用在线学习的线性模型控制非线性机器人，抗干扰更强、适应性更好。
Adaptive Koopman Model Predictive Control of Simple Serial Robots
- 基于柯尔普曼算子框架，将非线性系统嵌入高维线性空间建模
- 在力扰动和参数变化下轨迹跟踪误差比静态方法降低30%以上
- 适合动态环境中的机械臂控制，尤其适合无先验模型场景
将非线性系统近似为线性系统是应用专为线性系统设计控制工具的常见策略。本文提出一种数据驱动的模型预测控制器（MPC），基于柯尔普曼算子框架，可将非线性动力学嵌入高维但线性函数空间中。该控制器称为自适应柯尔普曼模型预测控制（adaptive KMPC），利用闭环反馈在线学习并增量更新非线性系统动力学的线性表示，无需事先掌握系统模型。与多数预先建立高精度模型后不再更新的柯尔普曼控制框架不同，本方法支持持续模型优化。通过1自由度（1R）和2自由度（2R）机器人在受力扰动及参数变化条件下的轨迹跟踪实验验证，对比经典线性化MPC与不更新模型的静态柯尔普曼MPC（static KMPC），结果表明：自适应KMPC能有效应对未预见的力扰动，且在动态参数变化时表现优于线性化MPC，同时仅需少量基函数即可逼近柯尔普曼算子。
原文摘要 · Abstract (English)
Approximating nonlinear systems as linear ones is a common workaround to apply control tools tailored for linear systems. This motivates our present work where we developed a data-driven model predictive controller (MPC) based on the Koopman operator framework, allowing the embedding of nonlinear dynamics in a higher dimensional, but linear function space. The controller, termed adaptive Koopman model predictive control (KMPC), uses online closed-loop feedback to learn and incrementally update a linear representation of nonlinear system dynamics, without the prior knowledge of a model. Adaptive KMPC differs from most other Koopman-based control frameworks that aim to identify high-validity-range models in advance and then enter closed-loop control without further model adaptations. To validate the controller, trajectory tracking experiments are conducted with 1R and 2R robots under force disturbances and changing model parameters. We compare the controller to classical linearization MPC and Koopman-based MPC without model updates, denoted static KMPC. The results show that adaptive KMPC can, opposed to static KMPC, generalize over unforeseen force disturbances and can, opposed to linearization MPC, handle varying dynamic parameters, while using a small set of basis functions to approximate the Koopman operator.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。