# American Institute of Mathematical Sciences

May  2022, 18(3): 2221-2235. doi: 10.3934/jimo.2021063

## Design of path planning and tracking control of quadrotor

 School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

* Corresponding author: Rui Li (lirui@uestc.edu.cn)

Received  December 2020 Revised  January 2021 Published  May 2022 Early access  March 2021

Fund Project: This work is supported in part by the National Natural Science Foundation of China under grant (No. 61973055), the Fundamental Research Funds for the Central Universities (No. ZYGX2019J062) and a grant from the applied basic research programs of Sichuan province (No. 2019YJ0206)

In this paper, we first design a motion planning system based on the Batch Informed Trees (BIT*) algorithm for quadrotor and a linear model predictive control (LMPC) is applied to solve the path tracking problem for a quadrotor. BIT* algorithm is used to plan a barrier-free trajectory quickly in an obstructed environment. Then we apply linear model predictive control for the full state quadrotor system model to track the generated trajectory. Finally, the BIT* algorithm simulation case is presented using RVIZ visual interface and some simulation cases are presented using MATLAB / Simulink. The results demonstrate the capability and the effectiveness of the control strategy in fast path tracking and the quadrotor stability, while the desired performance is achieved.

Citation: Yi Gao, Rui Li, Yingjing Shi, Li Xiao. Design of path planning and tracking control of quadrotor. Journal of Industrial and Management Optimization, 2022, 18 (3) : 2221-2235. doi: 10.3934/jimo.2021063
##### References:
 [1] Y. Bai, H. Liu, Z. Shi and Y. Zhong, Robust control of quadrotor unmanned air vehicles, in Proceedings of the 31st Chinese Control Conference, Hefei, (2012), 4462–4467. [2] J. Carsten, D. Ferguson and A. Stentz, 3Dfield d: Improved path planning and replanning in three dimensions, in 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, (2006), 3381–3386. [3] Y.-B. Chen, G.-C. Luo, Y.-S. Mei, J.-Q. Yu and X.-L. Su, UAV path planning using artificial potential field method updated by optimal control theory, Internat. J. Systems Sci., 47 (2016), 1407-1420.  doi: 10.1080/00207721.2014.929191. [4] F. Chen, J.-Q. Yu, X.-L. Su and G.-C. Luo, Path planning for multi-UAV formation, Journal of Intelligent and Robotic Systems, 77 (2015), 229-246.  doi: 10.1007/s10846-014-0077-y. [5] N. R. Council, Autonomous Vehicles in Support of Naval Operations, The National Academies Press, Washington, DC, 2005, https://www.nap.edu/catalog/11379/autonomous-vehicles-in-support-of-naval-operations. [6] L. de Filippis, G. Guglieri and F. Quagliotti, Path planning strategies for UAVs in 3D environments, Journal of Intelligent & Robotic Systems, 65 (2012), 247-264. [7] T. Dierks and S. Jagannathan, Output feedback control of a quadrotor UAV using neural networks, IEEE Transactions on Neural Networks, 21 (2010), 50-66. [8] E. W. Dijkstra, A note on two problems in connexion with graphs, Numer. Math., 1 (1959), 269-271.  