A PD-Type State-Dependent Riccati Equation With Iterative Learning Augmentation for Mechanical Systems

Saeed Rafee Nekoo; José Ángel Acosta; Guillermo Heredia; Anibal Ollero

doi:10.1109/JAS.2022.105533

Volume 9 Issue 8

Aug. 2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(8): 1499-1511

S. R. Nekoo, J. Á. Acosta, G. Heredia, and A. Ollero, “A PD-type state-dependent Riccati equation with iterative learning augmentation for mechanical systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 8, pp. 1499–1511, Aug. 2022. doi: 10.1109/JAS.2022.105533

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S. R. Nekoo, J. Á. Acosta, G. Heredia, and A. Ollero, “A PD-type state-dependent Riccati equation with iterative learning augmentation for mechanical systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 8, pp. 1499–1511, Aug. 2022. doi: 10.1109/JAS.2022.105533

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A PD-Type State-Dependent Riccati Equation With Iterative Learning Augmentation for Mechanical Systems

doi: 10.1109/JAS.2022.105533

GRVC Robotics Lab., Depto de Ingeniería de Sistemas y Automática, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Seville 41092, Spain

Funds: This work was supported by the European Commission H2020 Programme under HYFLIERS project contract 779411, AERIAL-CORE project contract number 871479 and the ARTIC (RTI2018-102224-B-I00) project, funded by the Spanish Agencia Estatal de Investigación

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Author Bio:
Saeed Rafee Nekoo is a Senior Postdoc Researcher at the GRVC Robotics Lab., Depto de Ingeniería de Sistemas y Automática, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Spain. He currently serves as a Researcher in aerial robotics and control engineering and is engaged with HYFLIERS (HYbrid FLying-rollIng with-snakE-aRm robot for contact inSpection) H2020 European Research Council project, focusing on design and development of variable-pitch-rotor drones for inspection: design, prototyping, control implementation, and experimentation. His research interests include robotics, nonlinear and optimal control, control engineering, manufacturing, cooperative robotics, flexible joint manipulators, observer, and estimator design, path planning, wheeled mobile robots, control of autonomous underwater vehicles, free-floating space manipulator design, and control, digital implementation of continuous-time nonlinear controllers, and design, manufacturing and control of mechatronics systems, aerial robotics, multirotor UAV and variable-pitch-rotor quadcopter control

José Ángel Acosta received both the servo-electrical and mechanical engineering degrees at the University of Huelva, Spain, and the electrical engineering degree at the University of Seville, Spain, respectively. He was Marie Curie Control Training Site Fellow as Member of the Centre National de la Recherche Scientifique (CNRS, France) in the Laboratoire des Signaux et Systèmes, France, in 2003 and 2005. He received the Ph.D. degree in 2004 at the Automatic Control and Systems Engineering Department at the University of Seville and the Ph.D. European Award in 2005. He was nominated for the George S. Axelby Outstanding Paper Award in the IEEE Transactions on Automatic Control journal in 2006. In 1999 he joined that department as Research Assistant, where he is currently Professor and Research Member of the Automatic Control and Robotics Institute, and is with the GRVC Robotics Lab., Depto de Ingeniería de Sistemas y Automática, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Spain. He has also been a Visitor at the Laboratoire des Signaux & Systèmes (CNRS, France) repeatedly since 2005 and Academic Visitor researching in the Electrical & Electronic Engineering Department as a Member of the Control & Power Group at Imperial College London, UK, in 2008-09-10 and 2011. His research interests are in the field of nonlinear control of dynamical systems with emphasis on electromechanical and robotic systems

Guillermo Heredia (Member, IEEE) is Full Professor at University of Seville (Spain). He was a Visiting Researcher at the Field Robotics Centre, Carnegie Mellon University (USA), and worked for an international automobile manu-facturer (General Motors). He participated as Senior Researcher in 65 R&D projects (EU, NASA and national projects), leading or co-leading 12 of them, including the FP7 ECSAFEMOBIL and the H2020 AEROBI and HYFLIERS projects. He is author or co-author of more than 100 publications on aerial robotics, aerial manipulation, autonomous vehicles and fault detection and reconfiguration

