{"kagg_id":"KAGG:2609.00001","slug":"2609.00001","title":"Predictive Terrain Range Maps for Energy-Efficient Quadruped Navigation","authors":[{"name":"Jialin Ma","affiliation":"Intelligent Mobility Lab, University of Science and Technology of China, Hefei, China"},{"name":"Mingxuan Li","affiliation":"Intelligent Mobility Lab, University of Science and Technology of China, Hefei, China"},{"name":"Yutong Zhou","affiliation":"Intelligent Mobility Lab, University of Science and Technology of China, Hefei, China"}],"affiliation":null,"abstract":"Energy-efficient quadruped navigation requires knowing not only where obstacles are but also which feasible routes waste energy in rough terrain. Control-aligned future-range prediction estimates free range along the directions the robot's controller can actually execute, but it treats every free meter as equally cheap. This paper extends that representation into a predictive terrain-range map. Each control-aligned ray is annotated with an effort cost obtained by integrating a calibrated interface energy model, which relates terrain class, slope, and speed to electrical power, along the ray's predicted path. The result is a cost-weighted range field that a receding-horizon local planner consumes together with a consistent global cost-to-go, and a single explicit scalar λ sets the exchange rate between distance and energy. For exact route optimization, increasing λ cannot increase route energy or shorten the route. The approach is evaluated on 10 Isaac Lab terrain maps with graded effort cost (5 seeds, 25 goal pairs each) and on a 2.4 km mixed-terrain field loop with a Unitree Go2 and battery telemetry. With λ = 1.0, the planner reaches 1184 J/km, 13.3 percent below a distance-only planner (1365 J/km), with a mean arrival time of 218 s versus 248 s and 96.8 percent goal success versus 90.7 percent. A sweep over λ traces an energy-time frontier from 1412 J/km at 187 s to 1086 J/km at 289 s with diminishing returns beyond λ = 2.0, while energy-only routing is vulnerable to detour loops.","publication_date":"2026-09-01","registered_at":"2026-09-08T15:23:00Z","updated_at":"2026-09-08T18:23:00Z","status":"published","html_path":null,"pdf_path":"articles/2609.00001/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, 4(26), 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, 5(47), 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, 7(62), 2022. arXiv:2201.08117.","identifier":"arXiv:2201.08117","url":"https://arxiv.org/abs/2201.08117"},{"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 (CoRL), 2021. arXiv:2109.11978.","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. Robotics: Science and Systems (RSS), 2021. arXiv:2107.04034.","identifier":"arXiv:2107.04034","url":"https://arxiv.org/abs/2107.04034"},{"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":"A. Agarwal, A. Kumar, J. Malik, and D. Pathak. Legged Locomotion in Challenging Terrains Using Egocentric Vision. Conference on Robot Learning (CoRL), 2022. arXiv:2211.07638.","identifier":"arXiv:2211.07638","url":"https://arxiv.org/abs/2211.07638"},{"text":"Z. Zhuang, Z. Fu, J. Wang, C. Atkeson, S. Schwertfeger, C. Finn, and H. Zhao. Robot Parkour Learning. Conference on Robot Learning (CoRL), 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. 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. Science Robotics, 9(88), 2024. arXiv:2306.14874.","identifier":"arXiv:2306.14874","url":"https://arxiv.org/abs/2306.14874"},{"text":"G. B. Margolis and P. Agrawal. Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behavior. Conference on Robot Learning (CoRL), 2022. arXiv:2212.03238.","identifier":"arXiv:2212.03238","url":"https://arxiv.org/abs/2212.03238"},{"text":"Z. Fu, A. Kumar, J. Malik, and D. Pathak. Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robots. Conference on Robot Learning (CoRL), 2021. arXiv:2111.01674.","identifier":"arXiv:2111.01674","url":"https://arxiv.org/abs/2111.01674"},{"text":"Y. Yang, T. Zhang, E. Coumans, J. Tan, and B. Boots. Fast and Efficient Locomotion via Learned Gait Transitions. Conference on Robot Learning (CoRL), 2021. arXiv:2104.04644.","identifier":"arXiv:2104.04644","url":"https://arxiv.org/abs/2104.04644"},{"text":"C. Li, T. Zhang, and D. I. Goldman. A Terradynamics of Legged Locomotion on Granular Media. Science, 339(6126):1408–1412, 2013.","identifier":"doi:10.1126/science.1229163","url":"https://doi.org/10.1126/science.1229163"},{"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 (IROS), 2022. arXiv:2204.12876.","identifier":"arXiv:2204.12876","url":"https://arxiv.org/abs/2204.12876"},{"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, 6(3), 2021. arXiv:2103.04351.","identifier":"arXiv:2103.04351","url":"https://arxiv.org/abs/2103.04351"},{"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 (IROS), 2022. arXiv:2209.12827.","identifier":"arXiv:2209.12827","url":"https://arxiv.org/abs/2209.12827"},{"text":"J. Lee, M. Bjelonic, A. Reske, L. Wellhausen, T. Miki, and M. Hutter. Learning Robust Autonomous Navigation and Locomotion for Wheeled-Legged Robots. Science Robotics, 9(89), 2024. arXiv:2405.01792.","identifier":"arXiv:2405.01792","url":"https://arxiv.org/abs/2405.01792"},{"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 (CVPR), 2022. arXiv:2112.02094.","identifier":"arXiv:2112.02094","url":"https://arxiv.org/abs/2112.02094"},{"text":"F. Yang, C. Wang, C. Cadena, and M. Hutter. iPlanner: Imperative Path Planning. Robotics: Science and Systems (RSS), 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 (ICRA), 2024. arXiv:2310.00982.","identifier":"arXiv:2310.00982","url":"https://arxiv.org/abs/2310.00982"},{"text":"A. Loquercio, E. Kaufmann, R. Ranftl, M. Müller, V. Koltun, and D. Scaramuzza. Learning High-Speed Flight in the Wild. Science Robotics, 6(59), 2021. arXiv:2110.05113.","identifier":"arXiv:2110.05113","url":"https://arxiv.org/abs/2110.05113"},{"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":"G. Williams, P. Drews, B. Goldfain, J. M. Rehg, and E. A. Theodorou. Information-Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving. IEEE Transactions on Robotics, 34(6), 2018. arXiv:1707.02342.","identifier":"arXiv:1707.02342","url":"https://arxiv.org/abs/1707.02342"},{"text":"G. Kahn, P. Abbeel, and S. Levine. BADGR: An Autonomous Self-Supervised Learning-Based Navigation System. IEEE Robotics and Automation Letters, 6(2), 2021. arXiv:2002.05700.","identifier":"arXiv:2002.05700","url":"https://arxiv.org/abs/2002.05700"},{"text":"M. G. Castro, S. Triest, W. Wang, J. M. Gregory, F. Sanchez, J. G. Rogers III, and S. Scherer. How Does It Feel? Self-Supervised Costmap Learning for Off-Road Vehicle Traversability. IEEE International Conference on Robotics and Automation (ICRA), 2023. arXiv:2209.10788.","identifier":"arXiv:2209.10788","url":"https://arxiv.org/abs/2209.10788"},{"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 (RSS), 2023. arXiv:2305.08510.","identifier":"arXiv:2305.08510","url":"https://arxiv.org/abs/2305.08510"},{"text":"A. J. Sathyamoorthy, K. Weerakoon, T. Guan, J. Liang, and D. Manocha. TerraPN: Unstructured Terrain Navigation Using Online Self-Supervised Learning. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2022. arXiv:2202.12873.","identifier":"arXiv:2202.12873","url":"https://arxiv.org/abs/2202.12873"},{"text":"T. Guan, D. Kothandaraman, R. Chandra, A. J. Sathyamoorthy, K. Weerakoon, and D. Manocha. GA-Nav: Efficient Terrain Segmentation for Robot Navigation in Unstructured Outdoor Environments. IEEE Robotics and Automation Letters, 7(3), 2022. arXiv:2103.04233.","identifier":"arXiv:2103.04233","url":"https://arxiv.org/abs/2103.04233"},{"text":"D. D. Fan, K. Otsu, Y. Kubo, A. Dixit, J. Burdick, and A.