doi: 10.1007/BF01386390. [9] J. D. Gammell, S. S. Srinivasa and T. D. Barfoot, Batch informed trees (BIT*): Sampling-based optimal planning via the heuristically guided search of implicit random geometric graphs, 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA, (2015), 3067–3074. doi: 10.1109/ICRA.2015.7139620. [10] S. R. Herwitz, L. F. Johnson, S. E. Dunagan, R. G. Higgins, D. V. Sullivan, J. Zheng, B. M. Lobitz, J. G. Leung, B. A. Gallmeyer, M. Aoyagi, R. E. Slye and J. A. Brass, Imaging from an unmanned aerial vehicle: Agricultural surveillance and decision support, Computers and Electronics in Agriculture, 44 (2004), 49-61. [11] Y. Kwangjin and S. Sukkarieh, Real-time continuous curvature path planning of UAVs in cluttered environments, in 2008 5th International Symposium on Mechatronics and its Applications, IEEE, (2008), 1–6. [12] X. Q. Li, L. Qiu, S. Aziz, J. F. Pan, J. P. Yuan and B. Zhang, Control method of UAV based on RRT* for target tracking in cluttered environment, in 2017 7th International Conference on Power Electronics Systems and Applications - Smart Mobility, Power Transfer & Security (PESA), (2017), 1–4. [13] R. Li, Y. Shi and K.-L. Teo, Coordination arrival control for multi-agent systems, Internat. J. Robust Nonlinear Control, 26 (2016), 1456-1474.  doi: 10.1002/rnc.3359. [14] Z. Ma, T. Hu, L. Shen, W. Kong, B. Zhao and K. Yao, An iterative learning controller for quadrotor UAV path following at a constant altitude, in 2015 34th Chinese Control Conference (CCC), Hangzhou, China, (2015), 4406–4411. [15] M. Nguyen Duc, T. N. Trong and Y. S. Xuan, The quadrotor MAV system using PID control, in 2015 IEEE International Conference on Mechatronics and Automation (ICMA), Beijing, (2015), 506–510. [16] R. Sharma, M. Kothari, C. N. Taylor and I. Postlethwaite, Cooperative target-capturing with inaccurate target information, in Proceedings of the 2010 American Control Conference, Baltimore, MD, (2010), 5520–5525. [17] Z. Shulong, A. Honglei, Z. Daibing and S. Lincheng, A new feedback linearization LQR control for attitude of quadrotor, in 2014 13th International Conference on Control Automation Robotics Vision (ICARCV), Singapore, (2014), 1593–1597. [18] M. Sumaila, Techniques for quadcopter modelling & design: A review, Journal of Unmanned System Technology. [19] J. Xiong and G. Zhang, Sliding mode control for a quadrotor UAV with parameter uncertainties, in 2016 2nd International Conference on Control, Automation and Robotics (ICCAR), Hong Kong, (2016), 207–212. [20] F. Yan, Y.-S. Liu and J.-Z. Xiao, Path planning in complex 3D environments using a probabilistic roadmap method, International Journal of Automation and Computing, 10 (2013), 525-533.  doi: 10.1007/s11633-013-0750-9. [21] B. Zhao, B. Xian, Y. Zhang and X. Zhang, Nonlinear robust adaptive tracking control of a quadrotor UAV via immersion and invariance methodology, IEEE Transactions on Industrial Electronics, 62 (2015), 2891-2902.

