کنترل بهینه مبتنی بر برنامه‌ریزی مسیر حداقل انرژی برای یک کوادروتور

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری، مهندسی مکانیک، دانشگاه شهید بهشتی، تهران، ایران،

2 دانشکده مهندسی مکانیک

3 هیئت علمی/ دانشگاه شهید بهشتی پردیس فنی عباسپور

4 هیات علمی

چکیده

کوادروتورها مصرف انرژی بالایی دارند و حداقل کردن انرژی مصرفی آنها به سبب افزایش زمان و برد پروازی، حائز اهمیت می‌باشد. در این مقاله، به منظور بیشینه کردن زمان عملیاتی کوادروتور، کنترل بهینه مبتنی بر الگوریتم برنامه‌ریزی مسیر حداقل انرژی برای حرکت بین دو موقعیت ارائه می‌شود. برای نیل به این هدف، ابتدا معادلات دینامیکی کوادروتور و موتور استخراج شده، سپس با معرفی انرژی کل مصرفی باتری بعنوان تابع هزینه و استفاده از تئوری کنترل ِ بهینه، مسیر حداقل انرژی تعیین می‌شود. قیود نیز از طریق ضرایب لاگرانژ به معادلات همیلتونین اضافه شد. در انتها نتایج شبیه‌سازی با نتایج پروفیل سرعت ذوزنقه‌ای مرسوم، مقایسه شده که ذخیره انرژی تا چهار درصد را نشان می‌دهد. نتایج نشان می‌دهند که مدت پرواز نسبت به طول مسیر تاثیر بیشتری در مصرف انرژی دارد. به منظور اعتبارسنجی، نتایج شبیه‌سازی با نتایج یک مدل آزمایشگاهی شامل موتور براشلس، سنسور و برد کنترلی مقایسه شده که نشان از نزدیکی نتایج شبیه‌سازی‌ها با مدل واقعی دارد. همچنین با استفاده از نتایج شبیه‌سازی در وضعیت‌های مختلف، یک رابطه کمی بین طول مسیر و مدت پرواز با میزان مصرف انرژی استخراج شده که می‌تواند در تخمین حداکثر برد یا مدت پرواز با توجه به میزان انرژی باتری بسیار سودمند باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Optimal Control Based on Minimum-Energy Trajectory Planning of a Quadrotor

نویسندگان [English]

  • mahmood mazare 1
  • ehsan davoodi 2
  • Mostafa Taghizadeh 3
  • mahdi pourgholi 4
1 School of Mechanical Engineering, ShahidBeheshtiUniversity, Tehran, Iran.
2 school of mechanical engineering
3 shahid beheshti university
4 school of electrical engineering
چکیده [English]

Quadrotors have high energy consumption, hence minimizing their energy consumption plays a crucial role in terms of enhancing their operational range and flight time. In this paper, optimal control based on a minimum-energy trajectory planning algorithm has introduced between two positions to maximize the operation time. To do this, first, dynamic equations of a quadrotor and brushless motor are derived. Energy consumption of quadrotor is introduced as a cost function and the minimum energy path is determined using the optimal control theory. All constraints are combined with the Hamiltonian equation using Lagrange multiplier. Finally, simulation results are compared with results of conventional trapezoidal velocity profile which shows energy saving up to 4%. Also, results reveal that the influence of operation time is far more than path length on energy consumption. In order to verify the validity of the simulation results, they are compared with the results of an experimental model which is consisting of brushless motor, sensor, and control board. As well as using simulation results in different situations, a mathematical equation was extracted among path length, operation time and energy consumption which can be useful to estimate the maximum flight range or operation time considering the amount of energy of the battery.

کلیدواژه‌ها [English]