-A. Agha-Mohammadi. STEP: Stochastic Traversability Evaluation and Planning for Risk-Aware Off-Road Navigation. Robotics: Science and Systems (RSS), 2021. arXiv:2103.02828.","identifier":"arXiv:2103.02828","url":"https://arxiv.org/abs/2103.02828"},{"text":"X. Cai et al. EVORA: Deep Evidential Traversability Learning for Risk-Aware Off-Road Autonomy. arXiv:2311.06234, 2023.","identifier":"arXiv:2311.06234","url":"https://arxiv.org/abs/2311.06234"},{"text":"R. T. Marler and J. S. Arora. Survey of Multi-Objective Optimization Methods for Engineering. Structural and Multidisciplinary Optimization, 26(6):369–395, 2004.","identifier":"doi:10.1007/s00158-003-0368-6","url":"https://doi.org/10.1007/s00158-003-0368-6"},{"text":"I. Das and J. E. Dennis. A Closer Look at Drawbacks of Minimizing Weighted Sums of Objectives for Pareto Set Generation in Multicriteria Optimization Problems. Structural Optimization, 14(1):63–69, 1997.","identifier":"doi:10.1007/BF01197559","url":"https://doi.org/10.1007/BF01197559"},{"text":"P. E. Hart, N. J. Nilsson, and B. Raphael. A Formal Basis for the Heuristic Determination of Minimum Cost Paths. IEEE Transactions on Systems Science and Cybernetics, 4(2):100–107, 1968.","identifier":"doi:10.1109/TSSC.1968.300136","url":"https://doi.org/10.1109/TSSC.1968.300136"},{"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. IEEE Robotics and Automation Letters, 8(6), 2023. arXiv:2301.04195.","identifier":"arXiv:2301.04195","url":"https://arxiv.org/abs/2301.04195"},{"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 (IROS), 2017. arXiv:1703.06907.","identifier":"arXiv:1703.06907","url":"https://arxiv.org/abs/1703.06907"},{"text":"A. Kadian et al. Sim2Real Predictivity: Does Evaluation in Simulation Predict Real-World Performance? IEEE Robotics and Automation Letters, 5(4), 2020. arXiv:1912.06321.","identifier":"arXiv:1912.06321","url":"https://arxiv.org/abs/1912.06321"}],"canonical_url":"https://academy.kaggleyes.top/abs/KAGG:2609.00001","metadata":{"title":"Predictive Terrain Range Maps for Energy-Efficient Quadruped Navigation","authors":[{"name":"Jialin Ma","affiliation":"Intelligent Mobility Lab, University of Science and Technology of China, Hefei, China"},{"name":"Mingxuan Li","affiliation":"Intelligent Mobility Lab, University of Science and Technology of China, Hefei, China"},{"name":"Yutong Zhou","affiliation":"Intelligent Mobility Lab, University of Science and Technology of China, Hefei, China"}],"publication_date":"2026-09-01","abstract":"Energy-efficient quadruped navigation requires knowing not only where obstacles are but also which feasible routes waste energy in rough terrain. Control-aligned future-range prediction estimates free range along the directions the robot's controller can actually execute, but it treats every free meter as equally cheap. This paper extends that representation into a predictive terrain-range map. Each control-aligned ray is annotated with an effort cost obtained by integrating a calibrated interface energy model, which relates terrain class, slope, and speed to electrical power, along the ray's predicted path. The result is a cost-weighted range field that a receding-horizon local planner consumes together with a consistent global cost-to-go, and a single explicit scalar λ sets the exchange rate between distance and energy. For exact route optimization, increasing λ cannot increase route energy or shorten the route. The approach is evaluated on 10 Isaac Lab terrain maps with graded effort cost (5 seeds, 25 goal pairs each) and on a 2.4 km mixed-terrain field loop with a Unitree Go2 and battery telemetry. With λ = 1.0, the planner reaches 1184 