Research Article
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Genetically Tuned Linear Quadratic Regulator for Trajectory Tracking of a Quadrotor

Year 2024, Volume: 12 Issue: 1, 37 - 46, 31.01.2024
https://doi.org/10.21541/apjess.1316025

Abstract

In this paper, a linear quadratic regulator (LQR) controller operating according to the genetically tuned inner-outer loop structure is proposed for trajectory tracking of a quadrotor. Setting the parameters of a linear controller operating according to the inner-outer loop structure is a matter that requires profound expertise. Optimization algorithms are used to cope with the solution of this problem. First, the dynamic equations of motion of the quadrotor are obtained and modelled in state-space form. The LQR controller, which will operate according to the inner-outer loop structure in the MATLAB/Simulink environment, has been developed separately for 6 degrees of freedom (DOF) of the quadrotor. Since adjusting these parameters will take a long time, a genetic algorithm has been used at this point. The LQR controller with optimized coefficients and a proposed LQR controller-based study in the literature are evaluated according to their success in following the reference trajectory and their responses to specific control inputs. According to the results obtained, it was observed that the genetically adjusted LQR controller produced more successful outcomes.

References

  • C.-C. Chang, J.-L. Wang, C.-Y. Chang, M.-C. Liang, and M.-R. Lin, “Development of a multicopter-carried whole air sampling apparatus and its applications in environmental studies,” Chemosphere, vol. 144, pp. 484–492, 2016.
  • J. A. Paredes, J. González, C. Saito, and A. Flores, “Multispectral imaging system with UAV integration capabilities for crop analysis,” in 2017 First IEEE International Symposium of Geoscience and Remote Sensing (GRSS-CHILE), 2017, pp. 1–4.
  • S. Anweiler and D. Piwowarski, “Multicopter platform prototype for environmental monitoring,” J Clean Prod, vol. 155, pp. 204–211, 2017.
  • B. E. Schäfer, D. Picchi, T. Engelhardt, and D. Abel, “Multicopter unmanned aerial vehicle for automated inspection of wind turbines,” in 2016 24th Mediterranean Conference on Control and Automation (MED), 2016, pp. 244–249.
  • M. Stokkeland, K. Klausen, and T. A. Johansen, “Autonomous visual navigation of unmanned aerial vehicle for wind turbine inspection,” in 2015 International Conference on Unmanned Aircraft Systems (ICUAS), 2015, pp. 998–1007.
  • D. Lee, H. Jin Kim, and S. Sastry, “Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter,” Int J Control Autom Syst, vol. 7, pp. 419–428, 2009.
  • J. Farrell, M. Sharma, and M. Polycarpou, “Backstepping-based flight control with adaptive function approximation,” Journal of Guidance, Control, and Dynamics, vol. 28, no. 6, pp. 1089–1102, 2005.
  • Z. Zuo and C. Wang, “Adaptive trajectory tracking control of output constrained multi-rotors systems,” IET Control Theory & Applications, vol. 8, no. 13, pp. 1163–1174, 2014.
  • J. Spencer, J. Lee, J. A. Paredes, A. Goel, and D. Bernstein, “An adaptive pid autotuner for multicopters with experimental results,” in 2022 International Conference on Robotics and Automation (ICRA), 2022, pp. 7846–7853.
  • Z. T. Dydek, A. M. Annaswamy, and E. Lavretsky, “Adaptive control of quadrotor UAVs: A design trade study with flight evaluations,” IEEE Transactions on control systems technology, vol. 21, no. 4, pp. 1400–1406, 2012.
