using 3D Representation. IEEE International Conference on Robotics and Automation, 2024. arXiv:2403.00187.","identifier":"arXiv:2403.00187","url":"https://arxiv.org/abs/2403.00187"},{"text":"D. Hoeller, N. Rudin, D. Sako, and M. Hutter. ANYmal Parkour: Learning Agile Navigation for Quadrupedal Robots. Science Robotics, 2024. arXiv:2306.14874.","identifier":"arXiv:2306.14874","url":"https://arxiv.org/abs/2306.14874"},{"text":"Z. Zhuang, Z. Fu, J. Wang, C. Atkeson, S. Schwertfeger, C. Finn, and H. Zhao. Robot Parkour Learning. Conference on Robot Learning, 2023. arXiv:2309.05665.","identifier":"arXiv:2309.05665","url":"https://arxiv.org/abs/2309.05665"},{"text":"X. Cheng, K. Shi, A. Agarwal, and D. Pathak. Extreme Parkour with Legged Robots. IEEE International Conference on Robotics and Automation, 2024. arXiv:2309.14341.","identifier":"arXiv:2309.14341","url":"https://arxiv.org/abs/2309.14341"},{"text":"S. L. Herbert, M. Chen, S. Han, S. Bansal, J. F. Fisac, and C. J. Tomlin. FaSTrack: A Modular Framework for Fast and Guaranteed Safe Motion Planning. IEEE Conference on Decision and Control, 2017. arXiv:1703.07373.","identifier":"arXiv:1703.07373","url":"https://arxiv.org/abs/1703.07373"},{"text":"S. Bansal, M. Chen, S. Herbert, and C. J. Tomlin. Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances. IEEE Conference on Decision and Control, 2017. arXiv:1709.07523.","identifier":"arXiv:1709.07523","url":"https://arxiv.org/abs/1709.07523"},{"text":"A. Majumdar and R. Tedrake. Funnel Libraries for Real-Time Robust Feedback Motion Planning. International Journal of Robotics Research, 2017. arXiv:1601.04037.","identifier":"arXiv:1601.04037","url":"https://arxiv.org/abs/1601.04037"},{"text":"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, 2017. arXiv:1609.06408.","identifier":"arXiv:1609.06408","url":"https://arxiv.org/abs/1609.06408"},{"text":"K. P. Wabersich and M. N. Zeilinger. A Predictive Safety Filter for Learning-Based Control of Constrained Nonlinear Dynamical Systems. Automatica, 2021. arXiv:1812.05506.","identifier":"arXiv:1812.05506","url":"https://arxiv.org/abs/1812.05506"},{"text":"J. F. Fisac, A. K. Akametalu, M. N. Zeilinger, S. Kaynama, J. 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Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2017. arXiv:1703.06907.","identifier":"arXiv:1703.06907","url":"https://arxiv.org/abs/1703.06907"},{"text":"X. B. Peng, M. Andrychowicz, W. Zaremba, and P. Abbeel. Sim-to-Real Transfer of Robotic Control with Dynamics Randomization. IEEE International Conference on Robotics and Automation, 2018. arXiv:1710.06537.","identifier":"arXiv:1710.06537","url":"https://arxiv.org/abs/1710.06537"}],"canonical_url":"https://academy.kaggleyes.top/abs/KAGG:2609.00009","metadata":{"title":"Adaptive Safety Margins for Quadruped Navigation with Calibrated Velocity Interfaces","authors":[{"name":"Junho Kang","affiliation":"Legged Locomotion and Control Lab, KAIST, Daejeon, South Korea"},{"name":"Hyesun Bae","affiliation":"Legged Locomotion and Control Lab, KAIST, Daejeon, South Korea"},{"name":"Daewon Ryu","affiliation":"Legged Locomotion and Control Lab, KAIST, Daejeon, South Korea"},{"name":"Minju Seo","affiliation":"Legged Locomotion and Control Lab, KAIST, Daejeon, South Korea"}],"publication_date":"2026-09-28","abstract":"Fixed safety margins for legged navigation are tuned once, so they ignore both how well the robot's velocity interface is currently calibrated and how much free space the robot is about to enter. This paper presents an adaptive safety margin for quadruped navigation that combines the two signals. A calibrated interface model obtained with GAUGE supplies a high-confidence upper bound on the lateral deviation caused by command lag, and the control-aligned future-range predictor FutureRay supplies a lower confidence bound on the free range along the directions the controller can actually execute. The margin is the sum of a kinematic term and a lag-error term, each blended between its model-based value and its worst-case value by an explicit confidence weight. We prove that the