Imperative Learning

Self-supervised Neuro-Symbolic Learning for Robot Autonomy

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Imperative learning (IL) is a self-supervised neuro-symbolic learning framework for robot autonomy.

A prototype of IL was first mentioned in the iSLAM paper, while it was then formally defined in this long article:

  1. Cover for Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomy
    Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomy.
    Chen Wang, Kaiyi Ji, Junyi Geng, Zhongqiang Ren, Taimeng Fu, Fan Yang, Yifan Guo, Haonan He, Xiangyu Chen, Zitong Zhan, Qiwei Du, Shaoshu Su, Bowen Li, Yuheng Qiu, Yi Du, Qihang Li, Yifan Yang, Xiao Lin, Zhipeng Zhao.
    International Journal of Robotics Research (IJRR), 2025.
    Unifying robot autonomy via neuro-symbolic learning

This iSeries collects articles from the SAIR lab, named after a leading character “i” from “imperative learning”. In the iSeries collection, IL has been applied to various tasks including path planning, feature matching, and multi-robot routing, etc.

The list of iSeries articles

  1. Cover for iA*: Imperative Learning-based A* Search for Path Planning
    iA*: Imperative Learning-based A* Search for Path Planning.
    Xiangyu Chen, Fan Yang, Chen Wang.
    IEEE Robotics and Automation Letters (RA-L), vol. 10, no. 12, pp. 12987–12994, 2025.
    Reducing 66% search area and 54% runtime via imperative learning
  2. Cover for iWalker: Imperative Visual Planning for Walking Humanoid Robot
    iWalker: Imperative Visual Planning for Walking Humanoid Robot.
    Xiao Lin, Yuhao Huang, Taimeng Fu, Xiaobin Xiong, Chen Wang.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2865–2872, 2025.
    Best Workshop Paper Award; Enabling humanoid walking via self-supervised footstep planning
  3. Cover for iKap: Kinematics-aware Planning with Imperative Learning
    iKap: Kinematics-aware Planning with Imperative Learning.
    Qihang Li, Zhuoqun Chen, Haoze Zheng, Haonan He, Shaoshu Su, Junyi Geng, Chen Wang.
    IEEE International Conference on Robotics and Automation (ICRA), pp. 10164–10170, 2025.
    First imperative learning planner that respects robot kinematics constraints
  4. Cover for iMatching: Imperative Correspondence Learning
    iMatching: Imperative Correspondence Learning.
    Zitong Zhan, Dasong Gao, Yun-Jou Lin, Youjie Xia, Chen Wang.
    European Conference on Computer Vision (ECCV), pp. 183–200, 2024.
    A self-supervised feature learning approach pushes SOTA by 30% accuracy gain
  5. iMTSP: Solving Min-Max Multiple Traveling Salesman Problem with Imperative Learning.
    Yifan Guo, Zhongqiang Ren, Chen Wang.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 10245–10252, 2024.
    A pioneer work on imperative learning with discrete optimization
  6. iSLAM: Imperative SLAM.
    Taimeng Fu, Shaoshu Su, Yiren Lu, Chen Wang.
    IEEE Robotics and Automation Letters (RA-L), vol. 9, no. 5, pp. 4607–4614, 2024.
    Presented at ICRA 2025 First to unify front-end odometry and back-end pose graph via reciprocal learning
  7. Cover for iPlanner: Imperative Path Planning
    iPlanner: Imperative Path Planning.
    Fan Yang, Chen Wang, Cesar Cadena, Marco Hutter.
    Robotics: Science and Systems (RSS), 2023.
    A pioneer work in visual planning using imperative learning