  • E. A. Niit and W. J. Smit, “Integration of model reference adaptive control (MRAC) with PX4 firmware for quadcopters,” in 2017 24th International Conference on Mechatronics and Machine Vision in Practice (M2VIP), 2017, pp. 1–6.
  • A. R. Dooraki and D.-J. Lee, “Reinforcement learning based flight controller capable of controlling a quadcopter with four, three and two working motors,” in 2020 20th International Conference on Control, Automation and Systems (ICCAS), 2020, pp. 161–166.
  • C. Guzay and T. Kumbasar, “Aggressive maneuvering of a quadcopter via differential flatness-based fuzzy controllers: From tuning to experiments,” Appl Soft Comput, vol. 126, p. 109223, 2022.
  • G. Unal, “Integrated design of fault-tolerant control for flight control systems using observer and fuzzy logic,” Aircraft Engineering and Aerospace Technology, vol. 93, no. 4, pp. 723–732, 2021.
  • E. Yazid, M. Garrat, F. S.-2018 I. Conference, and undefined 2018, “Optimal PD tracking control of a quadcopter drone using adaptive PSO algorithm,” in ieeexplore.ieee.org, 2018, pp. 146–151.
  • M. S. Can and H. Ercan, “Real-time tuning of PID controller based on optimization algorithms for a quadrotor,” Aircraft Engineering and Aerospace Technology, vol. 94, no. 3, pp. 418–430, 2021.
  • Ş. YILDIRIM, N. ÇABUK, and V. BAKIRCIOĞLU, “Optimal Pid Controller Design for Trajectory Tracking of a Dodecarotor Uav Based On Grey Wolf Optimizer,” Konya Journal of Engineering Sciences, vol. 11, no. 1, pp. 10–20, 2023.
  • I. Siti, M. Mjahed, H. Ayad, and A. El Kari, “New trajectory tracking approach for a quadcopter using genetic algorithm and reference model methods,” Applied Sciences, vol. 9, no. 9, p. 1780, 2019.
  • M. J. Mahmoodabadi and N. R. Babak, “Robust fuzzy linear quadratic regulator control optimized by multi-objective high exploration particle swarm optimization for a 4 degree-of-freedom quadrotor,” Aerosp Sci Technol, vol. 97, p. 105598, 2020.
  • M. N. Shauqee, P. Rajendran, and N. M. Suhadis, “Proportional double derivative linear quadratic regulator controller using improvised grey wolf optimization technique to control quadcopter,” Applied Sciences, vol. 11, no. 6, p. 2699, 2021.
  • L. Meier, … D. H.-2015 I. international, and undefined 2015, “PX4: A node-based multithreaded open-source robotics framework for deeply embedded platforms,” ieeexplore.ieee.org.
  • “ArduPilot Documentation — ArduPilot documentation.” Accessed: Jun. 13, 2023. [Online]. Available: https://ardupilot.org/ardupilot/
  • R. Mahony, V. Kumar, and P. Corke, “Multirotor aerial vehicles: Modeling, estimation, and control of quadrotor,” IEEE Robot Autom Mag, vol. 19, no. 3, pp. 20–32, 2012.
  • L. Martins, “Linear and nonlinear control of uavs: design and experimental validation,” Master’s Thesis, Instituto Superior Técnico, Lisbon, Portugal, 2019.
  • B. Siciliano, L. Sciavicco, L. Villani, and G. Oriolo, “Robotics,” 2009, doi: 10.1007/978-1-84628-642-1.
  • L. Martins, C. Cardeira, and P. Oliveira, “Linear quadratic regulator for trajectory tracking of a quadrotor,” IFAC-PapersOnLine, vol. 52, no. 12, pp. 176–181, 2019.
  • G. J. Leishman, Principles of helicopter aerodynamics with CD extra. Cambridge university press, 2006.
Year 2024, Volume: 12 Issue: 1, 37 - 46, 31.01.2024
https://doi.org/10.21541/apjess.1316025

