非线性机器人动力学的分段Koopman学习及其在多旋翼快速着陆中的应用
Episodic Koopman Learning of Nonlinear Robot Dynamics with Application to Fast Multirotor Landing
摘要：
本文提出了一种新的情景式方法来学习机器人的非线性动力学模型和一组任务的日益优化的控制序列。该方法是基于{ \em Koopman算子}的方法来分析非线性动力系统，它模拟了{ \em可观的}在函数空间中的流动，而不是在状态空间中的流动。实际上，这种方法估计了一个非线性的非线性同构，将动态提升到一个更高维的空间，在那里它们是线性的。然后，可以将有效的模型预测控制方法应用于提升的模型。这种方法允许在板上硬件的实时实现，在学习过程中严格纳入输入和状态约束。我们展示了该方法在快速多旋翼着陆的实时实现，其中的非线性地面效应的学习和使用，以提高着陆速度和质量。
英文摘要：
This paper presents a novel episodic method to learn a robot's nonlinear dynamics model and an increasingly optimal control sequence for a set of tasks. The method is based on the {\em Koopman operator} approach to nonlinear dynamical systems analysis, which models the flow of {\em observables} in a function space, rather than a flow in a state space. Practically, this method estimates a nonlinear diffeomorphism that lifts the dynamics to a higher dimensional space where they are linear. Efficient Model Predictive Control methods can then be applied to the lifted model. This approach allows for real time implementation in on-board hardware, with rigorous incorporation of both input and state constraints during learning. We demonstrate the method in a real-time implementation of fast multirotor landing, where the nonlinear ground effect is learned and used to improve landing speed and quality.
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