{"kagg_id":"KAGG:2609.00006","slug":"2609.00006","title":"System Identification versus Learned Models for Commodity Quadruped Velocity Interfaces","authors":[{"name":"Lin Zhao","affiliation":"Perception and Control Group, Technical University of Munich, Munich, Germany"},{"name":"Maximilian Weber","affiliation":"Perception and Control Group, Technical University of Munich, Munich, Germany"},{"name":"Julia Hoffmann","affiliation":"Perception and Control Group, Technical University of Munich, Munich, Germany"},{"name":"Omar Farouk","affiliation":"Perception and Control Group, Technical University of Munich, Munich, Germany"}],"affiliation":null,"abstract":"Navigation stacks for commodity quadrupeds command the robot through a vendor velocity interface whose response to commands, including delay, lag, cross-axis coupling, and saturation, is undocumented and differs between platforms. Planners therefore need a calibrated model of this interface, but it is unclear whether classical system identification or a learned model should provide it. This paper compares, under matched probe budgets and on the same planner-conditioned probe data, structured identification of a state-delay-plus-saturation model, a Gaussian-process surrogate, and a multilayer perceptron with one million parameters. Scoring uses navigation-relevant criteria: worst-direction tracking error, extrapolation error on unseen command regimes, calibration time, and sensitivity to command noise. On a Unitree Go2 and a Unitree B2, with 60 probe sessions per platform, 12 m of probe motion per session, and 100 held-out command regimes per platform, the structured model attains 9.2% worst-direction tracking error and 14.6% extrapolation error, against 9.7% and 16.3% for the Gaussian process and 9.5% and 15.6% for the perceptron, with the shortest calibration time (44 s) and the lowest noise sensitivity (2.4 points at 3% noise). The margins are modest, but the failure cases are informative: at 3% command noise the perceptron's extrapolation error on the B2 rises to 21%, whereas the structured model stays at 16.1%; conversely, the perceptron captures the B2's saturation knee 9% better in-regime. The resulting decision rule is to identify the structured model by default, and adopt a learned model only when the saturation shape is the binding constraint.","publication_date":"2026-09-14","registered_at":"2026-09-17T14:45:00Z","updated_at":"2026-09-17T18:09:00Z","status":"published","html_path":null,"pdf_path":"articles/2609.00006/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, 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":"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, 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. Science Robotics, arXiv:2010.11251, 2020.","identifier":"arXiv:2010.11251","url":"https://arxiv.org/abs/2010.11251"},{"text":"A. Kumar, Z. Fu, D. Pathak, and J. Malik. RMA: Rapid Motor Adaptation for Legged Robots. Robotics: Science and Systems, arXiv:2107.04034, 2021.","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, arXiv:2109.11978, 2021.","identifier":"arXiv:2109.11978","url":"https://arxiv.org/abs/2109.11978"},{"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, arXiv:2201.08117, 2022.","identifier":"arXiv:2201.08117","url":"https://arxiv.org/abs/2201.08117"},{"text":"G. B. Margolis, G. Yang, K. Paigwar, T. Chen, and P. Agrawal. Rapid Locomotion via Reinforcement Learning. Robotics: Science and Systems, 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. Conference on Robot Learning, arXiv:2212.03238, 2022.","identifier":"arXiv:2212.03238","url":"https://arxiv.org/abs/2212.03238"},{"text":"J. Tan, T. Zhang, E. Coumans, A. Iscen, Y. Bai, D. Hafner, S. Bohez, and V. Vanhoucke. Sim-to-Real: Learning Agile Locomotion for Quadruped Robots. Robotics: Science and Systems, arXiv:1804.10332, 