Other Publications Using Imperative Learning

  1. Learning When to Jump for Off-road Navigation.
    Zhipeng Zhao, Taimeng Fu, Shaoshu Su, Qiwei Du, Ehsan Tarkesh Esfahani, Karthik Dantu, Souma Chowdhury, Chen Wang.
    Robotics: Science and Systems (RSS), 2026.
  2. Cover for Bundle Adjustment in the Eager Mode
    Bundle Adjustment in the Eager Mode.
    Zitong Zhan, Huan Xu, Zihang Fang, Xinpeng Wei, Yaoyu Hu, Chen Wang.
    IEEE Transactions on Robotics (T-RO), 2026.
    A GPU implementation achieving 20x speedup
  3. Fast Task Planning with Neuro-Symbolic Relaxation.
    Qiwei Du, Bowen Li, Yi Du, Shaoshu Su, Taimeng Fu, Zitong Zhan, Zhipeng Zhao, Chen Wang.
    IEEE Robotics and Automation Letters (RA-L), vol. 11, no. 3, pp. 3684–3691, 2026.
    An elegant real-world demonstration of interactive navigation
  4. Cover for G-DRAGON: Geospatial Reasoning and Dynamic Planning for Retrieval-Augmented Outdoor Navigation
    G-DRAGON: Geospatial Reasoning and Dynamic Planning for Retrieval-Augmented Outdoor Navigation.
    Dongzhihan Wang, Yi Du, Jianan Sun, Yuan Xue, Yingchen Zhang, Bing Xiao, Chen Wang, Liang Xu.
    IEEE Robotics and Automation Letters (RA-L), 2026.
  5. Cover for DispViT: Direct Stereo Disparity Regression with a Single-Stream Vision Transformer
    DispViT: Direct Stereo Disparity Regression with a Single-Stream Vision Transformer.
    Tongfan Guan, Jiaxin Guo, Tianyu Huang, Jinhu Dong, Chen Wang, Yun-Hui Liu.
    International Conference on Learning Representations (ICLR), 2026.
  6. GSMem: 3D Gaussian Splatting as Persistent Spatial Memory for Zero-Shot Embodied Exploration and Reasoning.
    Yiren Lu, Yi Du, Disheng Liu, Yunlai Zhou, Chen Wang, Yu Yin.
    arXiv preprint arXiv:2603.19137, 2026.
  7. InstantSfM: Towards GPU-Native SfM for the Deep Learning Era.
    Jiankun Zhong, Zitong Zhan, Quankai Gao, Ziyu Chen, Haozhe Lou, Jiageng Mao, Ulrich Neumann, Chen Wang, Yue Wang.
    arXiv preprint arXiv:2510.13310, 2026.
  8. VL-Nav: A Neuro-Symbolic Approach for Reasoning-based Vision-Language Navigation.
    Yi Du, Taimeng Fu, Zhipeng Zhao, Shaoshu Su, Zitong Zhan, Qiwei Du, Zhuoqun Chen, Bowen Li, Chen Wang.
    arXiv preprint arXiv:2502.00931, 2026.
    Deployment-ready neuro-symbolic vision-language navigation
  9. Cover for CLEAR: A Semantic-Geometric Terrain Abstraction for Large-Scale Unstructured Environments
    CLEAR: A Semantic-Geometric Terrain Abstraction for Large-Scale Unstructured Environments.
    Pranay Meshram, Charuvahan Adhivarahan, Ehsan Tarkesh Esfahani, Souma Chowdhury, Chen Wang, Karthik Dantu.
    arXiv preprint arXiv:2601.13361, 2026.
  10. Cover for Vision to Geometry: 3D Spatial Memory for Sequential Embodied MLLM Reasoning and Exploration
    Vision to Geometry: 3D Spatial Memory for Sequential Embodied MLLM Reasoning and Exploration.
    Zhongyi Cai, Yi Du, Chen Wang, Yu Kong.
    arXiv preprint arXiv:2512.02458, 2026.
  11. Resilient Odometry via Hierarchical Adaptation.
    Shibo Zhao, Sifan Zhou, Yuchen Zhang, Ji Zhang, Chen Wang, Wenshan Wang, Sebastian Scherer.
    Science Robotics, vol. 10, no. 109, 2025.
    Top featured article in Science Robotics; Imperative learning enables all-weather resiliency; Exhibiting only 0.000067 (0.2m / 3km) drift without loop closure
  12. Spatially-Enhanced Recurrent Memory for Long-Range Mapless Navigation via End-to-End Reinforcement Learning.
    Fan Yang, Per Frivik, David Hoeller, Chen Wang, Cesar Cadena, Marco Hutter.
    International Journal of Robotics Research (IJRR), 2025.
  13. Cover for iA*: Imperative Learning-based A* Search for Path Planning
    iA*: Imperative Learning-based A* Search for Path Planning.
    Xiangyu Chen, Fan Yang, Chen Wang.
    IEEE Robotics and Automation Letters (RA-L), vol. 10, no. 12, pp. 12987–12994, 2025.
    Reducing 66% search area and 54% runtime via imperative learning
  14. BridgeDepth: Bridging Monocular and Stereo Reasoning with Latent Alignment.
    Tongfan Guan, Jiaxin Guo, Chen Wang, Yun-Hui Liu.
    International Conference on Computer Vision (ICCV), pp. 27681–27691, 2025.
    Selected as a highlight paper in ICCV 2025
  15. Cover for iWalker: Imperative Visual Planning for Walking Humanoid Robot
    iWalker: Imperative Visual Planning for Walking Humanoid Robot.
    Xiao Lin, Yuhao Huang, Taimeng Fu, Xiaobin Xiong, Chen Wang.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2865–2872, 2025.
    Best Workshop Paper Award; Enabling humanoid walking via self-supervised footstep planning
  16. Cover for Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomy
    Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomy.
    Chen Wang, Kaiyi Ji, Junyi Geng, Zhongqiang Ren, Taimeng Fu, Fan Yang, Yifan Guo, Haonan He, Xiangyu Chen, Zitong Zhan, Qiwei Du, Shaoshu Su, Bowen Li, Yuheng Qiu, Yi Du, Qihang Li, Yifan Yang, Xiao Lin, Zhipeng Zhao.
    International Journal of Robotics Research (IJRR), 2025.
    Unifying robot autonomy via neuro-symbolic learning
  17. Cover for Differentiable Optimization
    Differentiable Optimization.
    Chen Wang, Krishna Murthy Jatavallabhula, Mustafa Mukadam.
    SLAM Handbook: From Localization and Mapping to Spatial Intelligence
    Edited by Luca Carlone, Ayoung Kim, Timothy Barfoot, Daniel Cremers, and Frank Dellaert
    Cambridge University Press, 2025
  18. SuperPC: A Single Diffusion Model for Point Cloud Completion, Upsampling, Denoising, and Colorization.
    Yi Du, Zhipeng Zhao, Shaoshu Su, Sharath Golluri, Haoze Zheng, Runmao Yao, Chen Wang.
    IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 16953–16964, 2025.
