{"kagg_id":"KAGG:2609.00004","slug":"2609.00004","title":"High-Speed Obstacle Negotiation for Agile Quadrupeds with Range-Predictive Control","authors":[{"name":"Carlos Ramirez","affiliation":"Legged Robotics Lab, Stanford University, Stanford, CA, USA"},{"name":"Felix Wagner","affiliation":"Legged Robotics Lab, Stanford University, Stanford, CA, USA"},{"name":"Ethan Brooks","affiliation":"Legged Robotics Lab, Stanford University, Stanford, CA, USA"},{"name":"Ananya Iyer","affiliation":"Legged Robotics Lab, Stanford University, Stanford, CA, USA"}],"affiliation":null,"abstract":"At running speeds of 4 to 6 m/s, the reaction budget of a quadruped robot is dominated by the lag of its velocity controller rather than by perception, so a controller that reacts to obstacles already present in its range measurements acts too late. This paper presents a range-predictive negotiation controller built on FutureRay, a perception module that predicts future free range along control-aligned directions. The controller uses the predicted range field to pre-shape the forward and yaw velocity commands before a geometric conflict materializes, schedules the pre-shaping lead time from an identified lag model, and applies an explicit hysteretic rule that hands control to a braking policy when the predicted range collapses below the braking envelope. The design space was explored in Isaac Lab with five seeds, and the controller was evaluated on a Unitree Go2 in a controlled course with six obstacle classes, approach speeds from 4 to 6 m/s in 0.5 m/s steps, and 20 trials per class and speed. Compared with a present-range reactive baseline, the controller raises the mean maximum safe speed over obstacle classes from 4.72 to 4.90 m/s, lowers the miss rate from 4.2 to 3.8 percent, and raises braking handoff success from 90.2 to 97.2 percent. Ablations indicate that the handoff rule, the predicted range, and lead-time scheduling each contribute. Failure analysis shows that at 6.0 m/s the occluded gap class is limited by the unobserved range behind the occluder rather than by the controller.","publication_date":"2026-09-08","registered_at":"2026-09-13T12:52:00Z","updated_at":"2026-09-13T18:44:00Z","status":"published","html_path":null,"pdf_path":"articles/2609.00004/paper.pdf","source_type":"preprint","source_label":"Kaggleyes Academy Preprint","license":"CC BY 4.0","has_doi":false,"external_doi":null,"references":[{"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":"J. Hwangbo, J. Lee, A. Dosovitskiy, D. Bellicoso, V. Tsounis, V. Koltun, and M. Hutter. Learning Agile and Dynamic Motor Skills for Legged Robots. arXiv:1901.08652, 2019.","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. arXiv:2010.11251, 2020.","identifier":"arXiv:2010.11251","url":"https://arxiv.org/abs/2010.11251"},{"text":"N. Rudin, D. Hoeller, P. Reist, and M. Hutter. Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning. arXiv:2109.11978, 2021.","identifier":"arXiv:2109.11978","url":"https://arxiv.org/abs/2109.11978"},{"text":"A. Kumar, Z. Fu, D. Pathak, and J. Malik. RMA: Rapid Motor Adaptation for Legged Robots. arXiv:2107.04034, 2021.","identifier":"arXiv:2107.04034","url":"https://arxiv.org/abs/2107.04034"},{"text":"T. Miki, J. Lee, J. Hwangbo, L. Wellhausen, V. Koltun, and M. Hutter. Learning Robust Perceptive Locomotion for Quadrupedal Robots in the Wild. arXiv:2201.08117, 2022.","identifier":"arXiv:2201.08117","url":"https://arxiv.org/abs/2201.08117"},{"text":"G. Ji, J. Mun, H. Kim, and J. Hwangbo. Concurrent