2018.","identifier":"arXiv:1804.10332","url":"https://arxiv.org/abs/1804.10332"},{"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, arXiv:1710.06537, 2018.","identifier":"arXiv:1710.06537","url":"https://arxiv.org/abs/1710.06537"},{"text":"W. Yu, J. Tan, C. K. Liu, and G. Turk. Preparing for the Unknown: Learning a Universal Policy with Online System Identification. Robotics: Science and Systems, arXiv:1702.02453, 2017.","identifier":"arXiv:1702.02453","url":"https://arxiv.org/abs/1702.02453"},{"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. IEEE/RSJ International Conference on Intelligent Robots and Systems, arXiv:1703.06907, 2017.","identifier":"arXiv:1703.06907","url":"https://arxiv.org/abs/1703.06907"},{"text":"J. Schoukens and L. Ljung. Nonlinear System Identification: A User-Oriented Road Map. IEEE Control Systems Magazine, arXiv:1902.00683, 2019.","identifier":"arXiv:1902.00683","url":"https://arxiv.org/abs/1902.00683"},{"text":"G. Pillonetto, A. Aravkin, D. Gedon, L. Ljung, A. H. Ribeiro, and T. B. Schön. Deep Networks for System Identification: A Survey. arXiv:2301.12832, 2023.","identifier":"arXiv:2301.12832","url":"https://arxiv.org/abs/2301.12832"},{"text":"S. L. Brunton, J. L. Proctor, and J. N. Kutz. Discovering Governing Equations from Data by Sparse Identification of Nonlinear Dynamical Systems. Proceedings of the National Academy of Sciences, arXiv:1509.03580, 2016.","identifier":"arXiv:1509.03580","url":"https://arxiv.org/abs/1509.03580"},{"text":"H. Mania, M. I. Jordan, and B. Recht. Active Learning for Nonlinear System Identification with Guarantees. Journal of Machine Learning Research, arXiv:2006.10277, 2022.","identifier":"arXiv:2006.10277","url":"https://arxiv.org/abs/2006.10277"},{"text":"M. Buisson-Fenet, F. Solowjow, and S. Trimpe. Actively Learning Gaussian Process Dynamics. Learning for Dynamics and Control, arXiv:1911.09946, 2020.","identifier":"arXiv:1911.09946","url":"https://arxiv.org/abs/1911.09946"},{"text":"T. Lew, A. Sharma, J. Harrison, A. Bylard, and M. Pavone. Safe Active Dynamics Learning and Control: A Sequential Exploration-Exploitation Framework. IEEE Transactions on Robotics, arXiv:2008.11700, 2022.","identifier":"arXiv:2008.11700","url":"https://arxiv.org/abs/2008.11700"},{"text":"M. P. Deisenroth, D. Fox, and C. E. Rasmussen. Gaussian Processes for Data-Efficient Learning in Robotics and Control. IEEE Transactions on Pattern Analysis and Machine Intelligence, arXiv:1502.02860, 2015.","identifier":"arXiv:1502.02860","url":"https://arxiv.org/abs/1502.02860"},{"text":"C. E. Rasmussen and C. K. I. Williams. Gaussian Processes for Machine Learning. MIT Press, ISBN 0-262-18253-X, 2006.","identifier":"ISBN:0-262-18253-X","url":"http://gaussianprocess.org/gpml/"},{"text":"L. Hewing, J. Kabzan, and M. N. Zeilinger. Cautious Model Predictive Control Using Gaussian Process Regression. IEEE Transactions on Control Systems Technology, arXiv:1705.10702, 2017.","identifier":"arXiv:1705.10702","url":"https://arxiv.org/abs/1705.10702"},{"text":"F. Berkenkamp, M. Turchetta, A. P. Schoellig, and A. Krause. Safe Model-based Reinforcement Learning with Stability Guarantees. Advances in Neural Information Processing Systems, arXiv:1705.08551, 2017.","identifier":"arXiv:1705.08551","url":"https://arxiv.org/abs/1705.08551"},{"text":"K. Chua, R. Calandra, R. McAllister, and S. Levine. Deep Reinforcement Learning in a Handful of Trials Using Probabilistic Dynamics Models. Advances in Neural Information Processing Systems, arXiv:1805.12114, 2018.","identifier":"arXiv:1805.12114","url":"https://arxiv.org/abs/1805.12114"},{"text":"A. Nagabandi, G. Kahn, R. S. Fearing, and S. Levine. Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning. IEEE International Conference on Robotics and Automation, arXiv:1708.02596, 2018.","identifier":"arXiv:1708.02596","url":"https://arxiv.org/abs/1708.02596"},{"text":"A. Nagabandi, I. Clavera, S. Liu, R. S. Fearing, P. Abbeel, S. Levine, and C. Finn. Learning to Adapt in Dynamic, Real-World Environments through Meta-Reinforcement Learning. International Conference on Learning Representations, arXiv:1803.11347, 2019.","identifier":"arXiv:1803.11347","url":"https://arxiv.org/abs/1803.11347"},{"text":"G. Torrente, E. Kaufmann, P. Föhn, and D. Scaramuzza. Data-Driven MPC for Quadrotors. IEEE Robotics and Automation Letters, arXiv:2102.05773, 2021.","identifier":"arXiv:2102.05773","url":"https://arxiv.org/abs/2102.05773"},{"text":"L. Bauersfeld, E. Kaufmann, P. Foehn, S. Sun, and D. Scaramuzza. NeuroBEM: Hybrid Aerodynamic Quadrotor Model. Robotics: Science and Systems, arXiv:2106.08015, 2021.","identifier":"arXiv:2106.08015","url":"https://arxiv.org/abs/2106.08015"},{"text":"M. O'Connell, G. Shi, X. Shi, K. Azizzadenesheli, A. Anandkumar, Y. Yue, and S.-J. Chung. Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds. Science Robotics, arXiv:2205.06908, 2022.","identifier":"arXiv:2205.06908","url":"https://arxiv.org/abs/2205.06908"},{"text":"D. Kim, J. Di Carlo, B. Katz, G. Bledt, and S. Kim. Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Control. arXiv:1909.06586, 2019.","identifier":"arXiv:1909.06586","url":"https://arxiv.org/abs/1909.06586"},{"text":"R. Grandia, F. Jenelten, S. Yang, F. Farshidian, and M. Hutter. Perceptive Locomotion through Nonlinear Model-Predictive Control. IEEE Transactions on Robotics, arXiv:2208.08373, 2023.","identifier":"arXiv:2208.08373","url":"https://arxiv.org/abs/2208.08373"},{"text":"X. Xiao, B. Liu, G. Warnell, and P. Stone. Motion Planning and Control for Mobile Robot Navigation Using Machine Learning: A Survey. Autonomous Robots, arXiv:2011.13112, 2022.","identifier":"arXiv:2011.13112","url":"https://arxiv.org/abs/2011.13112"},{"text":"X. Xiao, J. Biswas, and P. Stone. Learning Inverse Kinodynamics for Accurate High-Speed Off-Road Navigation on Unstructured Terrain. IEEE Robotics and Automation Letters, arXiv:2102.12667, 2021.","identifier":"arXiv:2102.12667","url":"https://arxiv.org/abs/2102.12667"},{"text":"H. Karnan, K. S. Sikand, P. Atreya, S. Rabiee, X. Xiao, G. Warnell, P. Stone, and J. Biswas. VI-IKD: High-Speed Accurate Off-Road Navigation Using Learned Visual-Inertial Inverse Kinodynamics. IEEE International Conference on Robotics and Automation, arXiv:2203.15983, 2022.","identifier":"arXiv:2203.15983","url":"https://arxiv.org/abs/2203.15983"},{"text":"L. Wellhausen and M. Hutter. ArtPlanner: Robust Legged Robot Navigation in the Field. Field Robotics, arXiv:2303.01420, 2023.","identifier":"arXiv:2303.01420","url":"https://arxiv.org/abs/2303.01420"},{"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, arXiv:2209.12827, 2022.","identifier":"arXiv:2209.12827","url":"https://arxiv.org/abs/2209.12827"},{"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. IEEE/RSJ International Conference on Intelligent Robots and Systems, arXiv:2011.12255, 2021.","identifier":"arXiv:2011.12255","url":"https://arxiv.org/abs/2011.12255"},{"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, arXiv:2112.02094, 2022.","identifier":"arXiv:2112.02094","url":"https://arxiv.org/abs/2112.02094"},{"text":"D. Shah, A. Sridhar, A. Bhorkar, N. Hirose, and S. Levine. GNM: A General Navigation Model to Drive Any Robot. arXiv:2210.03370, 2022.","identifier":"arXiv:2210.03370","url":"https://arxiv.org/abs/2210.03370"},{"text":"B. Lakshminarayanan, A. Pritzel, and C. Blundell. Simple and Scalable Predictive Uncertainty Estimation Using Deep Ensembles. Advances in Neural Information Processing Systems, arXiv:1612.01474, 2017.","identifier":"arXiv:1612.01474","url":"https://arxiv.org/abs/1612.01474"},{"text":"C. Guo, G. Pleiss, Y. Sun, and K. Q. Weinberger. On Calibration of Modern Neural Networks. International