    Unifying point cloud processing via a single diffusion model
  19. Cover for Enhancing Scene Coordinate Regression with Efficient Keypoint Detection and Sequential Information
    Enhancing Scene Coordinate Regression with Efficient Keypoint Detection and Sequential Information.
    Kuan Xu, Zeyu Jiang, Haozhi Cao, Shenghai Yuan, Chen Wang, Lihua Xie.
    IEEE Robotics and Automation Letters (RA-L), vol. 10, no. 10, pp. 9932–9939, 2025.
  20. Cover for AirRoom: Objects Matter in Room Reidentification
    AirRoom: Objects Matter in Room Reidentification.
    Runmao Yao, Yi Du, Zhuoqun Chen, Haoze Zheng, Chen Wang.
    IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1385–1394, 2025.
  21. Cover for iKap: Kinematics-aware Planning with Imperative Learning
    iKap: Kinematics-aware Planning with Imperative Learning.
    Qihang Li, Zhuoqun Chen, Haoze Zheng, Haonan He, Shaoshu Su, Junyi Geng, Chen Wang.
    IEEE International Conference on Robotics and Automation (ICRA), pp. 10164–10170, 2025.
    First imperative learning planner that respects robot kinematics constraints
  22. MapEx: Indoor Structure Exploration with Probabilistic Information Gain from Global Map Predictions.
    Cherie Ho, Seungchan Kim, Brady Moon, Aditya Parandekar, Narek Harutyunyan, Chen Wang, Katia Sycara, Graeme Best, Sebastian Scherer.
    IEEE International Conference on Robotics and Automation (ICRA), pp. 13074–13080, 2025.
  23. AirSLAM: An Efficient and Illumination-Robust Point-Line Visual SLAM System.
    Kuan Xu, Yuefan Hao, Shenghai Yuan, Chen Wang, Lihua Xie.
    IEEE Transactions on Robotics (T-RO), vol. 41, pp. 1673–1692, 2025.
    Real-time visual SLAM at 70Hz with superior accuracy
  24. Cover for What Is The Best 3D Scene Representation for Robotics? From Geometric to Foundation Models
    What Is The Best 3D Scene Representation for Robotics? From Geometric to Foundation Models.
    Tianchen Deng, Yue Pan, Shenghai Yuan, Dong Li, Chen Wang, Mingrui Li, Long Chen, Lihua Xie, Danwei Wang, Jingchuan Wang, Javier Civera, Hesheng Wang, Weidong Chen.
    arXiv preprint arXiv:2512.03422, 2025.
  25. Cover for Vision-Language Memory for Spatial Reasoning
    Vision-Language Memory for Spatial Reasoning.
    Zuntao Liu, Yi Du, Taimeng Fu, Shaoshu Su, Cherie Ho, Chen Wang.
    arXiv preprint arXiv:2511.20644, 2025.
  26. AnyNav: Visual Neuro-symbolic Friction Learning for Off-road Navigation.
    Taimeng Fu, Zitong Zhan, Zhipeng Zhao, Shaoshu Su, Xiao Lin, Ehsan Tarkesh Esfahani, Karthik Dantu, Souma Chowdhury, Chen Wang.
    arXiv preprint arXiv:2501.12654, 2025.
    A self-supervised friction estimation framework
  27. Cover for Computer and Robot Vision: Past, Present, and Future [TC Spotlight]
    Computer and Robot Vision: Past, Present, and Future [TC Spotlight].
    Letizia Gionfrida, Chen Wang, Lu Gan, Margarita Chli, Luca Carlone.
    IEEE Robotics & Automation Magazine, vol. 31, no. 3, pp. 211–215, 2024.
  28. Cover for LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulation
    LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulation.
    Bowen Li, Zhaoyu Li, Qiwei Du, Jinqi Luo, Wenshan Wang, Yaqi Xie, Simon Stepputtis, Chen Wang, Katia P. Sycara, Pradeep Kumar Ravikumar, Alexander Gray, Xujie Si, Sebastian Scherer.
    Advances in Neural Information Processing Systems (NeurIPS), vol. 37, pp. 69840–69864, 2024.
  29. Cover for Map It Anywhere: Empowering BEV Map Prediction using Large-scale Public Datasets
    Map It Anywhere: Empowering BEV Map Prediction using Large-scale Public Datasets.
    Cherie Ho, Jiaye Zou, Omar Alama, Sai Mitheran, Benjamin Chiang, Taneesh Gupta, Chen Wang, Nikhil Keetha, Katia Sycara, Sebastian Scherer.
    Advances in Neural Information Processing Systems (NeurIPS), pp. 64433–64453, 2024.
  30. Cover for iMatching: Imperative Correspondence Learning
    iMatching: Imperative Correspondence Learning.
    Zitong Zhan, Dasong Gao, Yun-Jou Lin, Youjie Xia, Chen Wang.
    European Conference on Computer Vision (ECCV), pp. 183–200, 2024.
    A self-supervised feature learning approach pushes SOTA by 30% accuracy gain
  31. Cover for PhysORD: A Neuro-Symbolic Approach for Physics-infused Motion Prediction in Off-road Driving
    PhysORD: A Neuro-Symbolic Approach for Physics-infused Motion Prediction in Off-road Driving.
    Zhipeng Zhao, Bowen Li, Yi Du, Taimeng Fu, Chen Wang.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 11670–11677, 2024.
    Neuro-symbolic learning pushes SOTA by 46% higher accuracy using 3% model size
  32. iMTSP: Solving Min-Max Multiple Traveling Salesman Problem with Imperative Learning.
    Yifan Guo, Zhongqiang Ren, Chen Wang.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 10245–10252, 2024.
    A pioneer work on imperative learning with discrete optimization
  33. Learning-on-the-Drive: Self-supervised Adaptive Long-range Perception for High-speed Offroad Driving.
    Eric Chen, Cherie Ho, Mukhtar Maulimov, Chen Wang, Sebastian Scherer.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 9588–9595, 2024.
  34. Cover for AirShot: Efficient Few-Shot Detection for Autonomous Exploration
    AirShot: Efficient Few-Shot Detection for Autonomous Exploration.
    Zihan Wang, Bowen Li, Chen Wang, Sebastian Scherer.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 11654–11661, 2024.
  35. iSLAM: Imperative SLAM.
    Taimeng Fu, Shaoshu Su, Yiren Lu, Chen Wang.
    IEEE Robotics and Automation Letters (RA-L), vol. 9, no. 5, pp. 4607–4614, 2024.
    Presented at ICRA 2025 First to unify front-end odometry and back-end pose graph via reciprocal learning
  36. Salient Sparse Visual Odometry With Pose-Only Supervision.