Training of a Control Policy and a State Estimator for Dynamic and Robust Legged Locomotion. arXiv:2202.05481, 2022.","identifier":"arXiv:2202.05481","url":"https://arxiv.org/abs/2202.05481"},{"text":"G. B. Margolis, G. Yang, K. Paigwar, T. Chen, and P. Agrawal. Rapid Locomotion via Reinforcement Learning. arXiv:2205.02824, 2022.","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. arXiv:2212.03238, 2022.","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. arXiv:2301.10602, 2023.","identifier":"arXiv:2301.10602","url":"https://arxiv.org/abs/2301.10602"},{"text":"A. Agarwal, A. Kumar, J. Malik, and D. Pathak. Legged Locomotion in Challenging Terrains using Egocentric Vision. arXiv:2211.07638, 2022.","identifier":"arXiv:2211.07638","url":"https://arxiv.org/abs/2211.07638"},{"text":"R. Yang, G. Yang, and X. Wang. Neural Volumetric Memory for Visual Locomotion Control. arXiv:2304.01201, 2023.","identifier":"arXiv:2304.01201","url":"https://arxiv.org/abs/2304.01201"},{"text":"D. Hoeller, N. Rudin, C. Choy, A. Anandkumar, and M. Hutter. Neural Scene Representation for Locomotion on Structured Terrain. arXiv:2206.08077, 2022.","identifier":"arXiv:2206.08077","url":"https://arxiv.org/abs/2206.08077"},{"text":"Z. Zhuang, Z. Fu, J. Wang, C. Atkeson, S. Schwertfeger, C. Finn, and H. Zhao. Robot Parkour Learning. arXiv:2309.05665, 2023.","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. arXiv:2309.14341, 2023.","identifier":"arXiv:2309.14341","url":"https://arxiv.org/abs/2309.14341"},{"text":"D. Hoeller, N. Rudin, D. Sako, and M. Hutter. ANYmal Parkour: Learning Agile Navigation for Quadrupedal Robots. arXiv:2306.14874, 2023.","identifier":"arXiv:2306.14874","url":"https://arxiv.org/abs/2306.14874"},{"text":"S. Ha, J. Lee, M. van de Panne, Z. Xie, W. Yu, and M. Khadiv. Learning-based Legged Locomotion: State of the Art and Future Perspectives. arXiv:2406.01152, 2024.","identifier":"arXiv:2406.01152","url":"https://arxiv.org/abs/2406.01152"},{"text":"N. Rudin, D. Hoeller, M. Bjelonic, and M. Hutter. Advanced Skills by Learning Locomotion and Local Navigation End-to-End. arXiv:2209.12827, 2022.","identifier":"arXiv:2209.12827","url":"https://arxiv.org/abs/2209.12827"},{"text":"D. Hoeller, L. Wellhausen, F. Farshidian, and M. Hutter. Learning a State Representation and Navigation in Cluttered and Dynamic Environments. arXiv:2103.04351, 2021.","identifier":"arXiv:2103.04351","url":"https://arxiv.org/abs/2103.04351"},{"text":"J. Truong, D. Yarats, T. Li, F. Meier, S. Chernova, D. Batra, and A. Rai. Learning Navigation Skills for Legged Robots with Learned Robot Embeddings. arXiv:2011.12255, 2020.","identifier":"arXiv:2011.12255","url":"https://arxiv.org/abs/2011.12255"},{"text":"T. He, C. Zhang, W. Xiao, G. He, C. Liu, and G. Shi. Agile But Safe: Learning Collision-Free High-Speed Legged Locomotion. arXiv:2401.17583, 2024.","identifier":"arXiv:2401.17583","url":"https://arxiv.org/abs/2401.17583"},{"text":"Y. Kim, H. Oh, J. Lee, J. Choi, G. Ji, M. Jung, D. Youm, and J. Hwangbo. Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion. arXiv:2308.12517, 2023.","identifier":"arXiv:2308.12517","url":"https://arxiv.org/abs/2308.12517"},{"text":"M. Frey, M. Mattamala, N. Chebrolu, C. Cadena, M. Fallon, and M. Hutter. Fast Traversability Estimation for Wild Visual Navigation. arXiv:2305.08510, 2023.","identifier":"arXiv:2305.08510","url":"https://arxiv.org/abs/2305.08510"},{"text":"G. Kahn, P. Abbeel, and S. Levine. BADGR: An Autonomous Self-Supervised Learning-Based Navigation System. arXiv:2002.05700, 2020.","identifier":"arXiv:2002.05700","url":"https://arxiv.org/abs/2002.05700"},{"text":"D. Fox, W. Burgard, and S. Thrun. The Dynamic Window Approach to Collision Avoidance. IEEE Robotics and Automation Magazine, 4(1):23–33, 1997.","identifier":"doi:10.1109/100.580977","url":"https://doi.org/10.1109/100.580977"},{"text":"P. Fiorini and Z. Shiller. Motion Planning in Dynamic Environments Using Velocity Obstacles. International Journal of Robotics Research, 17(7):760–772, 1998.","identifier":"doi:10.1177/027836499801700706","url":"https://doi.org/10.1177/027836499801700706"},{"text":"A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada. Control Barrier Function Based Quadratic Programs for Safety Critical Systems. arXiv:1609.06408, 2016.","identifier":"arXiv:1609.06408","url":"https://arxiv.org/abs/1609.06408"},{"text":"A. D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K. Sreenath, and P. Tabuada. Control Barrier Functions: Theory and Applications. arXiv:1903.11199, 2019.","identifier":"arXiv:1903.11199","url":"https://arxiv.org/abs/1903.11199"},{"text":"K.-C. Hsu, H. Hu, and J. F. Fisac. The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems. arXiv:2309.05837, 2023.","identifier":"arXiv:2309.05837","url":"https://arxiv.org/abs/2309.05837"},{"text":"S. Bansal, M. Chen, S. Herbert, and C. J. Tomlin. Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances. arXiv:1709.07523, 2017.","identifier":"arXiv:1709.07523","url":"https://arxiv.org/abs/1709.07523"},{"text":"A. Bajcsy, S. Bansal, E. Bronstein, V. Tolani, and C. J. Tomlin. An Efficient Reachability-Based Framework for Provably Safe Autonomous Navigation in Unknown Environments. arXiv:1905.00532, 2019.","identifier":"arXiv:1905.00532","url":"https://arxiv.org/abs/1905.00532"},{"text":"K. P. Wabersich and M. N. Zeilinger. A Predictive Safety Filter for Learning-Based Control of Constrained Nonlinear Dynamical Systems. arXiv:1812.05506, 2018.","identifier":"arXiv:1812.05506","url":"https://arxiv.org/abs/1812.05506"},{"text":"S. Kousik, S. Vaskov, F. Bu, M. Johnson-Roberson, and R. Vasudevan. Bridging the Gap Between Safety and Real-Time Performance in Receding-Horizon Trajectory Design for Mobile Robots. arXiv:1809.06746, 2018.","identifier":"arXiv:1809.06746","url":"https://arxiv.org/abs/1809.06746"},{"text":"J. Tordesillas, B. T. Lopez, M. Everett, and J. P. How. FASTER: Fast and Safe Trajectory Planner for Navigation in Unknown Environments. arXiv:2001.04420, 2020.","identifier":"arXiv:2001.04420","url":"https://arxiv.org/abs/2001.04420"},{"text":"X. Zhou, Z. Wang, H. Ye, C. Xu, and F. Gao. EGO-Planner: An ESDF-free Gradient-based Local Planner for Quadrotors. arXiv:2008.08835, 2020.","identifier":"arXiv:2008.08835","url":"https://arxiv.org/abs/2008.08835"},{"text":"A. Loquercio, E. Kaufmann, R. Ranftl, M. Müller, V. Koltun, and D. Scaramuzza. Learning High-Speed Flight in the Wild. arXiv:2110.05113, 2021.","identifier":"arXiv:2110.05113","url":"https://arxiv.org/abs/2110.05113"},{"text":"E. Kaufmann, L. Bauersfeld, A. Loquercio, M. Müller, V. Koltun, and D. Scaramuzza. Champion-Level Drone Racing Using Deep Reinforcement Learning. Nature, 620:982–987, 2023.","identifier":"doi:10.1038/s41586-023-06419-4","url":"https://doi.org/10.1038/s41586-023-06419-4"},{"text":"Y. Song, A. Romero, M. Müller, V. Koltun, and D. Scaramuzza. Reaching the Limit in Autonomous Racing: Optimal Control versus Reinforcement Learning. arXiv:2310.10943, 2023.","identifier":"arXiv:2310.10943","url":"https://arxiv.org/abs/2310.10943"},{"text":"J. Di Carlo, P. M. Wensing, B. Katz, G. Bledt, and S. Kim. Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2018.","identifier":"doi:10.1109/IROS.2018.8594448","url":"https://doi.org/10.1109/IROS.2018.8594448"},{"text":"R. Grandia, F. Jenelten, S. Yang, F. Farshidian, and M. Hutter. Perceptive Locomotion through Nonlinear Model Predictive Control. arXiv:2208.08373, 2022.","identifier":"arXiv:2208.08373","url":"https://arxiv.org/abs/2208.08373"},{"text":"V. Makoviychuk et al.. Isaac Gym: High Performance GPU-Based Physics Simulation for Robot Learning. arXiv:2108.10470, 2021.","identifier":"arXiv:2108.10470","url":"https://arxiv.org/abs/2108.10470"},{"text":"M. Mittal et al.. Orbit: A Unified Simulation Framework for Interactive Robot Learning Environments. arXiv:2301.04195, 2023.","identifier":"arXiv:2301.04195","url":"https://arxiv.org/abs/2301.04195"},{"text":"J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov. Proximal Policy Optimization Algorithms. arXiv:1707.06347, 2017.","identifier":"arXiv:1707.06347","url":"https://arxiv.org/abs/1707.06347"},{"text":"J. Tobin, R. Fong, A. Ray, J. Schneider, W. Zaremba, and P. Abbeel. Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World. arXiv:1703.06907, 2017.","identifier":"arXiv:1703.06907","url":"https://arxiv.org/abs/1703.06907"}],"canonical_url":"https://academy.kaggleyes.top/abs/KAGG:2609.00004","metadata":{"title":"High-Speed Obstacle Negotiation for Agile Quadrupeds with Range-Predictive Control","authors":[{"name":"Carlos Ramirez","affiliation":"Legged Robotics Lab, Stanford University, Stanford, CA, USA"},{"name":"Felix Wagner","affiliation":"Legged Robotics Lab, Stanford University, Stanford, CA, USA"},{"name":"Ethan Brooks","affiliation":"Legged Robotics Lab, Stanford University, Stanford, CA, USA"},{"name":"Ananya Iyer","affiliation":"Legged Robotics Lab, Stanford University, Stanford, CA, USA"}],"publication_date":"2026-09-08","abstract":"At running speeds of 4 to 6 m/s, the reaction budget of a quadruped robot is dominated by the lag of its velocity controller rather than by perception, so a controller that reacts to obstacles already present in its range measurements acts too late. This paper presents a range-predictive negotiation controller built on FutureRay, a perception module that predicts future free range along control-aligned directions. The controller uses the predicted range field to pre-shape the forward and yaw velocity commands before a geometric conflict materializes, schedules the pre-shaping lead time from an identified lag model, and applies an explicit hysteretic rule that hands control to a braking policy when the predicted range collapses below the braking envelope. The design space was explored in Isaac Lab with five seeds, and the controller was evaluated on a Unitree Go2 in a controlled course with six obstacle classes, approach speeds from 4 to 6 m/s in 0.5 m/s steps, and 20 trials per class and speed. Compared with a present-range reactive baseline, the controller raises the mean maximum safe speed over obstacle classes from 4.72 to 4.90 m/s, lowers the miss rate from 4.2 to 3.8 percent, and raises braking handoff success from 90.2 to 97.2 percent. Ablations indicate that the handoff rule, the predicted range, and lead-time scheduling each contribute. Failure analysis shows that at 6.0 m/s the occluded gap class is limited by the unobserved range behind the occluder rather than by the controller.","references":[{"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":"J. Hwangbo, J. Lee, A. Dosovitskiy, D. Bellicoso, V. Tsounis, V. Koltun, and M. Hutter. Learning Agile and Dynamic Motor Skills for Legged Robots. arXiv:1901.08652, 2019.","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. arXiv:2010.11251, 2020.","identifier":"arXiv:2010.11251","url":"https://arxiv.org/abs/2010.11251"},{"text":"N. Rudin, D. Hoeller, P. Reist, and M. Hutter. Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning. arXiv:2109.11978, 2021.","identifier":"arXiv:2109.11978","url":"https://arxiv.org/abs/2109.11978"},{"text":"A. Kumar, Z. Fu, D. Pathak, and J. Malik. RMA: Rapid Motor Adaptation for Legged Robots. arXiv:2107.04034, 2021.","identifier":"arXiv:2107.04034","url":"https://arxiv.org/abs/2107.04034"},{"text":"T. Miki, J. Lee, J. Hwangbo, L. Wellhausen, V. Koltun, and M. Hutter. Learning Robust Perceptive Locomotion for Quadrupedal Robots in the Wild. arXiv:2201.08117, 2022.","identifier":"arXiv:2201.08117","url":"https://arxiv.org/abs/2201.08117"},{"text":"G. Ji, J. Mun, H. Kim, and J. Hwangbo. Concurrent Training of a Control Policy and a State Estimator for Dynamic and Robust Legged Locomotion. arXiv:2202.05481, 2022.","identifier":"arXiv:2202.05481","url":"https://arxiv.org/abs/2202.05481"},{"text":"G. B. Margolis, G. Yang, K. Paigwar, T. Chen, and P. Agrawal. Rapid Locomotion via Reinforcement Learning. arXiv:2205.02824, 2022.","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. arXiv:2212.03238, 2022.","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. arXiv:2301.10602, 2023.","identifier":"arXiv:2301.10602","url":"https://arxiv.org/abs/2301.10602"},{"text":"A. Agarwal, A. Kumar, J. Malik, and D. Pathak. Legged Locomotion in Challenging Terrains using Egocentric Vision. arXiv:2211.07638, 2022.","identifier":"arXiv:2211.07638","url":"https://arxiv.org/abs/2211.07638"},{"text":"R. Yang, G. Yang, and X. Wang. Neural Volumetric Memory for Visual Locomotion Control. arXiv:2304.01201, 2023.","identifier":"arXiv:2304.01201","url":"https://arxiv.org/abs/2304.01201"},{"text":"D. Hoeller, N. Rudin, C. Choy, A. Anandkumar, and M. Hutter. Neural Scene Representation for Locomotion on Structured Terrain. arXiv:2206.08077, 2022.","identifier":"arXiv:2206.08077","url":"https://arxiv.org/abs/2206.08077"},{"text":"Z. Zhuang, Z. Fu, J. Wang, C. Atkeson, S. Schwertfeger, C. Finn, and H. Zhao. Robot Parkour Learning. arXiv:2309.05665, 2023.","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. arXiv:2309.14341, 2023.","identifier":"arXiv:2309.14341","url":"https://arxiv.org/abs/2309.14341"},{"text":"D. Hoeller, N. Rudin, D. Sako, and M. Hutter. ANYmal Parkour: Learning Agile Navigation for Quadrupedal Robots. arXiv:2306.14874, 2023.","identifier":"arXiv:2306.14874","url":"https://arxiv.org/abs/2306.14874"},{"text":"S. Ha, J. Lee, M. van de Panne, Z. Xie, W. Yu, and M. Khadiv. Learning-based Legged Locomotion: State of the Art and Future Perspectives. arXiv:2406.01152, 2024.","identifier":"arXiv:2406.01152","url":"https://arxiv.org/abs/2406.01152"},{"text":"N. Rudin, D. Hoeller, M. Bjelonic, and M. Hutter. Advanced Skills by Learning Locomotion and Local Navigation End-to-End. arXiv:2209.12827, 2022.","identifier":"arXiv:2209.12827","url":"https://arxiv.org/abs/2209.12827"},{"text":"D. Hoeller, L. Wellhausen, F. Farshidian, and M. Hutter. Learning a State Representation and Navigation in Cluttered and Dynamic Environments. arXiv:2103.04351, 