Conference on Machine Learning, arXiv:1706.04599, 2017.","identifier":"arXiv:1706.04599","url":"https://arxiv.org/abs/1706.04599"},{"text":"J. R. Gardner, G. Pleiss, D. Bindel, K. Q. Weinberger, and A. G. Wilson. GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration. Advances in Neural Information Processing Systems, arXiv:1809.11165, 2018.","identifier":"arXiv:1809.11165","url":"https://arxiv.org/abs/1809.11165"},{"text":"D. P. Kingma and J. Ba. Adam: A Method for Stochastic Optimization. International Conference on Learning Representations, arXiv:1412.6980, 2015.","identifier":"arXiv:1412.6980","url":"https://arxiv.org/abs/1412.6980"}],"canonical_url":"https://academy.kaggleyes.top/abs/KAGG:2609.00006","metadata":{"title":"System Identification versus Learned Models for Commodity Quadruped Velocity Interfaces","authors":[{"name":"Lin Zhao","affiliation":"Perception and Control Group, Technical University of Munich, Munich, Germany"},{"name":"Maximilian Weber","affiliation":"Perception and Control Group, Technical University of Munich, Munich, Germany"},{"name":"Julia Hoffmann","affiliation":"Perception and Control Group, Technical University of Munich, Munich, Germany"},{"name":"Omar Farouk","affiliation":"Perception and Control Group, Technical University of Munich, Munich, Germany"}],"publication_date":"2026-09-14","abstract":"Navigation stacks for commodity quadrupeds command the robot through a vendor velocity interface whose response to commands, including delay, lag, cross-axis coupling, and saturation, is undocumented and differs between platforms. Planners therefore need a calibrated model of this interface, but it is unclear whether classical system identification or a learned model should provide it. This paper compares, under matched probe budgets and on the same planner-conditioned probe data, structured identification of a state-delay-plus-saturation model, a Gaussian-process surrogate, and a multilayer perceptron with one million parameters. Scoring uses navigation-relevant criteria: worst-direction tracking error, extrapolation error on unseen command regimes, calibration time, and sensitivity to command noise. On a Unitree Go2 and a Unitree B2, with 60 probe sessions per platform, 12 m of probe motion per session, and 100 held-out command regimes per platform, the structured model attains 9.2% worst-direction tracking error and 14.6% extrapolation error, against 9.7% and 16.3% for the Gaussian process and 9.5% and 15.6% for the perceptron, with the shortest calibration time (44 s) and the lowest noise sensitivity (2.4 points at 3% noise). The margins are modest, but the failure cases are informative: at 3% command noise the perceptron's extrapolation error on the B2 rises to 21%, whereas the structured model stays at 16.1%; conversely, the perceptron captures the B2's saturation knee 9% better in-regime. The resulting decision rule is to identify the structured model by default, and adopt a learned model only when the saturation shape is the binding constraint.","references":[{"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":"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, 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. Science Robotics, arXiv:2010.11251, 2020.","identifier":"arXiv:2010.11251","url":"https://arxiv.org/abs/2010.11251"},{"text":"A. Kumar, Z. Fu, D. Pathak, and J. Malik. RMA: Rapid Motor Adaptation for Legged Robots. Robotics: Science and Systems, arXiv:2107.04034, 2021.","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, arXiv:2109.11978, 2021.","identifier":"arXiv:2109.11978","url":"https://arxiv.org/abs/2109.11978"},{"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, arXiv:2201.08117, 2022.","identifier":"arXiv:2201.08117","url":"https://arxiv.org/abs/2201.08117"},{"text":"G. B. Margolis, G. Yang, K. Paigwar, T. Chen, and