Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. There is a growing interest in research to derive robustness (and/or safety) guarantees for systems the dynamics of which are extracted via the Koopman operator. In this paper, we propose a way to quantify the prediction error because of noisy measurements when the Koopman operator is approximated via Extended Dynamic Mode Decomposition. We further develop an enhanced robot control strategy to endow robustness to a class of data-driven (robotic) systems that rely on Koopman operator theory, and we show how part of the strategy can happen offline in an effort to make our algorithm capable of real-time implementation. We perform a parametric study to evaluate the (theoretical) performance of the algorithm using a Van der Pol oscillator and conduct a series of simulated experiments in Gazebo using a non-holonomic wheeled robot.
Differentiable Physics-Informed Adaptive Koopman Control for Stable Flight under Unknown Disturbances
Research Center for Intelligent Robotics, School of Astronautics, Northwestern Polytechnical University（西北工业大学航天学院智能机器人研究中心）；Department of Automation, Tsinghua University（清华大学自动化系）
Data-Driven Predictive Control of Nonholonomic Robots Based on a Bilinear Koopman Realization: Data Does Not Replace Geometry
Institute of Engineering and Computational Mechanics (ITM), University of Stuttgart（工程与计算力学研究所（ITM），斯图加特大学）；Optimization-based Control Group, Institute of Mathematics, Technische Universität Ilmenau（优化控制组，数学研究所，伊尔梅瑙技术大学）；Department of Mechanical Engineering, LUT University（机械工程系，卢托大学）
Koopman Linearization for Data-Driven Batch State Estimation of Control-Affine Systems
University of Toronto Institute for Aerospace Studies, University of Toronto（多伦多大学航空航天研究所）；Department of Mechanical Engineering, McGill University（麦吉尔大学机械工程系）
Dept. of Electrical and Computer Engineering, University of California, Riverside（加州大学河滨分校电气与计算机工程系）；Dept. of Mechanical and Aerospace Engineering, University of California San Diego（加州大学圣地亚哥分校机械与航空航天工程系）；Dept. of Planning and Control, Zoox Inc.（Zoox公司规划与控制部）；Dept. of Mechanical Engineering, University of Michigan（密歇根大学机械工程系）；Dept. of Mechanical Engineering, Yale University（耶鲁大学机械工程系）；Dept. of Mechanical Engineering, Northwestern University（西北大学机械工程系）；Institute of AI Industry Research (AIR), Tsinghua University（清华大学人工智能产业研究院）
A Koopman Operator-based NMPC Framework for Mobile Robot Navigation under Uncertainty
Department of Electrical and Computer Engineering, University of California, Riverside（加州大学河滨分校电气与计算机工程系）；Polytechnic School of Tunisia（突尼斯多技术学院）；Institute of AI Industry Research, Tsinghua University（清华大学人工智能产业研究院）
Evaluation of Three Vision Based Object Perception Methods for a Mobile Robot
Artificial Intelligence Research Institute (IIIA-CSIC)（人工智能研究所 (IIIA-CSIC)）；Computer Vision Center（计算机视觉中心）；Australian Centre for Field Robotics（澳大利亚野外机器人中心）；The University of Sydney（悉尼大学）
Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling
Florida Institute for Human and Machine Cognition（佛罗里达人机认知研究所）；University College London（伦敦大学学院）；Istituto Italiano di Tecnologia（意大利技术研究院）；Heriot-Watt University（赫瑞瓦特大学）
THUD++: Large-Scale Dynamic Indoor Scene Dataset and Benchmark for Mobile Robots
Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）
PREVENT: Proactive Risk Evaluation and Vigilant Execution of Tasks for Mobile Robotic Chemists using Multi-Modal Behavior Trees
Department of Chemistry and Material Innovation Factory, University of Liverpool（化学系和材料创新工厂，利物浦大学）；Center for Life Science Automation, University of Rostock（生命科学自动化中心，罗斯托克大学）
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Modeling and Control of a Pneumatic Soft Robotic Catheter Using Neural Koopman Operators
Laboratory for Computational Sensing and Robotics（计算感知与机器人实验室）；Johns Hopkins University（约翰霍普金斯大学）；Department of Mechanical Engineering（机械工程系）；University of Maryland（马里兰大学）
Active Learning of Dynamics for Data-Driven Control Using Koopman Operators
Northwestern University（西北大学）
本文提出了一种机器人系统的主动学习策略，考虑到任务信息，使快速学习，并允许控制很容易地综合利用Koopman算子表示。我们首先激励使用表示线性Koopman算子系统的非线性系统，说明了改进的基于模型的控制性能与驱动的Van der Pol系统。信息理论的方法，然后应用到Koopman运营商制定的动力系统，我们推导出一个控制器的机器人动力学的主动学习。示出的主动学习控制器，以增加有关的Koopman算子的信息的速率。此外，我们的主动学习控制器可以很容易地将建立在Koopman动态的政策，使快速主动学习和改进的控制的好处。使用四轴飞行器的结果示出了在自由落体期间的单执行主动学习和稳定能力。主动学习的结果被扩展为自动化Koopman可观的，我们实现我们的方法在真正的机器人系统。
Dynamic robotic cloth folding with efficient Koopman operator-based model predictive control
Istituto Italiano di Tecnologia（意大利技术研究院）；Institut de Robòtica i Informàtica Industrial（机器人与信息技术研究所）；MaLGa Center, DIBRIS, Università degli Studi di Genova（MaLGa中心，DIBRIS，热那亚大学）
Generalized Momenta-Based Koopman Formalism for Robust Control of Euler-Lagrangian Systems
Department of Mechanical Engineering, Indian Institute of Science（机械工程系，印度科学研究院）；Robert Bosch Centre for Cyber-Physical Systems, Indian Institute of Science（网络物理系统研究中心，印度科学研究院）