    Siyu Chen, Kangcheng Liu, Chen Wang, Shenghai Yuan, Jianfei Yang, Lihua Xie.
    IEEE Robotics and Automation Letters (RA-L), vol. 9, no. 5, pp. 4774–4781, 2024.
  37. Cover for Neural Markov Random Field for Stereo Matching
    Neural Markov Random Field for Stereo Matching.
    Tongfan Guan, Chen Wang, Yun-Hui Liu.
    IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 5459–5469, 2024.
  38. Cover for SubT-MRS Dataset: Pushing SLAM Towards All-weather Environments
    SubT-MRS Dataset: Pushing SLAM Towards All-weather Environments.
    Shibo Zhao, Yuanjun Gao, Tianhao Wu, Damanpreet Singh, Rushan Jiang, Haoxiang Sun, Mansi Sarawata, Warren C Whittaker, Ian Higgins, Shaoshu Su, Yi Du, Can Xu, John Keller, Jay Karhade, Lucas Nogueira, Sourojit Saha, Yuheng Qiu, Ji Zhang, Wenshan Wang, Chen Wang, Sebastian Scherer.
    IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 22647–22657, 2024.
  39. Cover for GroundSLAM: A Robust Visual SLAM System for Warehouse Robots Using Ground Textures
    GroundSLAM: A Robust Visual SLAM System for Warehouse Robots Using Ground Textures.
    Kuan Xu, Zheng Yang, Lihua Xie, Chen Wang.
    arXiv preprint arXiv:1710.05502, 2025.
    Deployment-ready localization system with superior robustness
  40. AirIMU: Learning Uncertainty Propagation for Inertial Odometry.
    Yuheng Qiu, Chen Wang, Xunfei Zhou, Youjie Xia, Sebastian Scherer.
    arXiv preprint arXiv:2310.04874, 2024.
  41. Cover for Toward General-Purpose Robots via Foundation Models: A Survey and Meta-Analysis
    Toward General-Purpose Robots via Foundation Models: A Survey and Meta-Analysis.
    Yafei Hu, Quanting Xie, Vidhi Jain, Jonathan Francis, Jay Patrikar, Nikhil Keetha, Seungchan Kim, Yaqi Xie, Tianyi Zhang, Shibo Zhao, Yu-Quan Chong, Chen Wang, Katia Sycara, Matthew Johnson-Roberson, Dhruv Batra, Xiaolong Wang, Sebastian Scherer, Zsolt Kira, Fei Xia, Yonatan Bisk.
    arXiv preprint arXiv:2312.08782, 2024.
  42. Cover for VoxDet: Voxel Learning for Novel Instance Detection
    VoxDet: Voxel Learning for Novel Instance Detection.
    Bowen Li, Jiashun Wang, Yaoyu Hu, Chen Wang, Sebastian Scherer.
    Advances in Neural Information Processing Systems (NeurIPS), vol. 36, pp. 10604–10621, 2023.
    Selected as spotlight
  43. Cover for FDCT: A Fast Depth Completion Network for Transparent Objects
    FDCT: A Fast Depth Completion Network for Transparent Objects.
    Tianan Li, Zhehan Chen, Huan Liu, Chen Wang.
    IEEE Robotics and Automation Letters (RA-L), vol. 8, no. 9, pp. 5823–5830, 2023.
  44. Cover for PyPose v0.6: The Imperative Programming Interface for Robotics
    PyPose v0.6: The Imperative Programming Interface for Robotics.
    Zitong Zhan, Xiangfu Li, Qihang Li, Haonan He, Abhinav Pandey, Haitao Xiao, Yangmengfei Xu, Xiangyu Chen, Kuan Xu, Kun Cao, Zhipeng Zhao, Zihan Wang, Huan Xu, Zihang Fang, Yutian Chen, Wentao Wang, Xu Fang, Yi Du, Tianhao Wu, Xiao Lin, Yuheng Qiu, Fan Yang, Jingnan Shi, Shaoshu Su, Yiren Lu, Taimeng Fu, Karthik Dantu, Jiajun Wu, Lihua Xie, Marco Hutter, Luca Carlone, Sebastian Scherer, Daning Huang, Yaoyu Hu, Junyi Geng, Chen Wang.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Workshop, 2023.
  45. Cover for iPlanner: Imperative Path Planning
    iPlanner: Imperative Path Planning.
    Fan Yang, Chen Wang, Cesar Cadena, Marco Hutter.
    Robotics: Science and Systems (RSS), 2023.
    A pioneer work in visual planning using imperative learning
  46. Cover for Off-Policy Evaluation with Online Adaptation for Robot Exploration in Challenging Environments
    Off-Policy Evaluation with Online Adaptation for Robot Exploration in Challenging Environments.
    Yafei Hu, Junyi Geng, Chen Wang, John Keller, Sebastian Scherer.
    IEEE Robotics and Automation Letters (RA-L), vol. 8, no. 6, pp. 3780–3787, 2023.
    Presented at IROS 2023
  47. Cover for AirVO: An Illumination-Robust Point-Line Visual Odometry
    AirVO: An Illumination-Robust Point-Line Visual Odometry.
    Kuan Xu, Yuefan Hao, Shenghai Yuan, Chen Wang, Lihua Xie.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3429–3436, 2023.
  48. Cover for AirLine: Efficient Learnable Line Detection with Local Edge Voting
    AirLine: Efficient Learnable Line Detection with Local Edge Voting.
    Xiao Lin, Chen Wang.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3270–3277, 2023.
  49. Cover for PyPose: A Library for Robot Learning with Physics-based Optimization
    PyPose: A Library for Robot Learning with Physics-based Optimization.
    Chen Wang, Dasong Gao, Kuan Xu, Junyi Geng, Yaoyu Hu, Yuheng Qiu, Bowen Li, Fan Yang, Brady Moon, Abhinav Pandey, Aryan, Jiahe Xu, Tianhao Wu, Haonan He, Daning Huang, Zhongqiang Ren, Shibo Zhao, Taimeng Fu, Pranay Reddy, Xiao Lin, Wenshan Wang, Jingnan Shi, Rajat Talak, Kun Cao, Yi Du, Han Wang, Huai Yu, Shanzhao Wang, Siyu Chen, Ananth Kashyap, Rohan Bandaru, Karthik Dantu, Jiajun Wu, Lihua Xie, Luca Carlone, Marco Hutter, Sebastian Scherer.
    IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 22024–22034, 2023.
    Python library accumulated over 160,000 downloads in 2025
  50. Cover for Lifelong Graph Learning
    Lifelong Graph Learning.
    Chen Wang, Yuheng Qiu, Dasong Gao, Sebastian Scherer.
    IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 13719–13728, 2022.
    Selected as Oral presentation (4.2%)
  51. Cover for Robotic Interestingness via Human-Informed Few-Shot Object Detection
    Robotic Interestingness via Human-Informed Few-Shot Object Detection.
    Seungchan Kim, Chen Wang, Bowen Li, Sebastian Scherer.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1756–1763, 2022.
