Abstract
In order to track the time-varying trajectory efficiently and accurately, a multilayer neural dynamic controller is proposed and exploited for quadrotor unmanned aerial vehicles (UAVs). Previous UAV controllers based on neural dynamic methods used forces and torques as control variables. However, in fact, the real control variables of a UAV are the PWM waves for controlling motors. What is more, the motors are always modeled as one-order systems since the existence of inertia and friction, which means that using forces and torques as control variables is not proper and may lead to low precision and inefficient tracking for UAVs. To solve this problem, a new UAV controller which uses exactly what inputs to motors as control variables is designed, so that the designed controller is more practical for UAVs. In the design process, a multilayer neural dynamic controller is obtained by applying the neural dynamic method to position layer, velocity, torque layer and motor layer successively. Both theoretical analysis and computer simulation results verify the effectiveness, convergence, stability and accuracy of the proposed multilayer neural dynamic controller for tracking time-varying trajectories.
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References
Yao, P., Xie, Z., Ren, P.: Optimal UAV route planning for coverage search of stationary target in river. IEEE Trans. Control Syst. Technol. 2(7), 822–829 (2019)
Shang, B., Liu, J., Zhang, Y., Wu, C., Chen, Y.: Fractional-order flight control of quadrotor UAS on vision-based precision hovering with larger sampling period. Nonlinear Dyn. 9(7), 1735–1746 (2019)
Cristofalo, E., Montijano, E., Schwager, M.: Vision-based control for fast 3-D reconstruction with an aerial robot. IEEE Trans. Control Syst. Technol. 2(8), 1–14 (2019)
Sandino, J., Pegg, G., Gonzalez, F., Smith, G.: Aerial mapping of forests affected by pathogens using UAVs, hyperspectral sensors, and artificial intelligence. Sensors 18, 944 (2018)
Rossi, G., Tanteri, L., Tofani, V., Vannocci, P., Moretti, S., Casagli, N.: Multitemporal UAV surveys for landslide mapping and characterization. Landslides 1(5), 1045–1052 (2018)
Motlagh, N.H., Bagaa, M., Taleb, T.: UAV-based IOT platform: A crowd surveillance use case. IEEE Commun. Mag. 5(5), 128–134 (2017)
Vanegas, F., Bratanov, D., Powell, K., Weiss, J., Gonzalez, F.: A novel methodology for improving plant pest surveillance in vineyards and crops using UAV-based hyperspectral and spatial data. Sensors 18, 260 (2018)
Xu, Q., Wang, Z., Zhen, Z.: Adaptive neural network finite time control for quadrotor UAV with unknown input saturation. Nonlinear Dyn. 9(8), 1973–1998 (2019)
Sanchez, A., Carrillo, L.R.G., Rondon, E., Lozano, R., Garcia, O.: Hovering flight improvement of a quad-rotor mini UAV using brushless DC motors. J. Intell. Robot. Syst. 6(1), 85–101 (2011)
Mohamed, M.K., Lanzon, A.: Design and control of novel tri-rotor UAV. Proceedings of 2012 UKACC International Conference on Control, Cardiff, pp 304–309 (2012)
Gao, F., Lin, Y., Shen, S.: Gradient-based online safe trajectory generation for quadrotor flight in complex environments. 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, BC, pp. 3681-3688 (2017)
Nandakumar, G., Saphal, R., Joishy, A., Thondiyath, A.: Performance analysis of vertically offset overlapped propulsion system based quadrotor in an aerial mapping mission. Int. J. Micro Air Veh. 1, 370–385 (2018)
Wang, H., Liu, Y.: A low-cost autonomous navigation system for a quadrotor in complex outdoor environments. Int. J. Adv. Rob. Syst. 1, 7 (2020). https://doi.org/10.1177/1729881420905150
Nex, F., Remondino, F.: UAV for 3D mapping applications: a review. Appl. Geom. 6(1), 1–15 (2014)
Dong, X., Yu, B., Shi, Z., Zhong, Y.: Time-varying formation control for unmanned aerial vehicles: theories and applications. IEEE Trans. Control Syst. Technol. 23(1), 340–348 (2015)
Ismail, Z.H., Sabri, A.Q.M.: PD control scheme with region formulation for slow time-varying tracking control of an unmanned aerial vehicle. 2014 International Conference on Information Science & Applications (ICISA), Seoul, (2014), pp 1–5, https://doi.org/10.1109/ICISA.2014.6847443.
