arXiv 2105.080362021-05-17cs.ROcs.SYeess.SY

Koopman NMPC: Koopman-based Learning and Nonlinear Model Predictive Control of Control-affine Systems

California Institute of Technology（加州理工学院）

Carl Folkestad, Joel W. Burdick

英文摘要：

Koopman-based learning methods can potentially be practical and powerful tools for dynamical robotic systems. However, common methods to construct Koopman representations seek to learn lifted linear models that cannot capture nonlinear actuation effects inherent in many robotic systems. This paper presents a learning and control methodology that is a first step towards overcoming this limitation. Using the Koopman canonical transform, control-affine dynamics can be expressed by a lifted bilinear model. The learned model is used for nonlinear model predictive control (NMPC) design where the bilinear structure can be exploited to improve computational efficiency. The benefits for control-affine dynamics compared to existing Koopman-based methods are highlighted through an example of a simulated planar quadrotor. Prediction error is greatly reduced and closed loop performance similar to NMPC with full model knowledge is achieved.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

基于Koopman算子学习与非线性模型预测控制的运行时不确定性下移动多机器人导航

Mobile Multi-Robot Navigation under Runtime Uncertainty via Koopman Operator Learning and Nonlinear Model Predictive Control

University of California, Riverside（加州大学河滨分校）

本文提出基于Koopman算子学习与非线性模型预测控制的框架，解决移动多机器人导航中的运行时不确定性（如车轮打滑），实现目标到达与编队控制，并通过数值模拟验证有效性。

2026-09-15cs.RO

基于Koopman算子的不确定性下移动机器人导航NMPC框架

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）

针对系统不确定性导致传统模型方法脆弱的问题，提出基于Koopman算子学习的双线性模型NMPC框架，在Koopman空间定义约束并在状态空间求解优化，通过仿真与物理实验验证了其在未知动力学下的闭环导航有效性。

2025-04-29cs.ROcs.SYeess.SY

Advantages of Bilinear Koopman Realizations for the Modeling and Control of Systems with Unknown Dynamics

University of Michigan（密歇根大学）

Nonlinear dynamical systems can be made easier to control by lifting them into the space of observable functions, where their evolution is described by the linear Koopman operator. This paper describes how the Koopman operator can be used to generate approximate linear, bilinear, and nonlinear model realizations from data, and argues in favor of bilinear realizations for characterizing systems with unknown dynamics. Necessary and sufficient conditions for a dynamical system to have a valid linear or bilinear realization over a given set of observable functions are presented and used to show th…

2020-11-12cs.RO

基于带分段投影的Koopman算子的模拟多段连续体机器人形状控制

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）

针对软连续体机器人因无限自由度导致难以实现全形状控制的问题，提出基于分段投影的数据驱动Koopman算子方法，结合线性MPC实现了计算高效且高精度的实时闭环形状控制。

2025-09-15cs.RO

Neural Koopman Lyapunov Control

The University of Texas at Austin（德克萨斯大学奥斯汀分校）

Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem for real-world and industrial applications. Koopman operator theory allows one to analyze nonlinear systems through the lens of linear systems and nonlinear control systems through the lens of bilinear control systems. The key idea of these methods lies in the transformation of the coordinates of the nonlinear system into the Koopman observables, which are coordinates that allow the representation of the original system (control system) as a higher dimensional linear (bilinear contr…

2022-05-23cs.LGcs.NEcs.RO

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）

We present the Koopman State Estimator (KoopSE), a framework for model-free batch state estimation of control-affine systems that makes no linearization assumptions, requires no problem-specific feature selections, and has an inference computational cost that is independent of the number of training points. We lift the original nonlinear system into a higher-dimensional Reproducing Kernel Hilbert Space (RKHS), where the system becomes bilinear. The time-invariant model matrices can be learned by solving a least-squares problem on training trajectories. At test time, the system is algebraically…

2021-12-03cs.RO

更多相关论文收起更多论文

鲁棒Koopman控制屏障滤波器用于安全演员-评论家强化学习

Robust Koopman Control Barrier Filters for Safe Actor-Critic Reinforcement Learning

University of California, Berkeley（加州大学伯克利分校）

提出鲁棒Koopman-CBF SAC框架，通过数据驱动学习Koopman预测器、构建提升空间中的仿射CBF约束并利用二次规划安全层实施，同时通过投影残差裕度处理近似误差，实现零约束违反或减少违规。

2026-06-05cs.LGcs.ROcs.SY

基于双线性Koopman实现的非完整机器人数据驱动预测控制：数据不能替代几何

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）

本文研究了将EDMD模型集成到非完整移动机器人预测控制器的方法，涵盖一阶运动学与二阶动态模型，实验证明其可实现高精度控制，但强调纯数据驱动无法替代系统几何洞察。

2024-11-11cs.LGcs.ROcs.SY