J/km, 13.3 percent below a distance-only planner (1365 J/km), with a mean arrival time of 218 s versus 248 s and 96.8 percent goal success versus 90.7 percent. A sweep over λ traces an energy-time frontier from 1412 J/km at 187 s to 1086 J/km at 289 s with diminishing returns beyond λ = 2.0, while energy-only routing is vulnerable to detour loops.","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, 4(26), 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, 5(47), 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, 7(62), 2022. arXiv:2201.08117.","identifier":"arXiv:2201.08117","url":"https://arxiv.org/abs/2201.08117"},{"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 (CoRL), 2021. arXiv:2109.11978.","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. Robotics: Science and Systems (RSS), 2021. arXiv:2107.04034.","identifier":"arXiv:2107.04034","url":"https://arxiv.org/abs/2107.04034"},{"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":"A. Agarwal, A. Kumar, J. Malik, and D. Pathak. Legged Locomotion in Challenging Terrains Using Egocentric Vision. Conference on Robot Learning (CoRL), 2022. arXiv:2211.07638.","identifier":"arXiv:2211.07638","url":"https://arxiv.org/abs/2211.07638"},{"text":"Z. Zhuang, Z. Fu, J. Wang, C. Atkeson, S. Schwertfeger, C. Finn, and H. Zhao. Robot Parkour Learning. Conference on Robot Learning (CoRL), 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. 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. Science Robotics, 9(88), 2024. arXiv:2306.14874.","identifier":"arXiv:2306.14874","url":"https://arxiv.org/abs/2306.14874"},{"text":"G. B. Margolis and P. Agrawal. Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behavior. Conference on Robot Learning (CoRL), 2022. arXiv:2212.03238.","identifier":"arXiv:2212.03238","url":"https://arxiv.org/abs/2212.03238"},{"text":"Z. Fu, A. Kumar, J. Malik, and D. Pathak. Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robots. Conference on Robot Learning (CoRL), 2021. arXiv:2111.01674.","identifier":"arXiv:2111.01674","url":"https://arxiv.org/abs/2111.01674"},{"text":"Y. Yang, T. Zhang, E. Coumans, J. Tan, and B. Boots. Fast and Efficient Locomotion via Learned Gait Transitions. Conference on Robot Learning (CoRL), 2021. arXiv:2104.04644.","identifier":"arXiv:2104.04644","url":"https://arxiv.org/abs/2104.04644"},{"text":"C. Li, T. Zhang, and D. I. Goldman. A Terradynamics of Legged Locomotion on Granular Media. Science, 339(6126):1408–1412, 2013.","identifier":"doi:10.1126/science.1229163","url":"https://doi.org/10.1126/science.1229163"},{"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 (IROS), 2022. arXiv:2204.12876.","identifier":"arXiv:2204.12876","url":"https://arxiv.org/abs/2204.12876"},{"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, 6(3), 2021. arXiv:2103.04351.","identifier":"arXiv:2103.04351","url":"https://arxiv.org/abs/2103.04351"},{"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 (IROS), 2022. arXiv:2209.12827.","identifier":"arXiv:2209.12827","url":"https://arxiv.org/abs/2209.12827"},{"text":"J. Lee, M. Bjelonic, A. Reske, L. Wellhausen, T. Miki, and M. Hutter. Learning Robust Autonomous Navigation and Locomotion for Wheeled-Legged Robots. Science Robotics, 9(89), 2024. arXiv:2405.01792.","identifier":"arXiv:2405.01792","url":"https://arxiv.org/abs/2405.01792"},{"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 (CVPR), 2022. arXiv:2112.02094.","identifier":"arXiv:2112.02094","url":"https://arxiv.org/abs/2112.02094"},{"text":"F. Yang, C. Wang, C. Cadena, and M. Hutter. iPlanner: Imperative Path Planning. Robotics: Science and Systems (RSS), 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 (ICRA), 2024. arXiv:2310.00982.","identifier":"arXiv:2310.00982","url":"https://arxiv.org/abs/2310.00982"},{"text":"A. Loquercio, E. Kaufmann, R. Ranftl, M. Müller, V. Koltun, and