Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

6 Issues per year


IMPACT FACTOR 2016: 1.156
5-year IMPACT FACTOR: 1.238

CiteScore 2016: 1.50

SCImago Journal Rank (SJR) 2016: 0.457
Source Normalized Impact per Paper (SNIP) 2016: 1.239

Open Access
Online
ISSN
2300-1917
See all formats and pricing
More options …
Volume 62, Issue 3 (Sep 2014)

Issues

Modelling and optimal control system design for quadrotor platform – an extended approach

R. Zawiski
  • Corresponding author
  • Institute of Automatics, Faculty of Automatics, Electronics and Computer Science, Silesian University of Technology, 16 Akademicka St., 44-100 Gliwice, Poland
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ M. Błachuta
  • Institute of Automatics, Faculty of Automatics, Electronics and Computer Science, Silesian University of Technology, 16 Akademicka St., 44-100 Gliwice, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-09-09 | DOI: https://doi.org/10.2478/bpasts-2014-0058

Abstract

This article presents the development of a mathematical model of a quadrotor platform and the design of a dedicated control system based on an optimal approach. It describes consecutive steps in development of equations forming the model and including all its physical aspects without commonly used simplifications. Aerodynamic phenomena, such as Vortex Ring State or blade flapping are accounted for during the modelling process. The influence of rotors’ gyroscopic effect is exposed. The structure of a control system is described with an application of the optimal LQ regulator and an intuitive way of creating various flight trajectories. Simulation tests of the control system performance are conducted. Comparisons with models available in the literature are made. Based on above, conclusions are drawn about the level of insight necessary in creation of control-oriented and useable model of a quadrotor platform. New possibilities of designing and verifying models of quadrotor platforms are also discussed.

Keywords : mathematical modelling; optimal control; quadrotor platform; autonomous flight

References

  • [1] J. Leishman, Principles of Helicopter Aerodynamics, 2nd ed., Cambridge University Press, New York, 2006.Google Scholar

  • [2] S. Anderson, “Historical overview of V/STOL aircraft technology”, in NASA Technical Memorandum 81280, Ames Research Center, Moffett Field, 1981.Google Scholar

  • [3] N. Metni, J-M. Pflimlin, T. Hamel, and P. Soueres, “Attitude and gyro bias estimation for a VTOL UAV”, Control Eng. Pract. 14, 1511-1520 (2006).CrossrefGoogle Scholar

  • [4] A. Babiarz, R. Bieda, K. Jaskot, and J. Klamka, “The dynamics of the human arm with an observer for the capture of body motion parameters”, Bull. Pol. Ac.: Tech. 61 (4), 955-971 (2013).Web of ScienceGoogle Scholar

  • [5] S. Bouabdallah, A. Noth, and R. Siegwart, “PID vs. LQ control techniques applied to an indoor micro quadrotor”, 2004 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems 3, 2451-2456 (2004).Google Scholar

  • [6] S. Bouabdallah, P. Murrieri, and R. Siegwart, “Design and control of an indoor micro quadrotor”, ICRA ’04 IEEE Int. Conf. on Robotics and Automation 5, 4393-4398 (2004).Google Scholar

  • [7] P. Corke, R. Mahony, and P. Pounds, “Modelling and control of a quad-rotor robot”, Proc. Australasian Conf. on Robotics and Automation 1, CD-ROM (2006).Google Scholar

  • [8] T. Hamel, R. Lozano, R. Mahony, and J. Ostrowski, “Dynamic modelling and configuration stabilization for an X4-flyer”, 15th Triennial World Congress Int. Federation of Automatic Control 1, 846-848 (2002).Google Scholar

  • [9] P. Hynes, R. Mahony, P. Pounds, and J. Roberts, “Design of a four rotor aerial robot”, Australasian Conf. on Robotics and Automation 1, 145-150 (2002).Google Scholar

  • [10] Penn State GRASP Laboratory https://www.grasp.upenn.edu/success stories (2012).Google Scholar

  • [11] ETH Flying Machine Arena http://www.idsc.ethz.ch/Research DAndrea/FMA (2012).Google Scholar

  • [12] G. Hoffman, H. Huang, C. Tomlin, and S. Waslander, “Quadrotor helicopter flight dynamics and control: theory and experiment”, AIAA Guidance, Navigation and Control Conf. and Exhibit 1, CD-ROM (2007).Google Scholar

  • [13] P. Corke, J. Gresham, R. Mahony, P. Pounds, and J. Roberts, “Towards dynamically-favourable quad-rotor aerial robots”, 2004 Australasian Conf. on Robotics & Automation 1, CDROM (2004).Google Scholar

  • [14] P. Corke, R. Mahony, and P. Pounds, “Modelling and control of a large quadrotor robot”, Control Eng. Pract. 18 (7), 691-699 (2010).Google Scholar

  • [15] P. Corke, R. Mahony, and P. Pounds, “Modelling and control of a large quadrotor robot”, http://eprints.qut.edu.au/33732/1/ cep2009 modelling and control paper sub final.pdf (2012).Google Scholar

  • [16] G. Hoffman, C. Tomlin, and S. Waslander, “Quadrotor helicopter trajectory tracking control”, AIAA Guidance, Navigation and Control Conf. and Exhibit 1, CD-ROM (2008).Google Scholar

