Learning Compositional Koopman Operators for Model-Based Control

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.

The first two authors contributed equally to this paper. Project Page: http://koopman.csail.mit.edu/ Video: https://youtu.be/MnXo_hjh1Q4 Code: https://github.com/YunzhuLi/CompositionalKoopmanOperators

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• Learning Physical Constraints with Neural Projections
• Learning Group Structure and Disentangled Representations of Dynamical Environments
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• A First Principles Approach for Data-Efficient System Identification of Spring-Rod Systems via Differentiable Physics Engines
• Faster Policy Learning with Continuous-Time Gradients
• Deformable Linear Object Prediction Using Locally Linear Latent Dynamics
• Koopman Q-learning: Offline Reinforcement Learning via Symmetries of Dynamics
• Learn Proportional Derivative Controllable Latent Space from Pixels
• Koopman Spectrum Nonlinear Regulators and Efficient Online Learning