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

Open access


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.

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

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

[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).

[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).

[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).

[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).

[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).

[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).

[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).

[10] Penn State GRASP Laboratory stories (2012).

[11] ETH Flying Machine Arena DAndrea/FMA (2012).

[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).

[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).

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

[15] P. Corke, R. Mahony, and P. Pounds, “Modelling and control of a large quadrotor robot”, cep2009 modelling and control paper sub final.pdf (2012).

[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).

[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).

[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).

[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).

[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).

[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.

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

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

[24] S. Baldursson, “BLDC motor modelling and controla MATLAB/SIMULINK implementation”, Master Thesis, Chalmers University of Technology, Gothenburg, http://webfiles. (as of 06.2012), 2005.

[25] M. Drela, “First-order DC electric motor model”, MIT Aero and Astro, 2007, qprop/motor1 theory.pdf (2012).

[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).

[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).

[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).

[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).

[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).

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

[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.

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

[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).

[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).

Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

Journal Information

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


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 114 114 14
PDF Downloads 53 53 5