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Rotorcraft with a 3DOF Rigid Manipulator: Quaternion-based Modeling and Real-time Control Tolerant to Multi-body Couplings

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Abstract

This paper proposes a simple solution for the stabilization of a mini-quadcopter carrying a 3DoF (degrees of freedom) manipulator robot in order to enhance its achievable workspace and application profile. Since the motion of the arm induces torques which degrade the stability of the system, in the present work, we consider the stabilization of both subsystems: the quadcopter and the robotic arm. The mathematical model of the system is based on quaternions. Likewise, an attitude control law consisting of a bounded quaternion-based feedback stabilizes the quadcopter to a desired attitude while the arm is evolving. The next stage is the translational dynamics which is simplified for control (nonlinear) design purposes. The aforementioned controllers are based on saturation functions whose stability is explicitly proved in the Lyapunov sense. Finally, experimental results and a statistical study validate the proposed control strategy.

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Acknowledgements

This work was supported by CONACYT-Mexico, LabEx PERSYVAL-Lab (No. ANR-11-LABX-0025) and Equipex ROBOTEX (No. ANR-10-EQPX-44-01).

Author information

Authors and Affiliations

  1. Polytechnic Institute of Advanced Sciences, FR 94200, Paris, France

    J. Alvarez-Munoz

  2. GIPSA-Lab, Univ. Grenoble Alpes, FR-38000, Grenoble, France

    N. Marchand & J. J. Tellez-Guzman

  3. Faculty of Electronics, Autonomous University of Puebla (BUAP), MX, 72570, Puebla, Mexico

    J. F. Guerrero-Castellanos

  4. XLIM Laboratory UMR CNRS 7252, University of Limoges ENSIL - ENSCI, Parc Ester Technopole, 16 rue Atlantis, Limoges, 87068, France

    J. Escareno

  5. Automatic Control and Micro-Mechatronic Department, FEMTO-ST Institute, UMR CNRS-UFC/ENSMM/UTBM, FR Besançon, France

    M. Rakotondrabe

Authors
  1. J. Alvarez-Munoz
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  2. N. Marchand
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  3. J. F. Guerrero-Castellanos
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  4. J. J. Tellez-Guzman
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  5. J. Escareno
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  6. M. Rakotondrabe
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Corresponding author

Correspondence to J. Alvarez-Munoz.

Additional information

Recommended by Guest Editor Jun-Zhi Yu

J. Alvarez-Munoz received the M. Sc. degree in electronics from the Autonomous University of Puebla, Mexico in 2012, and the Ph. D. degree in automatic control from GIPSA-Lab, University of Grenoble (UGA), France in 2017. Currently, he holds a post-doctoral fellowship position at the “Polytechnic Institute of Advanced Sciences”, Autonomous Aerial Systems Laboratory, France.

His research interests include modeling and control of convertible drones with interactive applications, time-delay systems and multi-agent control systems in the field of aerial robotics.

N. Marchand received the M. Sc. and Ph. D. degrees in automatic control from Grenoble Institute of Technology, France in 1995 and 1999, repectively. He was temporary teaching and researcher (ATER) at the Technological University Institute of Villeurbanne, France. From 2000 to 2002, he was an assistant professor at Paris-Sud University and Signals and Systems Laboratory, France. In 2013, he obtained the habilitation to direct research (HDR) from University of Grenoble, France. Since 2013, he is the National Center for Scientific Research (CNRS) senior researcher. Currently, he is deputy director of GIPSA-Lab laboratory, France. His work is focused on the control of systems on chips and cloud systems and more recently privacy.

His research interests include theoretical and applicative topics: event-based control, asynchronous control of linear and non linear systems, control and stabilization of flying robots using bio inspired strategies and control theory for computer sciences.

