Excellent Papers of the 2nd Aerospace Frontiers Conference/the 27th Annual Meeting of the China Association for Science and Technology

Design of reward functions for helicopter attitude control in reinforcement learning

  • Tao ZHANG ,
  • Pan LI ,
  • Zixu WANG ,
  • Zhenhua ZHU
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  • National Key Laboratory of Helicopter Dynamics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China
E-mail: lipan@nuaa.edu.cn

Received date: 2025-02-25

  Revised date: 2025-03-08

  Accepted date: 2025-05-06

  Online published: 2025-05-27

Supported by

National Level Project

Abstract

Design of the reward function is one of the core technologies for helicopter attitude control based on reinforcement learning, directly determining the training and performance of the controller. Designing a comprehensive and efficient reward function has become a key research topic in the field. To this end, a phased reward function framework is proposed, dividing the full-time domain control process into two control stages. Reward function sub-items are designed for each stage, while introducing adjustable parameters that allow macroscopic adjustment of control performance. Based on the Actor-Critic method, a simple neural network attitude controller structure is designed, and the Proximal Policy Optimization algorithm (PPO) is used for training. The effectiveness of the proposed method is validated through robustness tests involving sensor error introduction and comparative experiments with the baseline reward function. 100 step simulation trials show that compared to the baseline method, the number of cases where system steady-state error is less than 10% increases by 16%, the number of cases where system overshoot is less than 10% of the command amplitude increases by 9%, and the number of cases where system settling time is less than 4 s increases by 7%. Additionally, under conditions of significant sensor error, the controller can still successfully complete the attitude control task.

Cite this article

Tao ZHANG , Pan LI , Zixu WANG , Zhenhua ZHU . Design of reward functions for helicopter attitude control in reinforcement learning[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2025 , 46(S1) : 732184 -732184 . DOI: 10.7527/S1000-6893.2025.32184