Gomez-Balderas, J., Flores, G., Garcia Carrillo, L.R., Lozano, R.: Tracking a ground moving target with a quadrotor using switching control. J. Intell. Robot. Syst. 7, 65–78 (2013)
Esrafilian, O., Taghirad, H.D.: Autonomous flight and obstacle avoidance of a quadrotor by monocular SLAM. 2016 4th International Conference on Robotics and Mechatronics (ICROM), pp. 240-245 (2016)
Koszewnik, A.: The parrot UAV controlled by PID controllers. Acta Mech. Autom. 8(2), 65–69 (2014)
Reyes-Valeria, E., Enriquez-Caldera, R., Camacho-Lara, S., Guichard, J.: LQR control for a quadrotor using unit quaternions: modeling and simulation. CONIELECOMP 2013, 23rd International Conference on Electronics, Communications and Computing, pp. 172–178 (2013)
Herrera, M., Chamorro, W., Gmez, A., Camacho, O.: Sliding mode control: an approach to control a quadrotor. 2015 Asia-Pacific Conference on Computer Aided System Engineering, Quito, pp. 314–319 (2015)
Runcharoon, K., Srichatrapimuk, V.: Sliding mode control of quadrotor. Taeece 552–557 (2013)
Bouadi, H., Bouchoucha, M., Tadjine, M.: Sliding mode control based on backstepping approach for an UAV type-quadrotor. Int. J. Appl. Math. Comput. Sci. 4, 12–17 (2007)
Bouabdallah, S., Siegwart, R.: Backstepping and sliding mode techniques applied to an indoor micro quadrotor. Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pp. 2247–2252 (2005). https://doi.org/10.1109/ROBOT.2005.1570447
Madani, T., Benallegue, A.: Backstepping control for a quadrotor helicopter. 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3255–3260 (2006). https://doi.org/10.1109/IROS.2006.282433.
Mian, A., Daobo, W.: Modeling and backstepping-based nonlinear control strategy for a 6 DOF quadrotor helicopter. Chin. J. Aeronaut. 2(1), 261–268 (2008)
Liu, C., Pan, J., Chang, Y.: PID and LQR trajectory tracking control for an unmanned quadrotor helicopter: experimental studies. 2016 35th Chinese Control Conference (CCC), pp. 10845–10850 (2016)
KÖKSAL, N., Hao, A., Fidan, B.: Two-level nonlinear tracking control of a quadrotor unmanned aerial vehicle. IfAC Papersonline 49, 254–259 (2016)
Li, C., Zhang, Y., Li, P.: Full control of a quadrotor using parameter-scheduled backstepping method: implementation and experimental tests. Nonlinear Dyn. 8(9), 1259–1278 (2017)
Swaroop, D., Hedrick, J.K., Yip, P.P., Gerdes, J.C.: Dynamic surface control for a class of nonlinear systems. IEEE Trans. Autom. Control 45(10), 1893–1899 (2000)
Xia, Y.: A new neural network for solving linear and quadratic programming problems. IEEE Trans. Neural Netw. 7(6), 1544–8 (1996)
Xia, Y., Wang, J.: A general methodology for designing globally convergent optimization neural networks. IEEE Trans. Neural Netw. 9(6), 1331–1343 (1998)
Xia, Y., Wang, J.: A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints. IEEE Trans. Circuits Syst. Part I Fund. Theory Appl. 51(7), 1385–1394 (2004)
Xia, Y., Feng, G., Kamel, M.: Development and analysis of a neural dynamical approach to nonlinear programming problems. IEEE Trans. Autom. Control 52(11), 2154–2159 (2007)
Liu, Q., Wang, J.: l1-minimization algorithms for sparse signal reconstruction based on a projection neural network. IEEE Trans. Neural Netw. Learn. Syst. 27(3), 1–10 (2015)
Zhang, Y., Yang, M., Huang, H., Hu, H.: New discrete solution model for solving future different-level linear inequality and equality with robot manipulator control. IEEE Trans. Industr. Inf. 1(5), 1975–1984 (2018)
Zhang, Y., Li, J., Li, S., Chen, D., He, L.: Optimal zeroing dynamics with applications to control of serial and parallel manipulators. Optim. Control Appl. Methods 3, 9 (2018)
Zhang, Y., Guo, J., Zhang, D., Qiu, B., Yang, Z.: Output tracking of time-varying linear system using ZD controller with pseudo division-by-zero phenomenon illustrated. In: ECON 2017—43rd Annual Conference of the IEEE Industrial Electronics Society, pp. 3075–3080 (2017)
Hu, C., Guo, D., Kang, X., Zhang, Y.: Zhang dynamics tracking control of varactor system with stability analysis. 2017 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD), pp. 166–171 (2017)
Stebler, S., Campobasso, M., Kidambi, K., Mackunis, W., Reyhanoglu, M.: Dynamic neural network-based sliding mode estimation of quadrotor systems. American Control Conference, pp. 2600–2605 (2017)
Zhang, Z., Yu, J., Li, Y., Zhang, X.: A new neural-dynamic control method of position and angular stabilization for autonomous quadrotor UAVs. IEEE International Conference on Fuzzy Systems, pp. 850–855 (2016)
