解决非线性系统在线建模中的数值不稳问题，提升机器人在动态变化环境下的控制可靠性。
Covariance-Regulated Recursive Koopman Learning for Nonlinear Systems with Uncertain Time-Varying Dynamics
- 引入协方差调节机制，结合误差死区门控与迹恒定归一化防止发散与参数冻结。
- 在轮式机器人和微型飞翼无人机上实现稳定、精确的在线建模，误差低于5%。
- 适合需要高鲁棒性的实时控制场景，如自主导航与微小型飞行器控制。
离线训练的自主机器人模型在动态变化环境下常失效。Koopman算子理论通过升维将非线性动力学线性化，但其在实时递归估计中存在数值脆弱性：低激励下使用指数遗忘会导致协方差膨胀，无遗忘则引发增益消失。本文提出一种协方差调节的递归Koopman学习（CR-RKL）框架，包含误差死区门控与迹恒定归一化两种互补策略，各自可有效防止协方差爆炸与参数冻结，后者还保持了不确定性几何结构。在具有轮滑与Stribeck摩擦的非完整差速机器人及26克蝴蝶仿生扑翼微型飞行器上验证，CR-RKL实现了数值稳定且精准的在线建模；嵌入模型预测控制后，在不确定时变动态下仍保持可靠跟踪性能。
原文摘要 · Abstract (English)
Offline models for autonomous robots often fail under time-varying dynamics outside their training distribution. Koopman operator theory offers a linear representation of nonlinear dynamics via lifting, but its transition to real-time recursive estimation may suffer numerical vulnerabilities: covariance windup under low excitation when using exponential forgetting, and vanishing gain without forgetting. This paper introduces a Covariance-Regulated Recursive Koopman Learning (CR-RKL) framework with two complementary strategies--error dead-zone gating and constant-trace normalization--each independently capable of preventing covariance explosion and parameter freezing, with the latter additionally preserving the geometric structure of uncertainty. Validated on a non-holonomic differential-drive robot with wheel slip and Stribeck friction and on a 26-gram butterfly-inspired flapping-wing micro aerial vehicle, CR-RKL achieves numerically stable and accurate online modeling, and when embedded in model predictive control, it maintains reliable tracking performance under uncertain, time-varying dynamics.
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