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##### References:
 [1] Y. Bai, H. Liu, Z. Shi and Y. Zhong, Robust control of quadrotor unmanned air vehicles, in Proceedings of the 31st Chinese Control Conference, Hefei, (2012), 4462–4467. [2] J. Carsten, D. Ferguson and A. Stentz, 3Dfield d: Improved path planning and replanning in three dimensions, in 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, (2006), 3381–3386. [3] Y.-B. Chen, G.-C. Luo, Y.-S. Mei, J.-Q. Yu and X.-L. Su, UAV path planning using artificial potential field method updated by optimal control theory, Internat. J. Systems Sci., 47 (2016), 1407-1420.  doi: 10.1080/00207721.2014.929191. [4] F. Chen, J.-Q. Yu, X.-L. Su and G.-C. Luo, Path planning for multi-UAV formation, Journal of Intelligent and Robotic Systems, 77 (2015), 229-246.  doi: 10.1007/s10846-014-0077-y. [5] N. R. Council, Autonomous Vehicles in Support of Naval Operations, The National Academies Press, Washington, DC, 2005, https://www.nap.edu/catalog/11379/autonomous-vehicles-in-support-of-naval-operations. [6] L. de Filippis, G. Guglieri and F. Quagliotti, Path planning strategies for UAVs in 3D environments, Journal of Intelligent & Robotic Systems, 65 (2012), 247-264. [7] T. Dierks and S. Jagannathan, Output feedback control of a quadrotor UAV using neural networks, IEEE Transactions on Neural Networks, 21 (2010), 50-66. [8] E. W. Dijkstra, A note on two problems in connexion with graphs, Numer. Math., 1 (1959), 269-271.  doi: 10.1007/BF01386390. [9] J. D. Gammell, S. S. Srinivasa and T. D. Barfoot, Batch informed trees (BIT*): Sampling-based optimal planning via the heuristically guided search of implicit random geometric graphs, 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA, (2015), 3067–3074. doi: 10.1109/ICRA.2015.7139620. [10] S. R. Herwitz, L. F. Johnson, S. E. Dunagan, R. G. Higgins, D. V. Sullivan, J. Zheng, B. M. Lobitz, J. G. Leung, B. A. Gallmeyer, M. Aoyagi, R. E. Slye and J. A. Brass, Imaging from an unmanned aerial vehicle: Agricultural surveillance and decision support, Computers and Electronics in Agriculture, 44 (2004), 49-61. [11] Y. Kwangjin and S. Sukkarieh, Real-time continuous curvature path planning of UAVs in cluttered environments, in 2008 5th International Symposium on Mechatronics and its Applications, IEEE, (2008), 1–6. [12] X. Q. Li, L. Qiu, S. Aziz, J. F. Pan, J. P. Yuan and B. Zhang, Control method of UAV based on RRT* for target tracking in cluttered environment, in 2017 7th International Conference on Power Electronics Systems and Applications - Smart Mobility, Power Transfer & Security (PESA), (2017), 1–4. [13] R. Li, Y. Shi and K.-L. Teo, Coordination arrival control for multi-agent systems, Internat. J. Robust Nonlinear Control, 26 (2016), 1456-1474.  doi: 10.1002/rnc.3359. [14] Z. Ma, T. Hu, L. Shen, W. Kong, B. Zhao and K. Yao, An iterative learning controller for quadrotor UAV path following at a constant altitude, in 2015 34th Chinese Control Conference (CCC), Hangzhou, China, (2015), 4406–4411. [15] M. Nguyen Duc, T. N. Trong and Y. S. Xuan, The quadrotor MAV system using PID control, in 2015 IEEE International Conference on Mechatronics and Automation (ICMA), Beijing, (2015), 506–510. [16] R. Sharma, M. Kothari, C. N. Taylor and I. Postlethwaite, Cooperative target-capturing with inaccurate target information, in Proceedings of the 2010 American Control Conference, Baltimore, MD, (2010), 5520–5525. [17] Z. Shulong, A. Honglei, Z. Daibing and S. Lincheng, A new feedback linearization LQR control for attitude of quadrotor, in 2014 13th International Conference on Control Automation Robotics Vision (ICARCV), Singapore, (2014), 1593–1597. [18] M. Sumaila, Techniques for quadcopter modelling & design: A review, Journal of Unmanned System Technology. [19] J. Xiong and G. Zhang, Sliding mode control for a quadrotor UAV with parameter uncertainties, in 2016 2nd International Conference on Control, Automation and Robotics (ICCAR), Hong Kong, (2016), 207–212. [20] F. Yan, Y.-S. Liu and J.-Z. Xiao, Path planning in complex 3D environments using a probabilistic roadmap method, International Journal of Automation and Computing, 10 (2013), 525-533.  doi: 10.1007/s11633-013-0750-9. [21] B. Zhao, B. Xian, Y. Zhang and X. Zhang, Nonlinear robust adaptive tracking control of a quadrotor UAV via immersion and invariance methodology, IEEE Transactions on Industrial Electronics, 62 (2015), 2891-2902.
The system structure diagram
The earth-fixed inertial and body-fixed frames of a quadcopter
Path planning module test result
Reference trajectory
Path tracking of $x(t)$
Path tracking of $y(t)$