D. Scaramuzza. Learning High-Speed Flight in the Wild. Science Robotics, 6(59), 2021. arXiv:2110.05113.","identifier":"arXiv:2110.05113","url":"https://arxiv.org/abs/2110.05113"},{"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":"G. Williams, P. Drews, B. Goldfain, J. M. Rehg, and E. A. Theodorou. Information-Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving. IEEE Transactions on Robotics, 34(6), 2018. arXiv:1707.02342.","identifier":"arXiv:1707.02342","url":"https://arxiv.org/abs/1707.02342"},{"text":"G. Kahn, P. Abbeel, and S. Levine. BADGR: An Autonomous Self-Supervised Learning-Based Navigation System. IEEE Robotics and Automation Letters, 6(2), 2021. arXiv:2002.05700.","identifier":"arXiv:2002.05700","url":"https://arxiv.org/abs/2002.05700"},{"text":"M. G. Castro, S. Triest, W. Wang, J. M. Gregory, F. Sanchez, J. G. Rogers III, and S. Scherer. How Does It Feel? Self-Supervised Costmap Learning for Off-Road Vehicle Traversability. IEEE International Conference on Robotics and Automation (ICRA), 2023. arXiv:2209.10788.","identifier":"arXiv:2209.10788","url":"https://arxiv.org/abs/2209.10788"},{"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 (RSS), 2023. arXiv:2305.08510.","identifier":"arXiv:2305.08510","url":"https://arxiv.org/abs/2305.08510"},{"text":"A. J. Sathyamoorthy, K. Weerakoon, T. Guan, J. Liang, and D. Manocha. TerraPN: Unstructured Terrain Navigation Using Online Self-Supervised Learning. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2022. arXiv:2202.12873.","identifier":"arXiv:2202.12873","url":"https://arxiv.org/abs/2202.12873"},{"text":"T. Guan, D. Kothandaraman, R. Chandra, A. J. Sathyamoorthy, K. Weerakoon, and D. Manocha. GA-Nav: Efficient Terrain Segmentation for Robot Navigation in Unstructured Outdoor Environments. IEEE Robotics and Automation Letters, 7(3), 2022. arXiv:2103.04233.","identifier":"arXiv:2103.04233","url":"https://arxiv.org/abs/2103.04233"},{"text":"D. D. Fan, K. Otsu, Y. Kubo, A. Dixit, J. Burdick, and A.-A. Agha-Mohammadi. STEP: Stochastic Traversability Evaluation and Planning for Risk-Aware Off-Road Navigation. Robotics: Science and Systems (RSS), 2021. arXiv:2103.02828.","identifier":"arXiv:2103.02828","url":"https://arxiv.org/abs/2103.02828"},{"text":"X. Cai et al. EVORA: Deep Evidential Traversability Learning for Risk-Aware Off-Road Autonomy. arXiv:2311.06234, 2023.","identifier":"arXiv:2311.06234","url":"https://arxiv.org/abs/2311.06234"},{"text":"R. T. Marler and J. S. Arora. Survey of Multi-Objective Optimization Methods for Engineering. Structural and Multidisciplinary Optimization, 26(6):369–395, 2004.","identifier":"doi:10.1007/s00158-003-0368-6","url":"https://doi.org/10.1007/s00158-003-0368-6"},{"text":"I. Das and J. E. Dennis. A Closer Look at Drawbacks of Minimizing Weighted Sums of Objectives for Pareto Set Generation in Multicriteria Optimization Problems. Structural Optimization, 14(1):63–69, 1997.","identifier":"doi:10.1007/BF01197559","url":"https://doi.org/10.1007/BF01197559"},{"text":"P. E. Hart, N. J. Nilsson, and B. Raphael. A Formal Basis for the Heuristic Determination of Minimum Cost Paths. IEEE Transactions on Systems Science and Cybernetics, 4(2):100–107, 1968.","identifier":"doi:10.1109/TSSC.1968.300136","url":"https://doi.org/10.1109/TSSC.1968.300136"},{"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. IEEE Robotics and Automation Letters, 8(6), 2023. arXiv:2301.04195.","identifier":"arXiv:2301.04195","url":"https://arxiv.org/abs/2301.04195"},{"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 (IROS), 2017. arXiv:1703.06907.","identifier":"arXiv:1703.06907","url":"https://arxiv.org/abs/1703.06907"},{"text":"A. Kadian et al. 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