J. F. Guerrero-Castellanos received the B. Sc. degree in electronic science from Autonomous University of Puebla (BUAP), Mexico in 2002, and the M. Sc. and Ph. D. degrees in automatic control from Grenoble Institute of Technology and Joseph Fourier University, France, in 2004 and 2008, respectively. Between January and June 2008, he was a postdoctoral researcher at GIPSA-Lab Laboratory, France. After spending one year at the University Polytechnic of Puebla, Mexico as an assistant professor, he joined in 2009 Faculty of Electronics at BUAP, Mexico, as a full professor, where he established and directs the Control and Cyber-Physical Systems Laboratory. In 2016, he was a visiting research professor at the Laboratory of Image, Signal and Intelligent System (LISSI)-Paris-Est Creteil University (UPEC), France. Between August 2013 and December 2017, he was the head of Renewable Energy Engineering at BUAP, Mexico. He is a member of Mexican Academy of Science (AMC), Mexican Association on Automatic Control (AMCA), a member of IEEE and the National System of Researchers (Researcher Level I), Mexico.

His research interests include guidance and control of autonomous systems, wearable robots, microelectronics systems and control of renewable energy systems.

J. J. Tellez-Guzman received the M. Sc. degree in electronics from Autonomous University of Puebla, Mexico in 2012. Currently, he is a Ph. D. degree candidate in automatic control at GIPSA-Lab, University of Grenoble (UGA), France.

His research interests include modeling and control of aerial vehicles and vision-based control in the field of aerial robotics.

J. Escareno received the Ph. D. degree in automatic control from HEUDIASYC Laboratory, University of Technology of Compiegne (UTC), France in 2008. He has held a post-doctoral fellowship position at International Joint Unit of CNRS, 3175 LAFMIA hosted by CINVESTAV, from 2008 to 2010. He was a CNRS project researcher at University of Technology of Compiegne, France from 2010 to 2012. In March 2012, he was a visiting researcher at the French Nuclear Energy Commission (CEA), France. From July 2012 to October 2013, he was post-doctoral research associate at the Department of “Control and Micro-Mechatronics Systems” (AS2M) at FEMTO-ST (Franche-Comté Electronics Mechanics Thermal et Optical) UMR CNRS 6174, France. Currently, he holds an associate professor position at the “Polytechnic Institut of Advanced Sciences”, France.

His research interests include design, modeling and control of convertible and interactive drones in the field of aerial robotics. Likewise within the field of microrobotics, he is interested on embedded perception and control of piezoelectric actuators for micro-positioning applications.

M. Rakotondrabe received the HDR in control systems from Bourgogne Franche-Comte University, France in 2014. He is an associate professor at Bourgogne Franche-Comte University since 2007 with research affiliation at Automatic Control and Micromechatronic Systems Department of FEMTO02-ST Institute. He was the leader of the CODE Group ("Control and Design" Group) at FEMTO-02ST from 2015 to 2017. Since 2017, he founded the MACS Group (Methodologies for the Automatic Control and for the Design of Mechatronic Systems). He also founded and is the head of the international master on Control for Green Mechatronics (GREEM) of the Bourgogne Franche-Comte University, all in France. He is or was associate or guest editor in prestigious journals related to Automation and micro and nano Mechatronics: IEEE/ASME Transactions on Mechatronics, IFAC Mechatronics, IEEE Robotics and Automation Letters, IEEE Transactions on Industrial Electronics, MDPI Actuators. In 2016, he is recipient of the Big02-On-Small award delivered during the IEEE MARSS International Conference on Manipulation, Automation and Robotics at Small Scales. This award is to recognize a young professional (less than 40 years old) with excellent performance and international visibility in the topics of mechatronics and automation for manipulation at small scales.

His research interests include design, modeling, signal estimation and control techniques for piezoelectric actuators in general and for microsystems.

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Alvarez-Munoz, J., Marchand, N., Guerrero-Castellanos, J.F. et al. Rotorcraft with a 3DOF Rigid Manipulator: Quaternion-based Modeling and Real-time Control Tolerant to Multi-body Couplings. Int. J. Autom. Comput. 15, 547–558 (2018). https://doi.org/10.1007/s11633-018-1145-8

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