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Physics-guided neural network and GPU-accelerated nonlinear model predictive control for quadcopter

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Abstract

This paper presents a physics-guided residual recurrent neural network (PGRRNN) and graphics processing unit (GPU)-accelerated model predictive control (MPC) framework to combat two specific challenges in artificial neural network (ANN)-based nonlinear MPC of high-rate dynamics systems, i.e., low control latency and insufficient model accuracy or generalization ability. Different from traditional ANN models, PGRRNN utilizes approximate physics-based (PB) models (with parameter uncertainty) as a backbone to impose physical constraints/guidance for future state prediction, and reconciles the difference between PB model approximation and data collected from actual systems by propagating their residuals through a multilayer recurrent neural network, hence improving its accuracy and generalization and alleviating data volume requirement. For computing acceleration, both PGRRNN and particle swarm optimization (PSO) are implemented on a GPU platform to make use of its massive parallel processing threads. Numerical experiments for MPC trajectory tracking of a quadcopter are used to examine accuracy and robustness of PGRRNN, and its performance is compared with other ANN models and approximate PB models. PGRRNN outperforms the other models in both ideal and realistic environments, exhibiting 2–3 times lower tracking error than the pure data-driven model. Furthermore, it is demonstrated that GPU-based PSO is able to synthesize control signals at a rate of greater than 50 Hz and can be a promising approach for ANN-based nonlinear MPC.

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Data availability

The datasets generated and analyzed during the current study are not publicly available, but are available from the corresponding author on request.

References

  1. Choi YC, Ahn HS (2014) Nonlinear control of quadrotor for point tracking: actual implementation and experimental tests. IEEE/ASME Trans Mechatron 20(3):1179–1192

    Article  Google Scholar 

  2. Pérez-Alcocer R, Moreno-Valenzuela J, Miranda-Colorado R (2016) A robust approach for trajectory tracking control of a quadrotor with experimental validation. ISA Trans 65:262–274

    Article  Google Scholar 

  3. Mardan M, Esfandiari M, Sepehri N (2017) Attitude and position controller design and implementation for a quadrotor. Int J Adv Rob Syst 14(3):1729881417709242

    Google Scholar 

  4. Xiong JJ, Zheng EH (2014) Position and attitude tracking control for a quadrotor UAV. ISA Trans 53(3):725–731

    Article  Google Scholar 

  5. Liang X, Fang Y, Sun N, Lin H (2017) Nonlinear hierarchical control for unmanned quadrotor transportation systems. IEEE Trans Industr Electron 65(4):3395–3405

    Article  Google Scholar 

  6. Xuan-Mung N, Hong SK (2019) Improved altitude control algorithm for quadcopter unmanned aerial vehicles. Appl Sci 9(10):2122

    Article  Google Scholar 

  7. Lee BY, Lee HI, Tahk MJ (2013, October). Analysis of adaptive control using on-line neural networks for a quadrotor UAV. In: 2013 13th international conference on control, automation and systems (ICCAS 2013) (pp. 1840–1844). IEEE.

  8. Mofid O, Mobayen S (2018) Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties. ISA Trans 72:1–14

    Article  Google Scholar 

  9. Razmi H, Afshinfar S (2019) Neural network-based adaptive sliding mode control design for position and attitude control of a quadrotor UAV. Aerosp Sci Technol 91:12–27

    Article  Google Scholar 

  10. Zulu A, John S (2014) A review of control algorithms for autonomous quadrotors. Open J Appl Sci 4:547–556

    Google Scholar 

  11. Nascimento TP, Saska M (2019) Position and attitude control of multi-rotor aerial vehicles: a survey. Annu Rev Control 48:129–146

    Article  MathSciNet  Google Scholar 

  12. Raffo GV, Ortega MG, Rubio FR (2010) An integral predictive/nonlinear H∞ control structure for a quadrotor helicopter. Automatica 46(1):29–39

    Article  MathSciNet  MATH  Google Scholar 

  13. Lopes RV, Santana PHRQA, Borges G, Ishihara JY (2011, October). Model Predictive Control applied to tracking and attitude stabilization of a VTOL quadrotor aircraft. In: 21st international congress of mechanical engineering (pp. 176–185).

  14. Abdolhosseini M, Zhang YM, Rabbath CA (2013) An efficient model predictive control scheme for an unmanned quadrotor helicopter. J Intell Rob Syst 70(1–4):27–38

    Article  Google Scholar 

  15. Chen X, Wang L (2013, November). Cascaded model predictive control of a quadrotor UAV. In: 2013 australian control conference (pp. 354–359). IEEE.

  16. Cheng H, Yang Y (2017, June). Model predictive control and PID for path following of an unmanned quadrotor helicopter. In: 2017 12th IEEE conference on industrial electronics and applications (ICIEA) (pp. 768–773). IEEE.

  17. Jiajin L, Rui L, Yingjing S, Jianxiao Z (2017, October). Design of attitude controller using explicit model predictive control for an unmanned quadrotor helicopter. In: 2017 Chinese automation congress (CAC) (pp. 2853–2857). IEEE.

  18. Kuyumcu A, Bayezit I (2017, December). Augmented model predictive control of unmanned quadrotor vehicle. In 2017 11th Asian control conference (ASCC) (pp. 1626–1631). IEEE.