References

[1] 高正, 陈仁良. 直升机飞行动力学[M]. 北京: 科学出版社, 2003: 1-232.
  GAO Z, CHEN R L. Helicopter flight dynamics[M]. Beijing: Science Press, 2003: 1-232 (in Chinese).
[2] 陈仁良, 李攀, 吴伟, 等. 直升机飞行动力学数学建模问题[J]. 航空学报201738(7): 520915.
  CHEN R L, LI P, WU W, et al. A review of mathematical modeling of helicopter flight dynamics[J]. Acta Aeronautica et Astronautica Sinica201738(7): 520915 (in Chinese).
[3] 李攀. 旋翼非定常自由尾迹及高置信度直升机飞行力学建模研究[D]. 南京: 南京航空航天大学, 2010: 1-169.
  LI P. Research on unsteady free wake of rotor and high confidence helicopter flight mechanics modeling[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2010: 1-169 (in Chinese).
[4] BALAS G J, PACKARD A K, RENFROW J, et al. Control of the F-14 aircraft lateral-directional axis during powered approach[J]. Journal of Guidance, Control, and Dynamics199821(6): 899-908.
[5] 郑峰婴, 沈志敏, 李雅琴, 等. 共轴高速直升机增益自适应多模式切换控制[J]. 航空学报202445(9): 529088.
  ZHENG F Y, SHEN Z M, LI Y Q, et al. Gain adaptive multi-mode switching control for coaxial high-speed helicopter[J]. Acta Aeronautica et Astronautica Sinica202445(9): 529088 (in Chinese).
[6] CATAK A, ALTUNKAYA E C, DEMIR M, et al. Enhanced flight envelope protection: A novel reinforcement learning approach[J]. IFAC-PapersOnLine202458(30): 207-212.
[7] WISE K A. Design parameter tuning in adaptive observer-based flight control architectures[C]∥2018 AIAA Information Systems-AIAA Infotech @ Aerospace. Reston: AIAA, 2018.
[8] 仇钰清, 李俨, 郎金溪, 等. 高速直升机过渡模态鲁棒自适应姿态控制[J]. 航空学报202445(9): 529927.
  QIU Y Q, LI Y, LANG J X, et al. Robust adaptive attitude control of high-speed helicopters in transition mode[J]. Acta Aeronautica et Astronautica Sinica202445(9): 529927 (in Chinese).
[9] LAKE B M, BARONI M. Human-like systematic generalization through a meta-learning neural network[J]. Nature2023623(7985): 115-121.
[10] SUTTON R S, BARTO A G. Reinforcement learning: An introduction[J]. IEEE Transactions on Neural Networks19989(5): 1054.
[11] S?NMEZ S, RUTHERFORD M J, VALAVANIS K P. A survey of offline-and online-learning-based algorithms for multirotor UAVs [J]. Drones20248(4): 116.
[12] RICHTER D J, CALIX R A, KIM K. A review of reinforcement learning for fixed-wing aircraft control tasks[J]. IEEE Access202412: 103026-103048.
[13] SHADEED O, HASANZADE M, KOYUNCU E. Deep reinforcement learning based aggressive flight trajectory tracker[C]∥AIAA Scitech 2021 Forum. Reston: AIAA, 2021.
[14] MANUKYAN A, OLIVARES-MENDEZ M A, GEIST M, et al. Deep reinforcement learning-based continuous control for multicopter systems[C]∥2019 6th International Conference on Control, Decision and Information Technologies (CoDIT). Piscataway: IEEE Press, 2019: 1876-1881.
[15] HWANGBO J, SA I, SIEGWART R, et al. Control of a quadrotor with reinforcement learning[J]. IEEE Robotics and Automation Letters20172(4): 2096-2103.
[16] KOCH W, MANCUSO R, WEST R, et al. Reinforcement learning for UAV attitude control[J]. ACM Transactions on Cyber-Physical Systems20193(2): 1-21.
[17] XU J, DU T, FOSHEY M, et al. Learning to fly: Computational controller design for hybrid UAVs with reinforcement learning[J]. ACM Transactions on Graphics201938(4): 1-12.
[18] CANO LOPES G, FERREIRA M, SILVA SIM?ES A DA, et al. Intelligent control of a quadrotor with proximal policy optimization reinforcement learning[C]∥2018 Latin American Robotic Symposium, 2018 Brazilian Symposium on Robotics (SBR) and 2018 Workshop on Robotics in Education (WRE). Piscataway: IEEE Press, 2018: 503-508.
[19] MOLCHANOV A, CHEN T, H?NIG W, et al. Sim-to-(multi)-real: Transfer of low-level robust control policies to multiple quadrotors[C]∥2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Piscataway: IEEE Press, 2019: 59-66.
[20] LI Z, XUE S R, LIN W Y, et al. Training a robust reinforcement learning controller for the uncertain system based on policy gradient method[J]. Neurocomputing2018316: 313-321.
[21] ZHEN Y, HAO M R, SUN W D. Deep reinforcement learning attitude control of fixed-wing UAVs[C]∥2020 3rd International Conference on Unmanned Systems (ICUS). Piscataway: IEEE Press, 2020: 239-244.
[22] BEKAR C, YUKSEK B, INALHAN G. High fidelity progressive reinforcement learning for agile maneuvering UAVs[C]∥AIAA Scitech 2020 Forum. Reston: AIAA, 2020.
[23] KIM J, JUNG S. Enhancing UAV stability: A deep reinforcement learning strategy[C]∥2024 International Conference on Electronics, Information, and Communication (ICEIC). Piscataway: IEEE Press, 2024: 1-4.
[24] AOUN C, MONCAYO H. Disturbance observer-based reinforcement learning control and the application to a nonlinear dynamic system[C]∥AIAA Scitech 2020 Forum. Reston: AIAA, 2022.
[25] WANG Y D, SUN J, HE H B, et al. Deterministic policy gradient with integral compensator for robust quadrotor control[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems202050(10): 3713-3725.
[26] AKHTAR M, MAQSOOD A. Comparative analysis of deep reinforcement learning algorithms for hover-to-cruise transition maneuvers of a tilt-rotor unmanned aerial vehicle[J]. Aerospace202411(12): 1040-1042.
[27] PUTERMAN M L. Markov decision processes[M]∥Handbooks in Operations Research and Management Science. New York: Springer Science+Business Media, 19902: 331-434.
[28] SCHULMAN J, WOLSKI F, DHARIWAL P, et al. Proximal policy optimization algorithms[DB/OL]. ArXiv preprint: 1707. 06347, 2017.
[29] SCHULMAN J, MORITZ P, LEVINE S, et al. High-dimensional continuous control using generalized advantage estimation[DB/OL]. ArXiv preprint: 1506. 02438, 2015.
[30] GRONDMAN I, BUSONIU L, LOPES G A D, et al. A survey of actor-critic reinforcement learning: Standard and natural policy gradients[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews)201242(6): 1291-1307.
[31] BORISOV A, MAMAEV I S. Rigid body dynamics[M]. New York: Springer Science+Business Media, 2018: 1-271.
[32] LI P, CHEN R L. A mathematical model for helicopter comprehensive analysis[J]. Chinese Journal of Aeronautics201023(3): 320-326.
[33] PITT D M, PETERS D A. Theoretical prediction of dynamic inflow derivatives[J]. Vertica19815(1): 21-34.
[34] BALLIN M G. Validation of a real-time engineering simulation of the UH-60A helicopter: NASA-TM-88360 [R]. Washington, D.C.: NASA, 1987.
[35] ANDRYCHOWICZ M, RAICHUK A, STA?CZYK P, et al. What matters for on-policy deep actor-critic methods? A large-scale study[C]∥International Conference on Learning Representations: OpenReview. 2021: 1-10.
[36] WU Y F, ZHANG W, XU P, et al. A finite-time analysis of two time-scale actor-critic methods[J]. Advances in Neural Information Processing Systems202033: 17617-17628.
[37] WELCER M, SZCZEPA?SKI C, KRAWCZYK M. The impact of sensor errors on flight stability[J]. Aerospace20229(3): 169.
[38] TRIPATHI S, WAGH P, CHAUDHARY A B. Modelling, simulation & sensitivity analysis of various types of sensor errors and its impact on tactical flight vehicle navigation[C]∥2016 International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT). Piscataway: IEEE Press, 2016: 938-942.
[39] ZHENG T, XU A G, XU X C, et al. Modeling and compensation of inertial sensor errors in measurement systems[J]. Electronics202312(11): 2458.
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