Anibal Ollero (Fellow, IEEE) is Full Professor and Head of GRVC at University Seville, and Scientific Advisor of the Center for Aerospace Technologies (CATEC) also in Seville. He has been Full Professor at the Universities of Santiago and Malaga (Spain) and Researcher at the Robotics Institute of Carnegie Mellon University (USA) and LAAS-CNRS (France). He authored more than 750 publications, including 9 books and 200 papers in journals and has been editor of 15 books. He has delivered plenaries and keynotes in more than 100 events including IEEE ICRA 2016 and IEEE IROS 2018. He has been supervisor or co-supervisor of 45 Ph.D. Thesis that have received many awards. He led more than 160 research projects, participating in more than 25 projects of the European Research Programmes being coordinator of 7 and associated or deputy coordinator of 3, all of them dealing with unmanned aerial systems and aerial robots. From November 2018 he is running the GRIFFIN ERC-Advanced Grant with the objective of developing a new generation of aerial robots that will be able to glide, flapping the wings, perch and manipulate by maintaining the equilibrium, and from December 2019 he is the coordinator of the H2020-AERiAL-CORE project with the participation of 15 universities, research centers and companies dealing with aerial robotic manipulators and applications to inspection and maintenance. He has transferred technologies to more than 20 companies and has been awarded with 25 international research and innovation awards, including the recent Rei Jaume I in New Technologies (Spain), the Challenge 3 of the MBZIRC 2020 International Robotics Competition, the Overall Information and Communication Technologies Innovation Radar Prize 2017 of the European Commission, and has been also elected between the three European innovators of the year being candidate to the European personalities of the year 2017. He is IEEE Fellow “for contributions to the development and deployment of aerial robots”. Currently Co-Chair of the “IEEE Technical Committee on Aerial Robotics and Unmanned Aerial Vehicles”, Coordinator of the “Aerial Robotics Topic Group” of euRobotics and has been Member of the “Board of Directors” of euRobotics until March 2019. He has been also Founder and President of the Spanish Society for the Research and Development in Robotics (SEIDROB) until November 2017
Corresponding author: Saeed Rafee Nekoo, e-mail: saerafee@yahoo.com
Received Date: 2021-10-27
Revised Date: 2021-12-21
Accepted Date: 2022-01-13

Available Online: 2022-03-19

Abstract

Abstract

This work proposes a novel proportional-derivative (PD)-type state-dependent Riccati equation (SDRE) approach with iterative learning control (ILC) augmentation. On the one hand, the PD-type control gains could adopt many useful available criteria and tools of conventional PD controllers. On the other hand, the SDRE adds nonlinear and optimality characteristics to the controller, i.e., increasing the stability margins. These advantages with the ILC correction part deliver a precise control law with the capability of error reduction by learning. The SDRE provides a symmetric-positive-definite distributed nonlinear suboptimal gain K(x) for the control input law u = –R^–1(x)B^T(x)K(x)x. The sub-blocks of the overall gain R^–1(x)B^T(x)K(x), are not necessarily symmetric positive definite. A new design is proposed to transform the optimal gain into two symmetric-positive-definite gains like PD-type controllers as u = –K_SP(x)e–K_SD(x)ė. The new form allows us to analytically prove the stability of the proposed learning-based controller for mechanical systems; and presents guaranteed uniform boundedness in finite-time between learning loops. The symmetric PD-type controller is also developed for the state-dependent differential Riccati equation (SDDRE) to manipulate the final time. The SDDRE expresses a differential equation with a final boundary condition, which imposes a constraint on time that could be used for finite-time control. So, the availability of PD-type finite-time control is an asset for enhancing the conventional classical linear controllers with this tool. The learning rules benefit from the gradient descent method for both regulation and tracking cases. One of the advantages of this approach is a guaranteed-stability even from the first loop of learning. A mechanical manipulator, as an illustrative example, was simulated for both regulation and tracking problems. Successful experimental validation was done to show the capability of the system in practice by the implementation of the proposed method on a variable-pitch rotor benchmark.
- Closed-loop,
- iterative learning control (ILC),
- PD-type,
- SDRE,
- SDDRE,
- symmetric

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References

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A nonlinear finite-time PD-like controller is presented based on SDDRE augmented with ILC
A convex objective function is introduced for regulation training rule of gradient descent
Uniform boundedness in finite time is guaranteed, suitable for unstable mechanical systems
VP propeller pendulum is controlled experimentally with SDRE + ILC approach

A PD-Type State-Dependent Riccati Equation With Iterative Learning Augmentation for Mechanical Systems

doi: 10.1109/JAS.2022.105533

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通讯作者: 陈斌, bchen63@163.com

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