Position Control Using Trajectory Tracking and State Estimation of a Quad-rotor

Abstract

Quad-rotor aircrafts are unmanned aerial vehicles that have gained significant popularity in recent years and have been developed for use in many areas. Such vehicles are capable of vertical take-off and landing and are used in various applications. To operate a quad-rotor aircraft efficiently and safely, fundamental issues such as mathematical modeling, control, and state estimation need to be studied. Mathematical modeling involves creating a holistic model of the various subsystems of the aircraft including aerody-namic, kinematic, dynamic and control systems. The control system is a mechanism used for the aircraft to perform the desired movements. State estimation techniques are used to obtain and predict information about the state of the aircraft. This study includes position control using a trajectory generation algorithm. Attitude estimation of the quad-rotor is improved with the Explicit Complementary Filter (ECF) and the state estimations is improved with the Extended Kalman Filter (EKF). Different from other studies, the results are obtained by feeding the model with a state estimation filter. The performances of the filters used for state estimation are compared.

Keywords

• Position Control
• Trajectory Tracking
• State Estimation

References

1. Baldi, T.L., Farina, F., Garulli, A., Giannitrapani, A., and Prattichizzo, D. (2019). Upper Body Pose Estimation Using Wearable Inertial Sensors and Multiplicative Kalman Filter. IEEE Sens. J., 20, 492–500. DOI: https://doi.org/10.1109/JSEN.2019.2940612
2. Beck, H. Lesueur, J., Charland-Arcand, G., Akhrif, O., Gagne, S., Gagnon F., and Couillard, D. (2016). Autonomous takeoff and landing of a quadcopter. International Conference on Unmanned Aircraft Systems (lCUAS), 475-484. DOI: https://doi.org/10.1109/ICUAS.2016.7502614
3. Benic, Z, Piljek, P., and Kotarski, D. (2016). Mathematical modelling of unmanned aerial vehicle with four rotors. Interdisciplinary Description of Complex Systems, 14(1), 88-100. DOI: http://dx.doi.org/10.7906/indecs.14.1.9
4. Bouktir, Y. Haddad, M., and Chettibi, T.(2008).Trajectory planning for a quad-rotor helicopter. 16th Mediterranean Conference on Control and Automation, 1258–1263. DOI: https://doi.org/10.1109/MED.2008.4602025
5. Buskey, G., Roberts, J., Corke, P., Ridley, P., and Wyeth, G. (2004) Sensing and control for a small-size helicopter. Experimental Robotics VIII: Springer Tracts in Advanced Robotics, 5. DOI: https://doi.org/10.1007/3-540-36268-1_43
6. Castillo, C. L., Moreno, W., and Valavanis, K. P., (2007). Unmanned helicopter waypoint trajectory tracking using model predictive control. Mediterranean Conference on Control and Automation. DOI: https://doi.org/10.1109/MED.2007.4433726
7. Chamseddine, A., Li, T., Zhang, Y., Rabbath, C.-A. and Theilliol, D. (2012). Flatness-based trajectory planning for a quad-rotor unmanned aerial vehicle test-bed considering actuator and system constraints. American Control Conference (ACC), 920–925. DOI: https://doi.org/10.1109/ACC.2012.6315362
8. Crasidis, J. L., Junkis, J. L. (2011) Optimal Estimation of Dynamic Systems Second Edition –CRC. De Marina, H. G., Pereda, F. J., Giron-Sierra, J. M. and Espinosa, F. (2012). UAV attitude estimation using unscented Kalman filter and triad. IEEE Transactions on Industrial Electronics, 59(11), 4465-4474. DOI: https://doi.org/10.1109/TIE.2011.2163913