  52. Cover for AirDet: Few-Shot Detection without Fine-tuning for Autonomous Exploration
    AirDet: Few-Shot Detection without Fine-tuning for Autonomous Exploration.
    Bowen Li, Chen Wang, Pranay Reddy, Seungchan Kim, Sebastian Scherer.
    European Conference on Computer Vision (ECCV), pp. 427–444, 2022.
  53. Cover for AirObject: A Temporally Evolving Graph Embedding for Object Identification
    AirObject: A Temporally Evolving Graph Embedding for Object Identification.
    Nikhil Varma Keetha, Chen Wang, Yuheng Qiu, Kuan Xu, Sebastian Scherer.
    IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 8407–8416, 2022.
  54. Cover for AirLoop: Lifelong Loop Closure Detection
    AirLoop: Lifelong Loop Closure Detection.
    Dasong Gao, Chen Wang, Sebastian Scherer.
    International Conference on Robotics and Automation (ICRA), pp. 10664–10671, 2022.
  55. Cover for AirDOS: Dynamic SLAM benefits from Articulated Objects
    AirDOS: Dynamic SLAM benefits from Articulated Objects.
    Yuheng Qiu, Chen Wang, Wenshan Wang, Mina Henein, Sebastian Scherer.
    International Conference on Robotics and Automation (ICRA), pp. 8047–8053, 2022.
  56. AirCode: A Robust Object Encoding Method.
    Kuan Xu, Chen Wang, Chao Chen, Wei Wu, Sebastian Scherer.
    IEEE Robotics and Automation Letters (RA-L), vol. 7, no. 2, pp. 1816–1823, 2022.
    Presented at ICRA 2022
  57. Cover for Unsupervised Online Learning for Robotic Interestingness with Visual Memory
    Unsupervised Online Learning for Robotic Interestingness with Visual Memory.
    Chen Wang, Wenshan Wang, Yuheng Qiu, Yafei Hu, Seungchan Kim, Sebastian Scherer.
    IEEE Transactions on Robotics (T-RO), vol. 38, no. 4, pp. 2446–2461, 2021.
  58. Intensity-SLAM: Intensity Assisted Localization and Mapping for Large Scale Environment.
    Han Wang, Chen Wang, Lihua Xie.
    IEEE Robotics and Automation Letters (RA-L), vol. 6, no. 2, pp. 1715–1721, 2021.
    Presented at ICRA 2021
  59. Lightweight 3-D Localization and Mapping for Solid-State LiDAR.
    Han Wang, Chen Wang, Lihua Xie.
    IEEE Robotics and Automation Letters (RA-L), pp. 1801–1807, 2021.
    Presented at ICRA 2021
  60. Cover for Towards Real-time Semantic RGB-D SLAM in Dynamic Environments
    Towards Real-time Semantic RGB-D SLAM in Dynamic Environments.
    Tete Ji, Chen Wang, Lihua Xie.
    2021 International Conference on Robotics and Automation (ICRA), pp. 11175–11181, 2021.
  61. Cover for F-LOAM: Fast LiDAR Odometry And Mapping
    F-LOAM: Fast LiDAR Odometry And Mapping.
    Han Wang, Chen Wang, Chun-Lin Chen, Lihua Xie.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4390–4396, 2021.
  62. Intensity Scan Context: Coding Intensity and Geometry Relations for Loop Closure Detection.
    Han Wang, Chen Wang, Lihua Xie.
    International Conference on Robotics and Automation (ICRA), pp. 2095–2101, 2020.
  63. Cover for TartanAir: A Dataset to Push the Limits of Visual SLAM
    TartanAir: A Dataset to Push the Limits of Visual SLAM.
    Wenshan Wang, Delong Zhu, Xiangwei Wang, Yaoyu Hu, Yuheng Qiu, Chen Wang, Yafei Hu Hu, Ashish Kapoor, Sebastian Scherer.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4909–4916, 2020.
  64. Visual Memorability for Robotic Interestingness via Unsupervised Online Learning.
    Chen Wang, Wenshan Wang, Yuheng Qiu, Yafei Hu, Sebastian Scherer.
    European Conference on Computer Vision (ECCV), pp. 52–68, 2020.
    Selected as Oral presentation (2%)
  65. Online Visual Place Recognition via Saliency Re-identification.
    Han Wang, Chen Wang, Lihua Xie.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5030–5036, 2020.
  66. Cooperative Pursuit with Multi-Pursuer and One Faster Free-moving Evader.
    Xu Fang, Chen Wang, Lihua Xie, Jie Chen.
    IEEE Transactions on Cybernetics, vol. 52, no. 3, pp. 1405–1414, 2020.
  67. Cover for Graph Optimization Approach to Range-based Localization
    Graph Optimization Approach to Range-based Localization.
    Xu Fang, Chen Wang, Thien-Minh Nguyen, Lihua Xie.
    IEEE Transactions on Systems, Man and Cybernetics: Systems, vol. 51, no. 11, pp. 6830–6841, 2020.
  68. Kervolutional Neural Networks.
    Chen Wang, Jianfei Yang, Lihua Xie, Junsong Yuan.
    IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 31–40, 2019.
    Selected as Oral presentation (5.6%)
  69. Cover for Kernel Cross-Correlator
    Kernel Cross-Correlator.
    Chen Wang, Le Zhang, Lihua Xie, Junsong Yuan.
    Thirty-Second AAAI Conference on Artificial Intelligence (AAAI), pp. 4179–4186, 2018.
    The first theorem unifying correlation filters
  70. Cover for Correlation Flow: Robust Optical Flow Using Kernel Cross-Correlators
    Correlation Flow: Robust Optical Flow Using Kernel Cross-Correlators.
    Chen Wang, Tete Ji, Thien-Minh Nguyen, Lihua Xie.
    International Conference on Robotics and Automation (ICRA), pp. 836–841, 2018.
  71. Robust Target-relative Localization with Ultra-Wideband Ranging and Communication.
    Thien-Minh Nguyen, Abdul Hanif Zaini, Chen Wang, Kexin Guo, Lihua Xie.
    2018 International Conference on Robotics and Automation (ICRA), pp. 2312–2319, 2018.
  72. Cover for Ultra-Wideband Aided Fast Localization and Mapping System
    Ultra-Wideband Aided Fast Localization and Mapping System.
    Chen Wang, Handuo Zhang, Thien-Minh Nguyen, Lihua Xie.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1602–1609, 2017.
  73. Non-iterative SLAM.
    Chen Wang, Junsong Yuan, Lihua Xie.
    International Conference on Advanced Robotics, pp. 83–90, 2017.
    Best paper award in robotic planning