margin is monotone nondecreasing in both uncertainty sources, that it never falls below the model-based bounds, and that it reduces exactly to the worst-case fixed margin when both confidences vanish. On a Unitree Go2 evaluated on 12 obstacle-adjacent segments at speeds from 1.0 to 4.0 m/s, with matching Isaac Lab simulation, the adaptive margin raises the collision-free speed from 3.10 m/s for the worst-case fixed margin to 3.40 m/s and task success from 78.4 to 90.8 percent, while lowering the 95th-percentile margin from 42.0 to 38.2 cm. When the interface model becomes stale after a payload change, the margin inflates toward the worst-case value without manual intervention.","references":[{"text":"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, 2019. arXiv:1901.08652.","identifier":"arXiv:1901.08652","url":"https://arxiv.org/abs/1901.08652"},{"text":"J. Lee, J. Hwangbo, L. Wellhausen, V. Koltun, and M. Hutter. Learning Quadrupedal Locomotion over Challenging Terrain. Science Robotics, 2020. arXiv:2010.11251.","identifier":"arXiv:2010.11251","url":"https://arxiv.org/abs/2010.11251"},{"text":"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, 2022. arXiv:2201.08117.","identifier":"arXiv:2201.08117","url":"https://arxiv.org/abs/2201.08117"},{"text":"A. Kumar, Z. Fu, D. Pathak, and J. Malik. RMA: Rapid Motor Adaptation for Legged Robots. Robotics: Science and Systems, 2021. arXiv:2107.04034.","identifier":"arXiv:2107.04034","url":"https://arxiv.org/abs/2107.04034"},{"text":"N. Rudin, D. Hoeller, P. Reist, and M. Hutter. Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning. Conference on Robot Learning, 2021. arXiv:2109.11978.","identifier":"arXiv:2109.11978","url":"https://arxiv.org/abs/2109.11978"},{"text":"G. B. Margolis, G. Yang, K. Paigwar, T. Chen, and P. Agrawal. Rapid Locomotion via Reinforcement Learning. Robotics: Science and Systems, 2022. arXiv:2205.02824.","identifier":"arXiv:2205.02824","url":"https://arxiv.org/abs/2205.02824"},{"text":"G. B. Margolis and P. Agrawal. Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behavior. Conference on Robot Learning, 2022. arXiv:2212.03238.","identifier":"arXiv:2212.03238","url":"https://arxiv.org/abs/2212.03238"},{"text":"I. M. A. Nahrendra, B. Yu, and H. Myung. DreamWaQ: Learning Robust Quadrupedal Locomotion with Implicit Terrain Imagination via Deep Reinforcement Learning. IEEE International Conference on Robotics and Automation, 2023. arXiv:2301.10602.","identifier":"arXiv:2301.10602","url":"https://arxiv.org/abs/2301.10602"},{"text":"D. Hoeller, L. Wellhausen, F. Farshidian, and M. Hutter. Learning a State Representation and Navigation in Cluttered and Dynamic Environments. IEEE Robotics and Automation Letters, 2021. arXiv:2103.04351.","identifier":"arXiv:2103.04351","url":"https://arxiv.org/abs/2103.04351"},{"text":"L. Wellhausen and M. Hutter. ArtPlanner: Robust Legged Robot Navigation in the Field. Field Robotics, 2023. arXiv:2303.01420.","identifier":"arXiv:2303.01420","url":"https://arxiv.org/abs/2303.01420"},{"text":"M. Gaertner, M. Bjelonic, F. Farshidian, and M. Hutter. Collision-Free MPC for Legged Robots in Static and Dynamic Scenes. IEEE International Conference on Robotics and Automation, 2021. arXiv:2103.13987.","identifier":"arXiv:2103.13987","url":"https://arxiv.org/abs/2103.13987"},{"text":"J. Hu, S. Yuan, G. C. R. Bethala, A. Tzes, and Y. Fang. Learning Adaptive Safety Margins for Visual Navigation. arXiv:2607.18200, 2026.","identifier":"arXiv:2607.18200","url":"https://arxiv.org/abs/2607.18200"},{"text":"T. Zang, H. Huang, S. Cheng, and W. Zhang. GAUGE: Planner-Conditioned Active Calibration of Opaque Quadruped Velocity Interfaces. arXiv:2607.02841, 2026.","identifier":"arXiv:2607.02841","url":"https://arxiv.org/abs/2607.02841"},{"text":"T. Zang, S. Wang, H. Huang, and S. Cheng. FutureRay: Control-Aligned Future Range for Agile Quadruped Navigation. arXiv:2608.01197, 2026.","identifier":"arXiv:2608.01197","url":"https://arxiv.org/abs/2608.01197"},{"text":"T. Miki, L. Wellhausen, R. Grandia, F. Jenelten, T. Homberger, and M. Hutter. Elevation Mapping for Locomotion and Navigation using GPU. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2022. arXiv:2204.12876.","identifier":"arXiv:2204.12876","url":"https://arxiv.org/abs/2204.12876"},{"text":"W. Xu, Y. Cai, D. He, J. Lin, and F. Zhang. FAST-LIO2: Fast Direct LiDAR-Inertial Odometry. IEEE Transactions on Robotics, 2022. arXiv:2107.06829.","identifier":"arXiv:2107.06829","url":"https://arxiv.org/abs/2107.06829"},{"text":"N. Rudin, D. Hoeller, M. Bjelonic, and M. Hutter. Advanced Skills by Learning Locomotion and Local Navigation End-to-End. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2022. arXiv:2209.12827.","identifier":"arXiv:2209.12827","url":"https://arxiv.org/abs/2209.12827"},{"text":"F. Yang, C. Wang, C. Cadena, and M. Hutter. iPlanner: Imperative Path Planning. Robotics: Science and Systems, 2023. arXiv:2302.11434.","identifier":"arXiv:2302.11434","url":"https://arxiv.org/abs/2302.11434"},{"text":"P. Roth, J. Nubert, F. Yang, M. Mittal, and M. Hutter. ViPlanner: Visual Semantic Imperative Learning for Local Navigation. IEEE International Conference on Robotics and Automation, 2024. arXiv:2310.00982.","identifier":"arXiv:2310.00982","url":"https://arxiv.org/abs/2310.00982"},{"text":"Z. Fu, A. Kumar, A. Agarwal, H. Qi, J. Malik, and D. Pathak. Coupling Vision and Proprioception for Navigation of Legged Robots. IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022. arXiv:2112.02094.","identifier":"arXiv:2112.02094","url":"https://arxiv.org/abs/2112.02094"},{"text":"J. Frey, M. Mattamala, N. Chebrolu, C. Cadena, M. Fallon, and M. Hutter. Fast Traversability Estimation for Wild Visual Navigation. Robotics: Science and Systems, 2023. arXiv:2305.08510.","identifier":"arXiv:2305.08510","url":"https://arxiv.org/abs/2305.08510"},{"text":"T. Miki, J. Lee, L. Wellhausen, and M. Hutter. Learning to Walk in Confined Spaces Using 3D Representation. IEEE International Conference on Robotics and Automation, 2024. arXiv:2403.00187.","identifier":"arXiv:2403.00187","url":"https://arxiv.org/abs/2403.00187"},{"text":"D. Hoeller, N. Rudin, D. Sako, and M. Hutter. ANYmal Parkour: Learning Agile Navigation for Quadrupedal Robots. Science Robotics, 2024. arXiv:2306.14874.","identifier":"arXiv:2306.14874","url":"https://arxiv.org/abs/2306.14874"},{"text":"Z. Zhuang, Z. Fu, J. Wang, C. Atkeson, S. Schwertfeger, C. Finn, and H. Zhao. Robot Parkour Learning. Conference on Robot Learning, 2023. arXiv:2309.05665.","identifier":"arXiv:2309.05665","url":"https://arxiv.org/abs/2309.05665"},{"text":"X. Cheng, K. Shi, A. Agarwal, and D. Pathak. Extreme Parkour with Legged Robots. IEEE International Conference on Robotics and Automation, 2024. arXiv:2309.14341.","identifier":"arXiv:2309.14341","url":"https://arxiv.org/abs/2309.14341"},{"text":"S. L. Herbert, M. Chen, S. Han, S. Bansal, J. F. Fisac, and C. J. Tomlin. FaSTrack: A Modular Framework for Fast and Guaranteed Safe Motion Planning. IEEE Conference on Decision and Control, 2017. arXiv:1703.07373.","identifier":"arXiv:1703.07373","url":"https://arxiv.org/abs/1703.07373"},{"text":"S. Bansal, M. Chen, S. Herbert, and C. J. Tomlin. Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances. IEEE Conference on Decision and Control, 2017. arXiv:1709.07523.","identifier":"arXiv:1709.07523","url":"https://arxiv.org/abs/1709.07523"},{"text":"A. Majumdar and R. Tedrake. Funnel Libraries for Real-Time Robust Feedback Motion Planning. International Journal of Robotics Research, 2017. arXiv:1601.04037.","identifier":"arXiv:1601.04037","url":"https://arxiv.org/abs/1601.04037"},{"text":"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, 2017. arXiv:1609.06408.","identifier":"arXiv:1609.06408","url":"https://arxiv.org/abs/1609.06408"},{"text":"K. P. Wabersich and M. N. Zeilinger. A Predictive Safety Filter for Learning-Based Control of Constrained Nonlinear Dynamical Systems. Automatica, 2021. arXiv:1812.05506.","identifier":"arXiv:1812.05506","url":"https://arxiv.org/abs/1812.05506"},{"text":"J. F. Fisac, A. K. Akametalu, M. N. Zeilinger, S. Kaynama, J. 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