Koopman Operator Approach to Airdrop Mission Planning Under Uncertainty

Leonard, Andrew; Rogers, Jonathan; Gerlach, Adam R.

doi:10.2514/1.g004277

Cited by 10 publications

(4 citation statements)

References 31 publications

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“…A few other studies pertaining to the aeronautical domain have also been found to utilize Koopman operator-based methods. This includes the application of ballistic airdrop, where the adjoint Koopman operator is used to determine the optimal air release point for ariel delivery to a specified ground target under parametric uncertainty [10]. Modeling of missile dynamics from noisy data for model predictive control has also been undertaken using Sparse Identification of Nonlinear Dynamics (SINDy) and Stepwise Akaike Information Criteria (SAIC), where it has been shown to be superior in comparison with state-feedback control [89].…”

Section: Missiles/hypersonic Regimementioning

confidence: 99%

Vehicular Applications of Koopman Operator Theory—A Survey

2023

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Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering purposes. The introduction of a recent computationally efficient method in the context of fluid dynamics, which is based on the system dynamics decomposition to a set of normal modes in descending order, has overcome this long-lasting computational obstacle. The purely data-driven nature of Koopman operators holds the promise of capturing unknown and complex dynamics for reduced-order model generation and system identification, through which the rich machinery of linear control techniques can be utilized. Given the ongoing development of this research area and the many existing open problems in the fields of smart mobility and vehicle engineering, a survey of techniques and open challenges of applying Koopman operator theory to this vibrant area is warranted. This review focuses on the various solutions of the Koopman operator which have emerged in recent years, particularly those focusing on mobility applications, ranging from characterization and component-level control operations to vehicle performance and fleet management. Moreover, this comprehensive review of over 100 research papers highlights the breadth of ways Koopman operator theory has been applied to various vehicular applications with a detailed categorization of the applied Koopman operator-based algorithm type. Furthermore, this review paper discusses theoretical aspects of Koopman operator theory that have been largely neglected by the smart mobility and vehicle engineering community and yet have large potential for contributing to solving open problems in these areas.

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Section: Missiles/hypersonic Regimementioning

confidence: 99%

Vehicular Applications of Koopman Operator Theory—A Survey

2023

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“…Underpinned by Koopman operator theory, nonlinear systems represented with supernumerary state variables behave more linearly in the lifted space. The method has recently been applied to various robotics and automation challenges, including active learning [8], soft robotics [9], human-robot interaction [10], power systems [11], and mission planning [12]. More broadly, deep learning has proven a valuable tool for lifting linearization techniques [13]- [16].…”

Section: Introductionmentioning

confidence: 99%

Learning of Causal Observable Functions for Koopman-DFL Lifting Linearization of Nonlinear Controlled Systems and Its Application to Excavation Automation

Selby

Asada

2021

IEEE Robot. Autom. Lett.

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“…1 Nicholas S. Selby is a PhD Candidate in the Department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA, USA nselby@mit.edu 2 H. Harry Asada is with the Faculty of the Department of Mechanical Engineering at the Massachusetts Institute of Technology asada@mit.edu state variables behave more linearly in the lifted space. The method has recently been applied to various robotics and automation challenges, including active learning [7], soft robotics [8], human-robot interaction [9], power systems [10], and mission planning [11]. More broadly, deep learning has proven a valuable tool in a variety of lifting linearization techniques [12]- [15].…”

Section: Introductionmentioning

confidence: 99%

Learning of Causal Observable Functions for Koopman-DFL Lifting Linearization of Nonlinear Controlled Systems and Its Application to Excavation Automation

Selby,

Asada

2021

Preprint

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Effective and causal observable functions for loworder lifting linearization of nonlinear controlled systems are learned from data by using neural networks. While Koopman operator theory allows us to represent a nonlinear system as a linear system in an infinite-dimensional space of observables, exact linearization is guaranteed only for autonomous systems with no input, and finding effective observable functions for approximation with a low-order linear system remains an open question. Dual Faceted Linearization uses a set of effective observables for low-order lifting linearization, but the method requires knowledge of the physical structure of the nonlinear system. Here, a data-driven method is presented for generating a set of nonlinear observable functions that can accurately approximate a nonlinear control system to a low-order linear control system. A caveat in using data of measured variables as observables is that the measured variables may contain input to the system, which incurs a causality contradiction when lifting the system, i.e. taking derivatives of the observables. The current work presents a method for eliminating such anti-causal components of the observables and lifting the system using only causal observables. The method is applied to excavation automation, a complex nonlinear dynamical system, to obtain a low-order lifted linear model for control design.

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Koopman Operator Approach to Airdrop Mission Planning Under Uncertainty

Cited by 10 publications

References 31 publications

Vehicular Applications of Koopman Operator Theory—A Survey

Vehicular Applications of Koopman Operator Theory—A Survey

Learning of Causal Observable Functions for Koopman-DFL Lifting Linearization of Nonlinear Controlled Systems and Its Application to Excavation Automation

Learning of Causal Observable Functions for Koopman-DFL Lifting Linearization of Nonlinear Controlled Systems and Its Application to Excavation Automation

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