This blog will briefly explain IL in a high-level perspective, as the reader may find more in-depth explanation in the paper.

What is a unified framework for robot autonomy?

- Three Principles
The three principles of a unified framwork for robot autonomy.
  • Data-driven and Scalable: Self-Supervised
    • Different from computer vision or language models, labeling data for robotic tasks is often significantly more costly, as it typically requires specialized equipment rather than simple human annotations. To ensure the scalability of data-driven approaches in robot autonomy, the development of effective self-supervised learning frameworks is essential.
  • Generalizable and Interpretable: Neuro-Symbolic Learning with Physical and Logical Structure
    • Robotic tasks often involve underlying structured knowledge governed by both physical laws and logical relationships, such as kinematic and logical constraints, task preconditions, and safety rules. Neuro-Symbolic learning enables the system to make decisions that are easier to interpret, while also improving generalization to novel tasks and environments by leveraging prior knowledge about how the world works.
  • Modular and Global Optimal: End-to-end Trainable
    • A modular design reduces complexity by decomposing a system into independent yet interconnected components, making development, debugging, and interpretation more manageable. However, training neural and symbolic modules separately can lead to suboptimal integration, as errors may propagate and accumulate across components. Therefore, we expect a modular system to be end-to-end trainable, retaining the interpretability and flexibility of modular design, while enabling joint optimization across the entire pipeline.

Why do we need Imperative Leanring?

  • Imperative learning is a UNIFIED learning framework for robot autonomy following the three principles.
  • The imperative learning (IL) consists of three modules including a neural perceptual network, a symbolic reasoning engine, and a general memory system.
  • IL is formulated as a special bilevel optimization, enabling reciprocal learning and mutual correction among the three modules.
The framework of imperative learning.

Denote the neural system as \(\boldsymbol z = f({\boldsymbol{\theta}}, \boldsymbol{x})\), where \(\boldsymbol{x}\) represents the sensor measurements, \({\boldsymbol{\theta}}\) represents the perception-related learnable parameters, and \(\boldsymbol z\) represents the neural outputs such as semantic attributes; the reasoning engine as \(g(f, M, {\boldsymbol{\mu}})\) with reasoning-related parameters \({\boldsymbol{\mu}}\) and the memory system as \(M({\boldsymbol{\gamma}}, {\boldsymbol{\nu}})\), where \({\boldsymbol{\gamma}}\) is perception-related memory parameters and \({\boldsymbol{\nu}}\) is reasoning-related memory parameters. Therefore, imperative learning (IL) is formulated as a special BLO:

\[\begin{align} \min_{ \boldsymbol \psi \doteq [{\boldsymbol{\theta}}^\top,~{\boldsymbol{\gamma}}^\top]^\top} & U\left(f({\boldsymbol{\theta}}, \boldsymbol{x}), g({\boldsymbol{\mu}}^*), M({\boldsymbol{\gamma}}, {\boldsymbol{\nu}}^*)\right), \label{eq:high-il} \\ \textrm{s.t.} \quad & \boldsymbol \phi^* \in \arg\min_{ \boldsymbol \phi \doteq [{\boldsymbol{\mu}}^\top,~{\boldsymbol{\nu}}^\top]^\top} L(f({\boldsymbol{\theta}}, \boldsymbol{x}), g({\boldsymbol{\mu}}), M({\boldsymbol{\gamma}}, {\boldsymbol{\nu}})), \label{eq:low-il} \\ &\textrm{s.t.} \quad \xi(M({\boldsymbol{\gamma}}, {\boldsymbol{\nu}}), {\boldsymbol{\mu}}, f({\boldsymbol{\theta}}, \boldsymbol{x})) = \text{ or }\leq 0, \label{eq:il-constraint} \end{align}\]

where \(\xi\) is a general constraint (either equality or inequality); \(U\) and \(L\) are the upper-level (UL) and lower-level (LL) cost functions; and \(\boldsymbol \psi \doteq [{\boldsymbol{\theta}}^\top, {\boldsymbol{\gamma}}^\top]^\top\) are stacked UL variables and \(\boldsymbol \phi \doteq [{\boldsymbol{\mu}}^\top, {\boldsymbol{\nu}}^\top]^\top\) are stacked LL variables, respectively. Alternatively, \(U\) and \(L\) are also referred to as the neural cost and symbolic cost, respectively.

