Control-oriented Modeling of Soft Robotic Swimmer with Koopman Operators

Castaño, Maria L.; Hess, Andrew; Mamakoukas, Giorgos; Gao, Tong; Murphey, Todd D.; Tan, Xiaobo

doi:10.1109/aim43001.2020.9159033

Cited by 18 publications

(12 citation statements)

References 28 publications

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“…Such results merit further research on more complicated dynamics using more sophisticated noise reduction schemes. In fact, as part of early-stage efforts of underwater exploration, we have tested our derivative-based Koopman approach to the unknown dynamics of a soft robotic fish [75]. In this work, we numerically estimated state derivatives using high-gain observers and were able to predict with reasonable accuracy the evolution of the states.…”

Section: Discussion and Future Workmentioning

confidence: 99%

Local Koopman Operators for Data-Driven Control of Robotic Systems

Mamakoukas¹,

Castaño²,

Tan³

et al. 2019

Robotics: Science and Systems XV

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This paper presents a methodology for linear embedding of nonlinear systems that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using higher-order derivatives of general nonlinear dynamics that need not be known, we construct a Koopman operator-based linear representation and utilize Taylor series accuracy to derive an error bound. The error formula is used to choose the order of derivatives in the basis functions and obtain a data-driven Koopman model using a closed-form expression that can be computed in real time. The Koopman representation of the nonlinear system is then used to synthesize LQR feedback. The efficacy of the embedding approach is demonstrated with simulation and experimental results on the control of a tail-actuated robotic fish. Experimental results show that the proposed data-driven control approach outperforms a tuned PID (Proportional Integral Derivative) controller and that updating the data-driven model online significantly improves performance in the presence of unmodeled fluid disturbance. This paper is complemented with a video: https://youtu.be/9 wx0tdDta0.

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Section: Discussion and Future Workmentioning

confidence: 99%

Local Koopman Operators for Data-Driven Control of Robotic Systems

Mamakoukas¹,

Castaño²,

Tan³

et al. 2019

Robotics: Science and Systems XV

Self Cite

View full text Add to dashboard Cite

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“…The authors in [36] adopted this idea and formalized it as EDMD-Lie being applicable for a few nonlinear elementary functions. In [23], this strategy was transferred to the case where no prior knowledge exists, by estimating the higher derivatives of the states using high gain observers. In the following, we assume that basic prior knowledge of the systems, e.g., the form of nonlinearities, is known and choose the observable functions accordingly.…”

Section: Taking Prior Knowledge Into Accountmentioning

confidence: 99%

Data-Driven Models for Control Engineering Applications Using the Koopman Operator

Junker,

Timmermann,

Trächtler

2021

Preprint

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Within this work, we investigate how data-driven numerical approximation methods of the Koopman operator can be used in practical control engineering applications. We refer to the method Extended Dynamic Mode Decomposition (EDMD), which approximates a nonlinear dynamical system as a linear model. This makes the method ideal for control engineering applications, because a linear system description is often assumed for this purpose. Using academic examples, we simulatively analyze the prediction performance of the learned EDMD models and show how relevant system properties like stability, controllability, and observability are reflected by the EDMD model, which is a critical requirement for a successful control design process. Subsequently, we present our experimental results on a mechatronic test bench and evaluate the applicability to the control engineering design process. As a result, the investigated methods are suitable as a low-effort alternative for the design steps of model building and adaptation in the classical modelbased controller design method.

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“…Studies seek finite-dimensional approximations using methods such as the Dynamic Mode Decomposition (DMD) [32] extended DMD (EDMD) [33], [34], Hankel-DMD [35], or closedform solutions [36], [37] which use state measurements to approximate Koopman operators. Data-driven Koopman operators have already been used in many applications, such as robotics [1], [2], [38], human locomotion [39], neuroscience [40], fluid mechanics [41], and climate forecast [42]. Contrary to linearization methods that remain locally accurate and are often updated online increasing the computational workload, in most cases researchers seek Koopman representations that are calculated once [2].…”

Section: B Benefits and Applications Of Koopman Operatorsmentioning

confidence: 99%

Learning Stable Models for Prediction and Control

Mamakoukas¹,

Abraham²,

Murphey³

2020

Preprint

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In this paper, we consider the problem of improving the long-term accuracy of data-driven approximations of Koopman operators, which are infinite-dimensional linear representations of general nonlinear systems, by bounding the eigenvalues of the linear operator. We derive a formula for the global error of general Koopman representations and motivate imposing stability constraints on the data-driven model to improve the approximation of nonlinear systems over a longer horizon. In addition, constraints on admissible basis functions for a stable Koopman operator are presented, as well as conditions for constructing a Lyapunov function for nonlinear systems. The modified linear representation is the nearest stable (all eigenvalues are equal or less than 1) matrix solution to a least-squares minimization and bounds the prediction of the system response. We demonstrate the benefit of stable Koopman operators in prediction and control performance using the systems of a pendulum, a hopper, and a quadrotor.

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Control-oriented Modeling of Soft Robotic Swimmer with Koopman Operators

Cited by 18 publications

References 28 publications

Local Koopman Operators for Data-Driven Control of Robotic Systems

Local Koopman Operators for Data-Driven Control of Robotic Systems

Data-Driven Models for Control Engineering Applications Using the Koopman Operator

Learning Stable Models for Prediction and Control

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