Soft robots are challenging to model and control as inherent non-linearities (e.g., elasticity and deformation), often requires complex explicit physics-based analytical modeling (e.g., a priori geometric definitions). While machine learning can be used to learn non-linear control models in a data-driven approach, these models often lack an intuitive internal physical interpretation and representation, limiting dynamical analysis. To address this, this paper presents an approach using Koopman operator theory and deep neural networks to provide a global linear description of the non-linear control systems. Specifically, by globally linearising dynamics, the Koopman operator is analyzed using spectral decomposition to characterises important physics-based interpretations, such as functional growths and oscillations. Experiments in this paper demonstrate this approach for controlling non-linear soft robotics, and shows model outputs are interpretable in the context of spectral analysis.
Shape control of simulated multi-segment continuum robots via Koopman operators with per-segment projection
Department of Electrical Engineering and Computer Science University of Michigan, Ann Arbor, Michigan 48109, USA（密歇根大学电气工程与计算机科学系）；School for Engineering of Matter, Transport and Energy Arizona State University, Tempe, Arizona 85281, USA（亚利桑那州立大学工程物质、运输与能源学院）
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。
SKooP: Symmetric Koopman Predictions for Faster and More Generalizable Legged Robot Locomotion with Reinforcement Learning
Italian Institute of Technology (IIT)（意大利理工学院）；University of Manchester（曼彻斯特大学）；Dynamic Legged Systems Laboratory, IIT（意大利理工学院动态腿式系统实验室）；Generative Bionics S.R.L（生成仿生学有限公司）；DAUIN, Politecnico di Torino（都灵理工大学DAUIN）；Rehab Technologies Lab, IIT（意大利理工学院康复技术实验室）；Newcastle University（纽卡斯尔大学）
Multi-segment Soft Robot Control via Deep Koopman-based Model Predictive Control
Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University（上海智能自主系统研究院，同济大学）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）；School of Biomedical Engineering, Tsinghua University（清华大学生物医学工程学院）；Beijing Soft Robot Tech Co., Ltd.（北京软机器人技术有限公司）；School of Clinical Medicine, Tsinghua University（清华大学临床医学学院）；Department of Informatics, University of Hamburg（汉堡大学信息学院）；School of Mechanical Engineering and Automation, Beihang University（北航机械工程与自动化学院）；Huawei Noah’s Ark Lab（华为诺亚实验室）
DK-RRT: Deep Koopman RRT for Collision-Aware Motion Planning of Space Manipulators in Dynamic Debris Environments
University of California, Irvine（加州大学尔湾分校）；Illinois Institute of Technology（伊利诺伊理工学院）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of California, Davis（加州大学戴维斯分校）；University of California, Berkeley（加州大学伯克利分校）
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）
Hubei University（湖北大学）；Shenzhen Institute of Artificial Intelligence and Robotics for Society (AIRS)（深圳市人工智能与机器人研究院）；The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen)（香港中文大学（深圳））；Manchester Metropolitan Joint Institute, Hubei University（湖北大学曼城联合学院）
Deep Koopman Operator with Control for Nonlinear Systems
The Chinese University of Hong Kong（香港中文大学）；Southern University of Science and Technology（南方科技大学）；Shenzhen Research Institute of The Chinese University of Hong Kong（香港中文大学深圳研究院）
Koopman-Based Robust Model Predictive Control for Nonlinear Systems with Stochastic Intermittent Measurements
Harbin Institute of Technology（哈尔滨工业大学）；School of Astronautics, Harbin Institute of Technology（哈尔滨工业大学航天学院）；Nanyang Technological University（南洋理工大学）；Nanyang Environment and Water Research Institute (NEWRI)（南洋环境与水研究）
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）
Accurate Open-Loop Control of a Soft Continuum Robot Using Visually Learned Latent Dynamics
Department of Advanced Interdisciplinary Studies, The University of Tokyo（东京大学先进跨学科研究科）；Institute of Assembly Technology and Robotics, Leibniz University Hannover（莱比锡大学装配技术与机器人研究所）；Research Center for Advanced Science and Technology, The University of Tokyo（东京大学先进科学研究中心）
Dynamic Neural Koopman Distillation for Fast Robot Control Using Diffusion Models
Department of Electrical and Computer Engineering, National University of Singapore（国立新加坡大学电子与计算机工程系）；Department of Electrical and Computer Engineering, Carnegie Mellon University（卡内基梅隆大学电子与计算机工程系）；Robotics and Autonomous Systems Thrust, The Hong Kong University of Science and Technology（香港科学与技术大学机器人与自主系统方向）
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）