P. Agrawal. Rapid Locomotion via Reinforcement Learning. Robotics: Science and Systems, 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. Conference on Robot Learning, arXiv:2212.03238, 2022.","identifier":"arXiv:2212.03238","url":"https://arxiv.org/abs/2212.03238"},{"text":"J. Tan, T. Zhang, E. Coumans, A. Iscen, Y. Bai, D. Hafner, S. Bohez, and V. Vanhoucke. Sim-to-Real: Learning Agile Locomotion for Quadruped Robots. Robotics: Science and Systems, arXiv:1804.10332, 2018.","identifier":"arXiv:1804.10332","url":"https://arxiv.org/abs/1804.10332"},{"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, arXiv:1710.06537, 2018.","identifier":"arXiv:1710.06537","url":"https://arxiv.org/abs/1710.06537"},{"text":"W. Yu, J. Tan, C. K. Liu, and G. Turk. Preparing for the Unknown: Learning a Universal Policy with Online System Identification. Robotics: Science and Systems, arXiv:1702.02453, 2017.","identifier":"arXiv:1702.02453","url":"https://arxiv.org/abs/1702.02453"},{"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. IEEE/RSJ International Conference on Intelligent Robots and Systems, arXiv:1703.06907, 2017.","identifier":"arXiv:1703.06907","url":"https://arxiv.org/abs/1703.06907"},{"text":"J. Schoukens and L. Ljung. Nonlinear System Identification: A User-Oriented Road Map. IEEE Control Systems Magazine, arXiv:1902.00683, 2019.","identifier":"arXiv:1902.00683","url":"https://arxiv.org/abs/1902.00683"},{"text":"G. Pillonetto, A. Aravkin, D. Gedon, L. Ljung, A. H. Ribeiro, and T. B. Schön. Deep Networks for System Identification: A Survey. arXiv:2301.12832, 2023.","identifier":"arXiv:2301.12832","url":"https://arxiv.org/abs/2301.12832"},{"text":"S. L. Brunton, J. L. Proctor, and J. N. Kutz. Discovering Governing Equations from Data by Sparse Identification of Nonlinear Dynamical Systems. Proceedings of the National Academy of Sciences, arXiv:1509.03580, 2016.","identifier":"arXiv:1509.03580","url":"https://arxiv.org/abs/1509.03580"},{"text":"H. Mania, M. I. Jordan, and B. Recht. Active Learning for Nonlinear System Identification with Guarantees. Journal of Machine Learning Research, arXiv:2006.10277, 2022.","identifier":"arXiv:2006.10277","url":"https://arxiv.org/abs/2006.10277"},{"text":"M. Buisson-Fenet, F. Solowjow, and S. Trimpe. Actively Learning Gaussian Process Dynamics. Learning for Dynamics and Control, arXiv:1911.09946, 2020.","identifier":"arXiv:1911.09946","url":"https://arxiv.org/abs/1911.09946"},{"text":"T. Lew, A. Sharma, J. Harrison, A. Bylard, and M. Pavone. Safe Active Dynamics Learning and Control: A Sequential Exploration-Exploitation Framework. IEEE Transactions on Robotics, arXiv:2008.11700, 2022.","identifier":"arXiv:2008.11700","url":"https://arxiv.org/abs/2008.11700"},{"text":"M. P. Deisenroth, D. Fox, and C. E. Rasmussen. Gaussian Processes for Data-Efficient Learning in Robotics and Control. IEEE Transactions on Pattern Analysis and Machine Intelligence, arXiv:1502.02860, 2015.","identifier":"arXiv:1502.02860","url":"https://arxiv.org/abs/1502.02860"},{"text":"C. E. Rasmussen and C. K. I. Williams. Gaussian Processes for Machine Learning. MIT Press, ISBN 0-262-18253-X, 2006.","identifier":"ISBN:0-262-18253-X","url":"http://gaussianprocess.org/gpml/"},{"text":"L. Hewing, J. Kabzan, and M. N. Zeilinger. Cautious Model Predictive Control Using Gaussian Process Regression. IEEE Transactions on Control Systems Technology, arXiv:1705.10702, 2017.","identifier":"arXiv:1705.10702","url":"https://arxiv.org/abs/1705.10702"},{"text":"F. Berkenkamp, M. Turchetta, A. P. Schoellig, and A. Krause. Safe Model-based Reinforcement Learning with Stability Guarantees. Advances in Neural Information Processing Systems, arXiv:1705.08551, 2017.","identifier":"arXiv:1705.08551","url":"https://arxiv.org/abs/1705.08551"},{"text":"K. Chua, R. Calandra, R. McAllister, and S. Levine. Deep Reinforcement Learning in a Handful of Trials Using Probabilistic Dynamics Models. Advances in Neural Information Processing Systems, arXiv:1805.12114, 2018.","identifier":"arXiv:1805.12114","url":"https://arxiv.org/abs/1805.12114"},{"text":"A. Nagabandi, G. Kahn, R. S. Fearing, and S. Levine. Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning. IEEE International Conference on Robotics and Automation, arXiv:1708.02596, 2018.","identifier":"arXiv:1708.02596","url":"https://arxiv.org/abs/1708.02596"},{"text":"A. Nagabandi, I. Clavera, S. Liu, R. S. Fearing, P. Abbeel, S. Levine, and C. Finn. Learning to Adapt in Dynamic, Real-World Environments through Meta-Reinforcement Learning. International Conference on Learning Representations, arXiv:1803.11347, 2019.","identifier":"arXiv:1803.11347","url":"https://arxiv.org/abs/1803.11347"},{"text":"G. Torrente, E. Kaufmann, P. Föhn, and D. Scaramuzza. Data-Driven MPC for Quadrotors. IEEE Robotics and Automation Letters, arXiv:2102.05773, 2021.","identifier":"arXiv:2102.05773","url":"https://arxiv.org/abs/2102.05773"},{"text":"L. Bauersfeld, E. Kaufmann, P. Foehn, S. Sun, and D. Scaramuzza. NeuroBEM: Hybrid Aerodynamic Quadrotor Model. Robotics: Science and Systems, arXiv:2106.08015, 2021.","identifier":"arXiv:2106.08015","url":"https://arxiv.org/abs/2106.08015"},{"text":"M. O'Connell, G. Shi, X. Shi, K. Azizzadenesheli, A. Anandkumar, Y. Yue, and S.-J. Chung. Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds. Science Robotics, arXiv:2205.06908, 2022.","identifier":"arXiv:2205.06908","url":"https://arxiv.org/abs/2205.06908"},{"text":"D. Kim, J. Di Carlo, B. Katz, G. Bledt, and S. Kim. Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Control. arXiv:1909.06586, 2019.","identifier":"arXiv:1909.06586","url":"https://arxiv.org/abs/1909.06586"},{"text":"R. Grandia, F. Jenelten, S. Yang, F. Farshidian, and M. Hutter. Perceptive Locomotion through Nonlinear Model-Predictive Control. IEEE Transactions on Robotics, arXiv:2208.08373, 2023.","identifier":"arXiv:2208.08373","url":"https://arxiv.org/abs/2208.08373"},{"text":"X. Xiao, B. Liu, G. Warnell, and P. Stone. Motion Planning and Control for Mobile Robot Navigation Using Machine Learning: A Survey. Autonomous Robots, arXiv:2011.13112, 2022.","identifier":"arXiv:2011.13112","url":"https://arxiv.org/abs/2011.13112"},{"text":"X. Xiao, J. Biswas, and P. Stone. Learning Inverse Kinodynamics for Accurate High-Speed Off-Road Navigation on Unstructured Terrain. IEEE Robotics and Automation Letters, arXiv:2102.12667, 2021.","identifier":"arXiv:2102.12667","url":"https://arxiv.org/abs/2102.12667"},{"text":"H. Karnan, K. S. Sikand, P. Atreya, S. Rabiee, X. Xiao, G. Warnell, P. Stone, and J. Biswas. VI-IKD: High-Speed Accurate Off-Road Navigation Using Learned Visual-Inertial Inverse Kinodynamics. IEEE International Conference on Robotics and Automation, arXiv:2203.15983, 2022.","identifier":"arXiv:2203.15983","url":"https://arxiv.org/abs/2203.15983"},{"text":"L. Wellhausen and M. Hutter. ArtPlanner: Robust Legged Robot Navigation in the Field. Field Robotics, arXiv:2303.01420, 2023.","identifier":"arXiv:2303.01420","url":"https://arxiv.org/abs/2303.01420"},{"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, arXiv:2209.12827, 2022.","identifier":"arXiv:2209.12827","url":"https://arxiv.org/abs/2209.12827"},{"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. IEEE/RSJ International Conference on Intelligent Robots and Systems, arXiv:2011.12255, 2021.","identifier":"arXiv:2011.12255","url":"https://arxiv.org/abs/2011.12255"},{"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, arXiv:2112.02094, 2022.","identifier":"arXiv:2112.02094","url":"https://arxiv.org/abs/2112.02094"},{"text":"D. Shah, A. Sridhar, A. Bhorkar, N. Hirose, and S. Levine. 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