9. Euston, M., Coote, P., Mahony, R., Kim J., and Hamel, T. (2008). A complementary filter for attitude estimation of a fixed-wing UAV. 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, Nice, France, 340-345. DOI: https://doi.org/10.1109/IROS.2008.4650766
10. Hall, J. K., Knoebel, N. B., and McLain, T. W. (2008). Quaternion attitude estimation for miniature air vehicles using a multiplicative extended Kalman filter. IEEE Position, Location and Navigation Symposium,1230- 1237. DOI: https://doi.org/10.1109/PLANS.2008.4570043
11. Hetenyi, D., Gatzy, M. and Blazovics, L. (2016). Sensor fusion with enhanced Kalman Filter for altitude control of quad-rotors. IEEE 11th International Symposium on Applied Computational intelligence and Informatics (SACI), 413-418. DOI: https://doi.org/10.1109/SACI.2016.7507412
12. Hoffmann, G., Waslander, S., and Tomlin, C. (2008). Quad-rotor helicopter trajectory tracking control. AIAA Guidance, Navigation and Control Conference and Exhibit, 1–14. DOI: https://doi.org/10.2514/6.2008-7410
13. Markley, F.L., Crassidis, J.L. (2014). Fundamentals of Spacecraft Attitude Determination and Control. Space Technology Library, 33. Springer, New York, NY. DOI: https://doi.org/10.1007/978-1-4939-0802-8 Mahony, R., Hamel T., and Ptlimlin, J.-M. (2008). Nonlinear complementary filters on the special orthogonal group. IEEE Trans. on Automatic Control, 53(5), 1203-1218. DOI: https://doi.org/10.1109/TAC.2008.923738
14. Pines D. J., Bohorquez F. (2012). Challenges Facing Future Micro-Air-Vehicle Development, Journal of Aircraft, 43(2):290-305. DOI: https://doi.org/10.2514/1.4922
15. Sebesta, K.-D., Boizot, N. (2014). A real-time adaptive high-gain EKF, Applied to a quadcopter inertial navigation system. IEEE Trans. on Industrial Electronics, 61(1), 495-503. DOI: https://doi.org/10.1109/TIE.2013.2253063
16. Shen, C., Zhang, Y., Guo, X., Chen, X., Cao, H., Tang, J., Li, J., Liu, J. (2020). Seamless GPS/inertial navigation system based on self-learning square-root cubature Kalman filter. IEEE Transactions on Industrial Electronics, 68(1), 499–508. DOI: https://doi.org/10.1109/TIE.2020.2967671
17. Suh, Y.S. (2020). Attitude Estimation Using Inertial and Magnetic Sensors Based on Hybrid Four-Parameter Complementary Filter. IEEE Trans. Instrum. Meas., 69, 5149–5156. DOI: https://doi.org/10.1109/TIM.2019.2950826
18. Usman, M. (2020) Quad-rotor Modelling and Control with MATLAB/Simulink Implementation, Thesis (B.S.), LAB University of Applied Sciences. Vik, B., Fossen, T. I. (2001). A nonlinear observer for GPS and INS integration. 40th IEEE Conference on Decision and Control, 2001. DOI: https://doi.org/10.1109/CDC.2001.980726
19. Wang, M., Yang, Y., Hatch, R.R., and Zhang, Y. (2004). Adaptive filter for a miniature mems-based attitude and heading reference system. Position Location and Navigation Symposium, 193–200, 26-29 April, 2004. DOI: https://doi.org/10.1109/plans.2004.1308993
20. Yang, Y., Long, P., Song, X., Pan, J., and Zhang, L. (2021). Optimization-Based Framework for Excavation Trajectory Generation. IEEE Robotics and Automation Letters, 6(2), April, 2021. DOI: https://doi.org/10.1109/LRA.2021.3058071
21. Yoon, J., Doh, J. (2022). Optimal PID control for hovering stabilization of quadcopter using long short term memory. Advanced Engineering Informatics, 53, 101679. DOI: https://doi.org/10.1016/j.aei.2022.101679
22. Zheng, L., Zhan, X., Zhang, X. (2020). Nonlinear Complementary Filter for Attitude Estimation by Fusing Inertial Sensors and a Camera. Sensors, 20, 6752. DOI: https://doi.org/10.3390/s20236752
23. Zuo, Z. (2010). Trajectory tracking control design with command-filtered compensation for a quad-rotor, IET Control Theory Appl., 4, (11), 2343–2355. DOI: https://doi.org/10.1049/iet-cta.2009.0336