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This paper presents an active learning strategy for robotic systems that takes into account task information, enables fast learning, and allows control to be readily synthesized by taking advantage of the Koopman operator representation. We first motivate the use of representing nonlinear systems as linear Koopman operator systems by illustrating the improved model-based control performance with an actuated Van der Pol system. Information-theoretic methods are then applied to the Koopman operator formulation of dynamical systems where we derive a controller for active learning of robot dynamics. The active learning controller is shown to increase the rate of information about the Koopman operator. In addition, our active learning controller can readily incorporate policies built on the Koopman dynamics, enabling the benefits of fast active learning and improved control. Results using a quadcopter illustrate single-execution active learning and stabilization capabilities during free-fall. The results for active learning are extended for automating Koopman observables and we implement our method on real robotic systems.
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This content will become publicly available on December 19, 2025
Control-Coherent Koopman Modeling: A Physical Modeling Approach
The modeling of nonlinear dynamics based on Koopman operator theory, originally applicable only to autonomous systems with no control, is extended to nonautonomous control system without approximation of the input matrix. Prevailing methods using a least square estimate of the input matrix may result in an erroneous input matrix, misinforming the controller. Here, a new method for constructing a Koopman model that yields the exact input matrix is presented. A set of state variables are introduced so that the control inputs are linearly involved in the dynamics of actuators. With these variables, a lifted linear model with the exact input matrix, called a Control-Coherent Koopman Model, is constructed by superposing control input terms, which are linear in local actuator dynamics, to the Koopman operator of the associated autonomous nonlinear system. As an example, the proposed method is applied to multi degree-of-freedom robotic arms, which are controlled with Model Predictive Control (MPC). It is demonstrated that the prevailing Dynamic Mode Decomposition with Control (DMDc) using an approximate input matrix does not provide a satisfactory result, while the Control-Coherent Koopman Model performs well with the correct input matrix, even performing better than the bilinear formulation of the Koopman operator.
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- Award ID(s):
- 2021625
- PAR ID:
- 10561898
- Publisher / Repository:
- IEEE
- Date Published:
- Edition / Version:
- 63rd
- Issue:
- 63
- Subject(s) / Keyword(s):
- Koopman Operator Lifted linearization Non-autonomous systems with control, Koopman Model Predictive Control
- Format(s):
- Medium: X Size: 1.5 MB Other: PDF
- Size(s):
- 1.5 MB
- Location:
- Proceedings of the 63rd IEEE Conference on Decision and Control, Milan
- Sponsoring Org:
- National Science Foundation
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