  • [17] H. Bouadi, M. Bouchoucha, and M. Tadjine, “Sliding mode control based on backstepping approach for an UAV typequadrotor”, Int. J. App. Math. 4 (1), 12-17 (2007).Google Scholar

  • [18] R. Czyba, “Design of attitude control system for an UAV typequadrotor based on dynamic contraction method”, IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics 1, 644-649 (2009).Google Scholar

  • [19] A. Mokhtari, A. Benallegue, and B. Daachi, “Robust Feedback Linearization and H1 controller for a quadrotor unmanned aerial vechicle”, J. Electr. Eng. 57 (1), 20-27 (2006).Google Scholar

  • [20] R. Zawiski and M. Błachuta, “Dynamics and optimal control of quadrotor platform”, AIAA Guidance, Navigation and Control Conf. and Exhibit 1, CD-ROM (2012).Google Scholar

  • [21] R. Zawiski, “Control-oriented modelling of quadrotor UAV platform”, Ph.D. Dissertation, Institute of Automatics, Faculty of Automatics, Electronics and Computer Science, Silesian University of Technology, Gliwice, 2012.Google Scholar

  • [22] R. Prouty, Helicopter Performance, Stability and Control, Krieger Publishing Company, Malabar, 2002.Google Scholar

  • [23] A. Bramwell, G. Done, and D. Blamford, Bramwell’s Helicopter Dynamics, 2nd ed., Butterworth-Heinemann, Woburn, 2001.Google Scholar

  • [24] S. Baldursson, “BLDC motor modelling and controla MATLAB/SIMULINK implementation”, Master Thesis, Chalmers University of Technology, Gothenburg, http://webfiles. portal.chalmers.se/et/MSc/BaldurssonStefanMSc.pdf (as of 06.2012), 2005.Google Scholar

  • [25] M. Drela, “First-order DC electric motor model”, MIT Aero and Astro, 2007, http://web.mit.edu/drela/Public/web/ qprop/motor1 theory.pdf (2012).Google Scholar

  • [26] B. Szlachetko and M. Lower “Stabilisation and steering of quadrocopters using fuzzy logic regulators”, 11th Int. Conf. on Artificial Intelligence and Soft Computing PT 1, 691-698 (2012).Google Scholar

  • [27] A. Dzieliński and P.M. Czyronis, “Fixed final time and free final state optimal control problem for fractional dynamic systems - linear quadratic discrete-time case”, Bull. Pol. Ac.: Tech. 61 (3), 681-690 (2013).Web of ScienceGoogle Scholar

  • [28] R. Zawiski and M. Błachuta, “Model development and optimal control of quadrotor aerial robot”, IEEE 17th Int. Conf. on Methods and Models in Automation and Robotics 1, 475-480 (2012).Google Scholar

  • [29] R. Zawiski and M. Błachuta, “Chosen aspects of modelling and control of quadrotor platform”, 9th Int. Conf. on Mathematical Problems in Engineering, Aerospace and Sciences 1, 1116-1123 (2012).Google Scholar

  • [30] R. Czyba and G. Szafrański “Control structure impact on the flying performance of the multi-rotor VTOL platform - design, analysis and experimental validation”, Int. J. Adv. Robot. Syst. 10 (62), 1-9 (2013).Web of ScienceCrossrefGoogle Scholar

  • [31] M.G. Ballin, Validation of Real-Time Engineering Simulation of the UH-60 Helicopter, NASA Technical Memorandum 88360, 1987.Google Scholar

  • [32] A. Noth, “Synth`ese et impl´ementation d’un contrˆoleur pour micro h´elicopt`ere `a 4 rotors”, Diploma Project, Swiss Federal Institute of Technology, Lausanne, 2004.Google Scholar

  • [33] G. Padfield, Helicopter Flight Dynamics: the Theory and Application of Flying Qualities and Simulation Modelling, 2nd ed., Blackwell Publishing, Oxford, 2007.Google Scholar

  • [34] M. Cutler, J. How, B. Michini, and N. Ure, “Comparison of fixed and variable pitch actuators for agile quadrotors”, AIAA Guidance, Navigation, and Control Conf. and Exhibit 1, CDROM (2011).Google Scholar

  • [35] G. Szafrański, R. Czyba, W. Janusz, and W. Błotnicki, “Altitude estimation for the UAV’s applications based on sensors fusion algorithm”, Int. Conf. on Unmanned Aircraft Systems 1, 508-515 (2013).Google Scholar

About the article

Published Online: 2014-09-09

Published in Print: 2014-09-01


Citation Information: Bulletin of the Polish Academy of Sciences Technical Sciences, ISSN (Online) 2300-1917, DOI: https://doi.org/10.2478/bpasts-2014-0058.

Export Citation

© Bulletin of the Polish Academy of Sciences. Technical Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Nurul Dayana Salim, Dafizal Derawi, Hairi Zamzuri, Kenzo Nonami, and Mohd Azizi Abdul Rahman
Mathematical Problems in Engineering, 2016, Volume 2016, Page 1

Comments (0)

Please log in or register to comment.
Log in