Learning Compositional Koopman Operators for Model-Based Control
Yunzhu Li MIT CSAIL、Hao He MIT CSAIL、Jiajun Wu MIT CSAIL、Dina Katabi MIT CSAIL、Antonio Torralba MIT CSAIL indicates equal contributions. Our project page: http://koopman.csail.mit.edu
Abstract
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear coordinate transformations with data-driven methods. Recently, researchers have proposed to use deep neural networks as a more expressive class of basis functions for calculating the Koopman operators. These approaches, however, assume a fixed dimensional state space; they are therefore not applicable to scenarios with a variable number of objects. In this paper, we propose to learn compositional Koopman operators, using graph neural networks to encode the state into object-centric embeddings and using a block-wise linear transition matrix to regularize the shared structure across objects. The learned dynamics can quickly adapt to new environments of unknown physical parameters and produce control signals to achieve a specified goal. Our experiments on manipulating ropes and controlling soft robots show that the proposed method has better efficiency and generalization ability than existing baselines.
中文速览
非线性动力学系统的建模与控制通常面临两难困境：线性化方法（Koopman算子理论）计算高效但难以推广到物体数量可变的场景，而图神经网络虽然泛化能力强，却因参数量庞大导致系统辨识缓慢、样本效率低下。本文提出"组合式Koopman算子"（Compositional Koopman Operators），用图神经网络将系统状态编码为以单个物体为中心的嵌入表示，再利用分块线性转移矩阵在同类物体对之间共享参数，从而把Koopman算子的线性高效性与图网络的组合泛化能力融为一体。在绳索操控和软体机器人控制的实验中，该方法的预测精度和新环境适应速度均显著优于现有的学习型物理引擎和传统深度Koopman方法。这项工作的意义在于，它为物体数量动态变化的复杂物理系统提供了一套既高效又通用的建模与控制框架，在机器人操控等实际场景中具有较强的落地潜力。
原文 arXiv:1910.08264;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1910.08264v2