  • The term “imperative” is used to denote the passive nature of the learning process:
    • Once optimized, the neural system \(f\) in the UL cost will be driven to align with the LL reasoning engine \(g\)
      • E.g., logical, physical, or geometrical reasoning process with constraint \(\xi\).
    • Therefore, IL can learn to generate logically, physically, or geometrically feasible semantic attributes or predicates.
  • In some applications, \(\boldsymbol \psi\) and \(\boldsymbol \phi\) are also referred to as neuron-like and symbol-like parameters, respectively.
Self-supervised and End-to-end Trainable
  • Since many symbolic reasoning engines including geometric, physical, and logical reasoning, can be optimized or solved without providing labels.
    • For example, A\(^*\) search, geometrical reasoning such as bundle adjustment (BA), and physical reasoning like model predictive control (MPC) can be optimized without providing labels.
  • The IL framework leverages this phenomenon and jointly optimizes the three modules by bilevel optimization, which enforces the three modules to mutually correct each other.
  • Consequently, all three modules can be trained in a self-supervised and end-to-end manner by observing the world.
  • Although IL is designed for self-supervised learning, it can easily adapt to supervised or weakly supervised learning by involving labels either in UL or LL cost functions or both.
Overcoming the other Challenges.
  • The symbolic module offers better Interpretability and Generalization Ability due to its explainable design.
  • The Optimality is brought by bilevel optimization, compared to separately training the neural and symbolic modules.
Optimization Challenge
  • The solution to IL mainly involves solving the UL parameters \({\boldsymbol{\theta}}\) and \({\boldsymbol{\gamma}}\) and the LL parameters \({\boldsymbol{\mu}}\) and \({\boldsymbol{\nu}}\).
  • Intuitively, the UL parameters which are often neuron-like weights can be updated with the gradients of the UL cost $U$:
\[\begin{aligned}\label{eq:solution} \nabla_{\boldsymbol{\theta}} U &= \frac{\partial U}{\partial f} \frac{\partial f}{\partial {\boldsymbol{\theta}}} + \frac{\partial U}{\partial g} \frac{\partial g}{\partial {\boldsymbol{\mu}}^*}{\color{blue}\frac{\partial {\boldsymbol{\mu}}^*}{\partial {\boldsymbol{\theta}}}} + \frac{\partial U}{\partial M}\frac{\partial M}{\partial {\boldsymbol{\nu}}^*}{\color{blue}\frac{\partial {\boldsymbol{\nu}}^*}{\partial {\boldsymbol{\theta}}}}, \\\nabla_{\boldsymbol{\gamma}} U& = \frac{\partial U}{\partial M} \frac{\partial M}{\partial {\boldsymbol{\gamma}}} + \frac{\partial U}{\partial g} \frac{\partial g}{\partial {\boldsymbol{\mu}}^*} {\color{blue}\frac{\partial {\boldsymbol{\mu}}^*}{\partial {\boldsymbol{\gamma}}}} +\frac{\partial U}{\partial M} \frac{\partial M}{\partial {\boldsymbol{\nu}}^*} {\color{blue}\frac{\partial {\boldsymbol{\nu}}^*}{\partial {\boldsymbol{\gamma}}}}. \end{aligned}\]
  • Since \(U\), \(L\), \(M\), \(g\), and \(f\) are often well defined, the challenge is to compute the derivative of lower-level (symbol-like) parameters w.r.t the upper-level (neuron-like) parameters, \(\color{blue}\frac{\partial \boldsymbol \phi^*}{\partial \boldsymbol \psi}\), which takes the form:
\[{\color{blue} \frac{\partial \boldsymbol \phi^*}{\partial \boldsymbol \psi}} = \left[\begin{aligned} {\color{blue} \frac{\partial \boldsymbol \mu^*}{\partial \boldsymbol \theta}} & \quad {\color{blue}\frac{\partial \boldsymbol \mu^*}{\partial \boldsymbol \gamma}} \\ {\color{blue}\frac{\partial \boldsymbol \nu^*}{\partial \boldsymbol \theta}} & \quad {\color{blue}\frac{\partial \boldsymbol \nu^*}{\partial \boldsymbol \gamma}} \\ \end{aligned} \right]\]
  • There are generally two ways to compute it, i.e., unrolled differentiation and implicit differentiation. See paper for more details.
  • Since \(\boldsymbol \psi \doteq [{\boldsymbol{\theta}}^\top, {\boldsymbol{\gamma}}^\top]^\top\) are LL parameters, the solution depends on the specific LL tasks.

Applications and Examples

  • The paper provides five distinct examples covering the different cases of LL tasks.
The five distinct examples and their LL optimization methods.

Path Planning

In the case of LL tasks have closed-form solutions, we provide examples in both global and local path planning.

Global Path Planning
  1. Cover for iA*: Imperative Learning-based A* Search for Path Planning
    iA*: Imperative Learning-based A* Search for Path Planning.
    Xiangyu Chen, Fan Yang, Chen Wang.
    IEEE Robotics and Automation Letters (RA-L), vol. 10, no. 12, pp. 12987–12994, 2025.
    Reducing 66% search area and 54% runtime via imperative learning
  • A\(^*\) is widely used due to its optimality, but often suffers low efficiency due to its large search space.
  • Therefore, we could leverage a neural module to predict a confined search space, leading to overall improved efficiency.
  • We take A\(^*\) as the symbolic reasoning engine and train the neural module in a self-supervised way based on IL.
  • This results in a new framework, which is referred to as iA\(^*\).
The framework of iAstar.
  • Due to the confined search space and generalization ability from A*, iA\(^*\) outperforms both classic and other learning methods.
  • The following figure shows the qualitative results of path planning algorithms on datasets, including MP, Maze, and Matterport3D.
The qualitative results of path planning algorithms on three widely used datasets, including MP, Maze, and Matterport3D. The symbols S and G indicate the randomly selected start and goal positions. The optimal paths found by different path planning algorithms and their associated search space are indicated by red trajectories and green areas, respectively.
Local Path Planning
  1. Cover for iPlanner: Imperative Path Planning
    iPlanner: Imperative Path Planning.
    Fan Yang, Chen Wang, Cesar Cadena, Marco Hutter.
    Robotics: Science and Systems (RSS), 2023.
    A pioneer work in visual planning using imperative learning
  • End-to-end local path planning has recently attracted considerable interest, particularly for its potential to enable efficient inference.
  • Reinforcement learning-based methods often suffer from sample inefficiency and difficulties in directly processing depth images.
  • Imitation learning-based methods rely heavily on the availability and quality of labeled trajectories.
  • To solve those problems, we leverage a neural module to predict sparse waypoints, leading to overall improved efficiency.
  • The waypoints are then interpolated using a trajectory optimization engine based on a cubic spline.
  • We use IL to train this new framework, which is referred to as iPlanner.
The framework of iPlanner.
  • The following figure shows real-world experiment for local path planning using iPlanner with a legged robot.
Real-world experiment for local path planning using iPlanner with a legged robot. The red curve indicates the robot's trajectory from right to left, beginning inside a building and then navigating to the outdoors. The robot follows a series of waypoints (blue) and plans in different scenarios marked by green boxes including (A) passing through doorways, (B, D, E) circumventing both static and dynamic obstacles, and (B, F) ascending and descending stairs.