Abstract

References

  • C.-C. Chang, J.-L. Wang, C.-Y. Chang, M.-C. Liang, and M.-R. Lin, “Development of a multicopter-carried whole air sampling apparatus and its applications in environmental studies,” Chemosphere, vol. 144, pp. 484–492, 2016.
  • J. A. Paredes, J. González, C. Saito, and A. Flores, “Multispectral imaging system with UAV integration capabilities for crop analysis,” in 2017 First IEEE International Symposium of Geoscience and Remote Sensing (GRSS-CHILE), 2017, pp. 1–4.
  • S. Anweiler and D. Piwowarski, “Multicopter platform prototype for environmental monitoring,” J Clean Prod, vol. 155, pp. 204–211, 2017.
  • B. E. Schäfer, D. Picchi, T. Engelhardt, and D. Abel, “Multicopter unmanned aerial vehicle for automated inspection of wind turbines,” in 2016 24th Mediterranean Conference on Control and Automation (MED), 2016, pp. 244–249.
  • M. Stokkeland, K. Klausen, and T. A. Johansen, “Autonomous visual navigation of unmanned aerial vehicle for wind turbine inspection,” in 2015 International Conference on Unmanned Aircraft Systems (ICUAS), 2015, pp. 998–1007.
  • D. Lee, H. Jin Kim, and S. Sastry, “Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter,” Int J Control Autom Syst, vol. 7, pp. 419–428, 2009.
  • J. Farrell, M. Sharma, and M. Polycarpou, “Backstepping-based flight control with adaptive function approximation,” Journal of Guidance, Control, and Dynamics, vol. 28, no. 6, pp. 1089–1102, 2005.
  • Z. Zuo and C. Wang, “Adaptive trajectory tracking control of output constrained multi-rotors systems,” IET Control Theory & Applications, vol. 8, no. 13, pp. 1163–1174, 2014.
  • J. Spencer, J. Lee, J. A. Paredes, A. Goel, and D. Bernstein, “An adaptive pid autotuner for multicopters with experimental results,” in 2022 International Conference on Robotics and Automation (ICRA), 2022, pp. 7846–7853.
  • Z. T. Dydek, A. M. Annaswamy, and E. Lavretsky, “Adaptive control of quadrotor UAVs: A design trade study with flight evaluations,” IEEE Transactions on control systems technology, vol. 21, no. 4, pp. 1400–1406, 2012.
  • E. A. Niit and W. J. Smit, “Integration of model reference adaptive control (MRAC) with PX4 firmware for quadcopters,” in 2017 24th International Conference on Mechatronics and Machine Vision in Practice (M2VIP), 2017, pp. 1–6.
  • A. R. Dooraki and D.-J. Lee, “Reinforcement learning based flight controller capable of controlling a quadcopter with four, three and two working motors,” in 2020 20th International Conference on Control, Automation and Systems (ICCAS), 2020, pp. 161–166.
  • C. Guzay and T. Kumbasar, “Aggressive maneuvering of a quadcopter via differential flatness-based fuzzy controllers: From tuning to experiments,” Appl Soft Comput, vol. 126, p. 109223, 2022.
  • G. Unal, “Integrated design of fault-tolerant control for flight control systems using observer and fuzzy logic,” Aircraft Engineering and Aerospace Technology, vol. 93, no. 4, pp. 723–732, 2021.
  • E. Yazid, M. Garrat, F. S.-2018 I. Conference, and undefined 2018, “Optimal PD tracking control of a quadcopter drone using adaptive PSO algorithm,” in ieeexplore.ieee.org, 2018, pp. 146–151.
  • M. S. Can and H. Ercan, “Real-time tuning of PID controller based on optimization algorithms for a quadrotor,” Aircraft Engineering and Aerospace Technology, vol. 94, no. 3, pp. 418–430, 2021.
  • Ş. YILDIRIM, N. ÇABUK, and V. BAKIRCIOĞLU, “Optimal Pid Controller Design for Trajectory Tracking of a Dodecarotor Uav Based On Grey Wolf Optimizer,” Konya Journal of Engineering Sciences, vol. 11, no. 1, pp. 10–20, 2023.
  • I. Siti, M. Mjahed, H. Ayad, and A. El Kari, “New trajectory tracking approach for a quadcopter using genetic algorithm and reference model methods,” Applied Sciences, vol. 9, no. 9, p. 1780, 2019.
  • M. J. Mahmoodabadi and N. R. Babak, “Robust fuzzy linear quadratic regulator control optimized by multi-objective high exploration particle swarm optimization for a 4 degree-of-freedom quadrotor,” Aerosp Sci Technol, vol. 97, p. 105598, 2020.
  • M. N. Shauqee, P. Rajendran, and N. M. Suhadis, “Proportional double derivative linear quadratic regulator controller using improvised grey wolf optimization technique to control quadcopter,” Applied Sciences, vol. 11, no. 6, p. 2699, 2021.
  • L. Meier, … D. H.-2015 I. international, and undefined 2015, “PX4: A node-based multithreaded open-source robotics framework for deeply embedded platforms,” ieeexplore.ieee.org.
  • “ArduPilot Documentation — ArduPilot documentation.” Accessed: Jun. 13, 2023. [Online]. Available: https://ardupilot.org/ardupilot/
  • R. Mahony, V. Kumar, and P. Corke, “Multirotor aerial vehicles: Modeling, estimation, and control of quadrotor,” IEEE Robot Autom Mag, vol. 19, no. 3, pp. 20–32, 2012.
  • L. Martins, “Linear and nonlinear control of uavs: design and experimental validation,” Master’s Thesis, Instituto Superior Técnico, Lisbon, Portugal, 2019.
  • B. Siciliano, L. Sciavicco, L. Villani, and G. Oriolo, “Robotics,” 2009, doi: 10.1007/978-1-84628-642-1.
  • L. Martins, C. Cardeira, and P. Oliveira, “Linear quadratic regulator for trajectory tracking of a quadrotor,” IFAC-PapersOnLine, vol. 52, no. 12, pp. 176–181, 2019.
  • G. J. Leishman, Principles of helicopter aerodynamics with CD extra. Cambridge university press, 2006.
There are 27 citations in total.

Details

Primary Language English
Subjects Computer Software
Journal Section Research Articles
Authors

Ali Tahir Karaşahin 0000-0002-7440-1312

Publication Date January 31, 2024
Submission Date June 17, 2023
Published in Issue Year 2024 Volume: 12 Issue: 1

Cite

IEEE A. T. Karaşahin, “Genetically Tuned Linear Quadratic Regulator for Trajectory Tracking of a Quadrotor”, APJESS, vol. 12, no. 1, pp. 37–46, 2024, doi: 10.21541/apjess.1316025.

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