  • Quadrotor
  • minimum energy trajectory
  • Optimal control
  • Hamiltonian equations
[1]  L. Derafa, A. Benallegue, L. Fridman, Super twisting control algorithm for the attitude tracking of a four rotors UAV. Journal of the Franklin Institute, 349(2) (2012) 685-699.
[2]  H. Kim, B.K. Kim, Online Minimum-Energy Trajectory Planning and Control on a Straight-Line Path for Three-Wheeled Omnidirectional Mobile Robots. IEEE Trans. Industrial Electronics, 61(9) (2014) 4771-4779.
[3]  Y. Bestaoui, An optimal velocity generation of a rear wheel drive tricycle along a specified path, in: American Control Conference, 2000. Proceedings of the 2000, IEEE, )2000(, pp. 2907-2911.
[4]  J. Kim, H. Yeom, F.C. Park, Y.I. Park, M. Kim, On the energy efficiency of CVT-based mobile robots, in:  Robotics and Automation, 2000. Proceedings. ICRA’00. IEEE International Conference on, IEEE, (2000), pp. 1539-1544.
[5]  E.S. Sergaki, G.S. Stavrakakis, A.D. Pouliezos, Optimal robot speed trajectory by minimization of the actuator motor electromechanical losses. Journal of Intelligent and Robotic Systems, 33(2) (2002) 187.702
[6]  M. Haddad, W. Khalil, H. Lehtihet, Trajectory planning of unicycle mobile robots with a trapezoidalvelocity constraint. IEEE Transactions on Robotics, .269-459 )0102( )5(62
[7]  C.H. Kim, B.K.J.J.o.I. Kim, Minimum-energy translational trajectory generation for differentialdriven wheeled mobile robots. Journal of Intelligent and Robotic Systems, 49(4) (2007) 367-383.
[8]  Y .Mei, Y.-H. Lu, Y.C. Hu, C.G. Lee, Deployment strategy for mobile robots with energy and timing constraints, in:  Robotics and Automation, 2005. ICRA 2005. Proceedings of the 2005 IEEE International Conference on, IEEE, (2005), pp. 2816-2821.
[9]  G. Doukas ,K.J.I.T.o.I.E. Thramboulidis, A real-timelinux-based framework for model-driven engineering in control and automation. IEEE Transactions on Industrial Electronics, 58(3) (2011) 914-924.
[10] C. Leng, Q. Cao, Y.J.I.J.o.A.R.S. Huang, A motion planning method for omnidirectional mobile robot based on the anisotropic characteristics. International Journal of Advanced Robotic Systems, 5(4) (2008) 45.
[11] C.-C. Tsai, H.-C. Huang, C.-K.J.I.T.o.I.E. Chan, Parallel elite genetic algorithm and its application to global path planning for autonomous robot navigation. IEEE Transactions on Industrial Electronics, 58(10) (2011) 4813-4821.
[12] J. Wu, R.L .Williams, J.J.J.o.d.s. Lew, measurement,, control, Velocity and acceleration cones for kinematic and dynamic constraints on omni-directional mobile robots. Journal of dynamic systems, measurement, and control, 128(4) (2006) 788-799.
[13] S.X. Yang, A. Zhu, G. Yuan, M.Q.-H.J.I.T.o.I.E. Meng, A bioinspired neurodynamics-based approach to tracking control of mobile robots. IEEE Transactions on Industrial Electronics, 59(8) (2012) 3211-3220.
[14] M.G. Earl, R. D’andrea, Iterative MILP methods for vehicle-control problems. IEEE Transactions on Robotics, 21(6) (2005) 1158-1167.
[15] Y. Mei, Y.-H. Lu, Y.C. Hu, C.G. Lee, Energy-efficient motion planning for mobile robots, in:  Robotics and Automation, 2004. Proceedings. ICRA’04. 2004 IEEE International Conference on, IEEE, 2004, pp. 4344.4349.
[16]  A. Tayebi, S. McGilvray, Attitude stabilization of a VTOL quadrotor aircraft. IEEE Transactions on control systems technology, 14(3) (2006) 562-571.
[17]  Y. Morel, A. Leonessa, Direct adaptive tracking control of quadrotor aerial vehicles, in:  ASME 2006 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, (2006), pp. 155-.161
[18]           G. Hoffmann, D.G. Rajnarayan, S.L. Waslander,
D. Dostal, J.S. Jang, C.J. Tomlin, The Stanford testbed of autonomous rotorcraft for multi agent control (STARMAC), in: Digital Avionics Systems Conference, 2004. DASC 04. The 23rd, IEEE, (2004), pp .12 .E. 14-121.
[19] A.Ö. Kivrak, Design of control systems for a quadrotor flight vehicle equipped with inertial sensors, Master’s Thesis, Atilim University, 2006.
[20] A.A. Mian, W. Daobo, Modeling and backstepping- based nonlinear control strategy for a 6 DOF quadrotor
helicopter. Chinese Journal of Aeronautics, 21(3) (2008) 261-268.
[21] A. Soumelidis, P. Gáspár, G. Regula, B. Lantos, Control of an experimental mini quad-rotor UAV, in: Control and Automation, 2008 16th Mediterranean Conference on, IEEE, (2008), pp. 1252-1257.
[22] A. Benallegue, A. Mokhtari, L. Fridman, Feedback linearization and high order sliding mode observer for a quadrotor UAV, in: Variable Structure Systems, 2006. VSS’06. International Workshop on, IEEE,
(2006), pp. 365-372.
[23] E. Davoodi, M. Mazare, P. Safarpour, Dynamic modeling and control of a quadrotor using nonlinear approaches based on MEMS sensors’ experimental data. Modares Mechanical Engineering, 16(10) (2017) 31-41 (in presian).
[24] L. Luque-Vega, B. Castillo-Toledo, A. G. Loukianov, Robust block second order sliding mode control for  a quadrotor. Journal of the Franklin Institute, 349(2) (2012) 719-739.
[25]  V. Nekoukar, A. Erfanian, Systems, Adaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systems. Fuzzy Sets and Systems, 179(1) (2011) 34-49.
[26]   L. Wu, C. Wang, Q. Zeng, Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems. Journal of the Franklin Institute, 345(3) (2008) 233-253.
[27]   T. Dierks, S. Jagannathan, Output feedback control of a quadrotor UAV using neural networks. IEEE transactions on neural networks, 21(1) (2010) 50-66.
[28]  N. Guenard, T. Hamel ,R.J.I.T.o.R. Mahony, A practical visual servo control for an unmanned aerial vehicle. IEEE Transactions on Robotics, 24(2) (2008) 331-340.
[29]  F. Kendoul, I. Fantoni, K.J.R. Nonami, A. Systems, Optic flow-based vision system for autonomous 3D localization and control of small aerial vehicles. Robotics and Autonomous Systems, 57(6-7) (2009) 591-602.
[30]   K.M. Zemalache, H.J.A.S.C. Maaref, Controlling a drone: Comparison between a based model method and a fuzzy inference system. Applied Soft Computing, 9(2) (2009) 553-562.
[31]  T. Bresciani, Modelling, identification and control of a quadrotor helicopter. Master’s Thesis, 2008.
[32]    C.H. Kim, B.K. Kim, Minimum-energy motion planning for differential-driven wheeled mobile robots, in: Motion Planning. Motion Planning, InTech, 2008.