Logical Reasoning

  • In the case of the LL task needs first-order optimization, we provide an example in inductive logical reasoning.
  • Existing works only focus on toy examples, such as Visual Sudoku, and binary vector representations in BlocksWorld.
  • They cannot simultaneously perform grounding (high dimensional data) and rule induction.
  • Based on IL, we use a neural network for concept and relationship prediction, and a neural logical machine (NLM) for rule induction.
  • We denote this new framework as iLogic.
The framework of iLogic.
  • In the following figure, iLogic conducts rule induction with perceived groundings and the constraining rules exhibited on the right side and finally gets the accurate action prediction exhibited on the left side.
The examples of learned rules using iLogic.

Optimal Control

  1. Cover for A Self-Supervised Learning Approach with Differentiable Optimization for UAV Trajectory Planning
    A Self-Supervised Learning Approach with Differentiable Optimization for UAV Trajectory Planning.
    Yufei Jiang, Yuanzhu Zhan, Harsh Vardhan Gupta, Chinmay Borde, Junyi Geng.
    IEEE International Conference on Robotics and Automation (ICRA), 2026.
  2. Cover for Imperative MPC: An End-to-End Self-Supervised Learning with Differentiable MPC for UAV Attitude Control
    Imperative MPC: An End-to-End Self-Supervised Learning with Differentiable MPC for UAV Attitude Control.
    Haonan He, Yuheng Qiu, Junyi Geng.
    Annual Learning for Dynamics & Control Conference (L4DC), vol. 283, pp. 1140–1153, 2025.
  • In the case of the LL task needs constrained optimization, we provide an example of UAV attitude control based on IMU.
  • Differentiable model predictive control (MPC) to combine the physics-based modeling with data-driven methods, enabling learning dynamic models and control policies in an end-to-end manner.
  • However, many prior studies depend on expert demonstrations or labeled data for supervised learning.
  • They often suffer from challenging conditions such as unseen environments and external disturbances.
  • Based on IL, we use a neural network for IMU denoising and predict the hyperparameters for MPC.
  • We denote this new framework as iMPC.
The framework of iMPC.
  • We evaluate the control performance under the wind disturbance to validate the robustness of the proposed approach.
Control performance of iMPC under different levels of wind disturbance.

Visual Odometry

  1. iSLAM: Imperative SLAM.
    Taimeng Fu, Shaoshu Su, Yiren Lu, Chen Wang.
    IEEE Robotics and Automation Letters (RA-L), vol. 9, no. 5, pp. 4607–4614, 2024.
    Presented at ICRA 2025 First to unify front-end odometry and back-end pose graph via reciprocal learning
  • In the case of the LL task needs second-order optimization, we provide an example of simultaneous localization and mapping (SLAM).
  • Existing SLAM systems only have single connection between the front-end odometry and back-end pose graph optimization.
  • This leads to sub-optimal solutions since there is no feedback from the back-end to the front-end.
  • We proposed to optimize the entire SLAM system based on IL, leading the self-supervised reciprocal correction between the front-end and the back-end.
  • We refer to this new framework as iSLAM.
The framework of iSLAM. On the forward path, the odometry module (front-end) predicts the robot trajectory. The pose graph optimization (back-end) minimizes the LL cost in several iterations to get optimal poses. On the backward path, the UL cost is back-propagated through the map with a "one-step" strategy to update the network.
  • With more training iterations, the front-end odometry can be kept improving in the following figure.
The predicted trajectories from the front-end are improved concerning the number of imperative iterations in iSLAM.

Multi-agent Routing

  1. iMTSP: Solving Min-Max Multiple Traveling Salesman Problem with Imperative Learning.
    Yifan Guo, Zhongqiang Ren, Chen Wang.
    IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 10245–10252, 2024.
    A pioneer work on imperative learning with discrete optimization
  • In the case of the LL task needs discrete optimization, we provide an example of multiple traveling salesman problem (MTSP).
  • Traditional methods for MTSP needs combinatorial optimization, which is discrete optimization in a very large space.
  • Classic MTSP solvers such as Google’s OR-Tools routing library meet difficulties for large-scale problems (>500 cities).
  • We introduce IL and use a neural network for city allocation to agents and then use single TSP solvers for divided smaller problems.
  • To compute the differentiation in discrete space, we introduce a surrogate network to estimate the gradient based on control variate.
  • We refer this new framework as iMTSP.
The framework of iMTSP. A surrogate network is introduced as the memory in the IL framework, constructing a low-variance gradient for the allocation network through the non-differentiable and discrete TSP solvers.
  • Due to the generalization abilities of IL, iMTSP outperforms both classic solvers and RL-based methods.
  1. [1]
    Joint Sparse Optical Flow Estimation and Keypoint Detection via Dual-task Imperative Learning.
    Qiang Liu, Baojia Chen, Zhiqiang Hao, Xinlong Li, Leilei Xiang, Juan Liu.
    IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI), vol. 48, no. 3, pp. 2659–2675, 2026.
  2. [2]
    A Self-Supervised Learning Approach with Differentiable Optimization for UAV Trajectory Planning.
    Yufei Jiang, Yuanzhu Zhan, Harsh Vardhan Gupta, Chinmay Borde, Junyi Geng.
    IEEE International Conference on Robotics and Automation (ICRA), 2026.
  3. [3]
    Imperative MPC: An End-to-End Self-Supervised Learning with Differentiable MPC for UAV Attitude Control.
    Haonan He, Yuheng Qiu, Junyi Geng.
    Annual Learning for Dynamics & Control Conference (L4DC), vol. 283, pp. 1140–1153, 2025.

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