Das, A., Lewis, F., Subbarao, K.: Neural network based robust backstepping control approach for quadrotors. Aiaa J. 1–17 (2013)
Zhang, Z., Zheng, L., Qi, G.: A varying-parameter convergent neural dynamic controller of multi-rotor UAVs for tracking time-varying tasks. IEEE Trans. Veh. Technol. 67(6), 4793–4805 (2018)
Zheng, L., Zhang, Z.: Convergence and robustness analysis of novel adaptive multilayer neural dynamics-based controllers of multirotor UAVs. IEEE Trans. Cybern. 1–14 (2019). https://doi.org/10.1109/TCYB.2019.2923642
Zhang, Z., Zhou, B., Zheng, L., Zhang, Z., Song, C., Pei, H.: A varying-parameter adaptive multi-layer neural dynamic method for designing controllers and application to unmanned aerial vehicles. IEEE Trans. Intell. Transp. Syst. 1–13 (2020). https://doi.org/10.1109/TITS.2020.2983522
Glida, H., Abdou, L., Chelihi, A., Sentouh, C., Hasseni, S.E.I.: Optimal model-free backstepping control for a quadrotor helicopter. Nonlinear Dyn. 100, 3449–3468 (2020)
Zhu, W., Du, H., Cheng, Y., Chu, Z.: Hovering control for quadrotor aircraft based on finite-time control algorithm. Nonlinear Dyn. 8(8), 2359–2369 (2017)
Dolatabadi, S.H., Yazdanpanah, M.J.: MIMO sliding mode and backstepping control for a quadrotor UAV. Electr. Eng. 994–999 (2015). https://doi.org/10.1109/IranianCEE.2015.7146356
Guo, D., Zhang, Y.: Novel recurrent neural network for time-varying problems solving. IEEE Comput. Intell. Mag. 7(4), 61–65 (2012)
Zhang, Y., Guo, X., Ma, W., Chen, K., and Cai, B.: MATLAB simulink modeling and simulation of Zhang neural network for online time-varying matrix inversion. IEEE International Conference on Networking, Sensing and Control, pp. 1480–1485 (2008)
Hopfield, J.: Neural networks and physical systems with emergent collective computational abilities. PNAS, USA 7, 9 (1982)
Hopfield, J., Tank, D.: Neural computation of decisions in optimization problems. Biol. Cybern. 5(2), 141–152 (1985)
Xia, Y.: A new neural network for solving linear and quadratic programming problems. IEEE Trans. Neural Netw. 7(6), 1544–1548 (1996)
Xia, Y., Wang, J.: A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints. IEEE Trans. Circuits Syst. 51(7), 1385–1394 (2004)
Koteich, M., Moing, T.L., Janot, A., Defay, F.: A real-time observer for UAVs brushless motors. Electronics, control, measurement, signals and their application to mechatronics, pp. 1–5 (2013)
Sanchez, A., Carrillo, L.R.G., Rondon, E., Lozano, R., Garcia, O.: Hovering flight improvement of a quad-rotor mini UAV using brushless dc motors. J. Intell. Robot. Syst. 61(1–4), 85–101 (2011)
Fornasini, E., Lepschy, A.: A controllability criterion for continuous linear time-invariant systems. IEEE Trans. Autom. Control 20(5), 716–716 (1975)
Julkananusart, A., Nilkhamhang, I.: Quadrotor tuning for attitude control based on double-loop PID controller using fictitious reference iterative tuning (FRIT). IECON 2015—41st Annual Conference of the IEEE Industrial Electronics Society, pp. 4865–4870 (2015)
Li, J., Zhang, Y., Li, S., Mao, M.: New discretization-formula-based zeroing dynamics for real-time tracking control of serial and parallel manipulators. IEEE Trans. Ind. Inf. 14, 3416–3425 (2018)
Acknowledgements
The paper was submitted for review in May 19, 2020. This work was supported in part by the National Natural Science Foundation under Grants 61976096, 61603142 and 61633010, Guangdong Basic and Applied Basic Research Foundation under Grant 2020B1515120047, the Guangdong Foundation for Distinguished Young Scholars under Grant 2017A030306009, the Guangdong Special Support Program under Grant 2017TQ04X475, the Fundamental Research Funds for Central Universities under Grant x2zdD2182410, the Scientific Research Starting Foundation of South China University of Technology, the National Key Research and Development Program of China under Grant 2017YFB1002505, the National Key Basic Research Program of China (973 Program) under Grant 2015CB351703, Guangdong Key Research and Development Program under Grant 2018B030339001, Guangdong Natural Science Foundation Research Team Program 1414060000024.
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Zhang, Z., Chen, T. & Zheng, L. A multilayer neural dynamic controller design method of quadrotor UAV for completing time-varying tasks. Nonlinear Dyn 104, 3597–3616 (2021). https://doi.org/10.1007/s11071-021-06445-9
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DOI: https://doi.org/10.1007/s11071-021-06445-9