2021.","identifier":"arXiv:2103.04351","url":"https://arxiv.org/abs/2103.04351"},{"text":"J. Truong, D. Yarats, T. Li, F. Meier, S. Chernova, D. Batra, and A. Rai. Learning Navigation Skills for Legged Robots with Learned Robot Embeddings. arXiv:2011.12255, 2020.","identifier":"arXiv:2011.12255","url":"https://arxiv.org/abs/2011.12255"},{"text":"T. He, C. Zhang, W. Xiao, G. He, C. Liu, and G. Shi. Agile But Safe: Learning Collision-Free High-Speed Legged Locomotion. arXiv:2401.17583, 2024.","identifier":"arXiv:2401.17583","url":"https://arxiv.org/abs/2401.17583"},{"text":"Y. Kim, H. Oh, J. Lee, J. Choi, G. Ji, M. Jung, D. Youm, and J. Hwangbo. Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion. arXiv:2308.12517, 2023.","identifier":"arXiv:2308.12517","url":"https://arxiv.org/abs/2308.12517"},{"text":"M. Frey, M. Mattamala, N. Chebrolu, C. Cadena, M. Fallon, and M. Hutter. Fast Traversability Estimation for Wild Visual Navigation. arXiv:2305.08510, 2023.","identifier":"arXiv:2305.08510","url":"https://arxiv.org/abs/2305.08510"},{"text":"G. Kahn, P. Abbeel, and S. Levine. BADGR: An Autonomous Self-Supervised Learning-Based Navigation System. arXiv:2002.05700, 2020.","identifier":"arXiv:2002.05700","url":"https://arxiv.org/abs/2002.05700"},{"text":"D. Fox, W. Burgard, and S. Thrun. The Dynamic Window Approach to Collision Avoidance. IEEE Robotics and Automation Magazine, 4(1):23–33, 1997.","identifier":"doi:10.1109/100.580977","url":"https://doi.org/10.1109/100.580977"},{"text":"P. Fiorini and Z. Shiller. Motion Planning in Dynamic Environments Using Velocity Obstacles. International Journal of Robotics Research, 17(7):760–772, 1998.","identifier":"doi:10.1177/027836499801700706","url":"https://doi.org/10.1177/027836499801700706"},{"text":"A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada. Control Barrier Function Based Quadratic Programs for Safety Critical Systems. arXiv:1609.06408, 2016.","identifier":"arXiv:1609.06408","url":"https://arxiv.org/abs/1609.06408"},{"text":"A. D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K. Sreenath, and P. Tabuada. Control Barrier Functions: Theory and Applications. arXiv:1903.11199, 2019.","identifier":"arXiv:1903.11199","url":"https://arxiv.org/abs/1903.11199"},{"text":"K.-C. Hsu, H. Hu, and J. F. Fisac. The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems. arXiv:2309.05837, 2023.","identifier":"arXiv:2309.05837","url":"https://arxiv.org/abs/2309.05837"},{"text":"S. Bansal, M. Chen, S. Herbert, and C. J. Tomlin. Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances. arXiv:1709.07523, 2017.","identifier":"arXiv:1709.07523","url":"https://arxiv.org/abs/1709.07523"},{"text":"A. Bajcsy, S. Bansal, E. Bronstein, V. Tolani, and C. J. Tomlin. An Efficient Reachability-Based Framework for Provably Safe Autonomous Navigation in Unknown Environments. arXiv:1905.00532, 2019.","identifier":"arXiv:1905.00532","url":"https://arxiv.org/abs/1905.00532"},{"text":"K. P. Wabersich and M. N. Zeilinger. A Predictive Safety Filter for Learning-Based Control of Constrained Nonlinear Dynamical Systems. arXiv:1812.05506, 2018.","identifier":"arXiv:1812.05506","url":"https://arxiv.org/abs/1812.05506"},{"text":"S. Kousik, S. Vaskov, F. Bu, M. Johnson-Roberson, and R. Vasudevan. Bridging the Gap Between Safety and Real-Time Performance in Receding-Horizon Trajectory Design for Mobile Robots. arXiv:1809.06746, 2018.","identifier":"arXiv:1809.06746","url":"https://arxiv.org/abs/1809.06746"},{"text":"J. 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