  19. Du X, Htet KKK, Tan KK (2016) Development of a genetic-algorithm-based nonlinear model predictive control scheme on velocity and steering of autonomous vehicles. IEEE Trans Industr Electron 63(11):6970–6977

    Article  Google Scholar 

  20. Negri GH, Cavalca MSM, Parpinelli RS (2016) Model-based predictive control using differential evolution applied to a pressure system. IEEE Lat Am Trans 14(1):89–95

    Article  Google Scholar 

  21. Chen L, Du S, He Y, Liang M, Xu D (2018) Robust model predictive control for greenhouse temperature based on particle swarm optimization. Information processing in agriculture 5(3):329–338

    Article  Google Scholar 

  22. Mohammadi A, Asadi H, Mohamed S, Nelson K, Nahavandi S (2018) Optimizing model predictive control horizons using genetic algorithm for motion cueing algorithm. Expert Syst Appl 92:73–81

    Article  Google Scholar 

  23. Rodríguez del Nozal Á, Gutiérrez Reina D, Alvarado-Barrios L, Tapia A, Escaño JM (2019) A mpc strategy for the optimal management of microgrids based on evolutionary optimization. Electronics 8(11):1371

    Article  Google Scholar 

  24. Zhang B, Sun X, Liu S, Deng X (2019) Recurrent neural network-based model predictive control for multiple unmanned quadrotor formation flight. Int J Aeros Eng. https://doi.org/10.1155/2019/7272387

    Article  Google Scholar 

  25. Hong SH, Cornelius J, Wang Y, Pant K (2019) Fault compensation by online updating of genetic algorithm-selected neural network model for model predictive control. SN Appl Sci 1(11):1–16

    Article  Google Scholar 

  26. Hong SH, Cornelius J, Wang Y, Pant K (2021) Optimized artificial neural network model and compensator in model predictive control for anomaly mitigation. J Dyn Syst Meas Contr 143(5):051005

    Article  Google Scholar 

  27. Kani JN, Elsheikh AH (2017) DR-RNN: A deep residual recurrent neural network for model reduction. arXiv preprint arXiv:1709.00939.

  28. Kani JN, Elsheikh AH (2019) Reduced-order modeling of subsurface multi-phase flow models using deep residual recurrent neural networks. Transp Porous Media 126(3):713–741

    Article  MathSciNet  Google Scholar 

  29. Yu Y, Yao H, Liu Y (2019) Aircraft dynamics simulation using a novel physics-based learning method. Aerosp Sci Technol 87:254–264

    Article  Google Scholar 

  30. Yu Y, Yao H, Liu Y (2020) Structural dynamics simulation using a novel physics-guided machine learning method. Eng Appl Artif Intell 96:103947

    Article  Google Scholar 

  31. Karpatne A, Watkins W, Read J, Kumar V (2017). Physics-guided neural networks (pgnn): An application in lake temperature modeling. arXiv preprint arXiv:1710.11431.

  32. Karniadakis GE, Kevrekidis IG, Lu L, Perdikaris P, Wang S, Yang L (2021) Physics-informed machine learning. Nat Rev Phys 3(6):422–440

    Article  Google Scholar 

  33. ElKholy HM (2014) Dynamic modeling and control of a quadrotor using linear and nonlinear approaches. M.S. thesis. American University in Cairo, Egypt

    Google Scholar 

  34. Nguyen NP, Hong SK (2018) Sliding mode thau observer for actuator fault diagnosis of quadcopter UAVs. Appl Sci 8(10):1893

    Article  Google Scholar 

  35. Gomez V, Gomez N, Rodas J, Paiva E, Saad M, Gregor R (2020) Pareto optimal pid tuning for Px4-Based unmanned aerial vehicles by using a multi-objective particle swarm optimization algorithm. Aerospace 7(6):71

    Article  Google Scholar 

  36. Scokaert POM, Clarke DW (1994) Stabilising properties of constrained predictive control. IEE Proceedings-Control Theory and Applications 141(5):295–304

    Article  MATH  Google Scholar 

  37. Mayne DQ, Rawlings JB, Rao CV, Scokaert PO (2000) Constrained model predictive control: stability and optimality. Automatica 36(6):789–814

    Article  MathSciNet  MATH  Google Scholar 

  38. Mayne D, Falugi P (2016) Generalized stabilizing conditions for model predictive control. J Optim Theory Appl 169(3):719–734

    Article  MathSciNet  MATH  Google Scholar 

  39. Patan K (2014) Neural network-based model predictive control: Fault tolerance and stability. IEEE Trans Control Syst Technol 23(3):1147–1155

    Article  Google Scholar 

  40. Kulkarni MNK, Patekar MS, Bhoskar MT, Kulkarni MO, Kakandikar GM, Nandedkar VM (2015) Particle swarm optimization applications to mechanical engineering-a review. Mater Today Proc 2(4–5):2631–2639

    Article  Google Scholar 

  41. Ma D, Xia Y, Li T, Chang K (2016) Active disturbance rejection and predictive control strategy for a quadrotor helicopter. IET Control Theory Appl 10(17):2213–2222

    Article  MathSciNet  Google Scholar 

  42. Alexis K, Nikolakopoulos G, Tzes A (2012) Model predictive quadrotor control: attitude, altitude and position experimental studies. IET Control Theory Appl 6(12):1812–1827

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Florida Institute of Technology, Melbourne, FL, 32901, USA

    Seong Hyeon Hong

  2. University of South Carolina, Columbia, SC, 29208, USA

    Junlin Ou & Yi Wang

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  1. Seong Hyeon Hong
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  2. Junlin Ou
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Correspondence to Yi Wang.

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Hong, S.H., Ou, J. & Wang, Y. Physics-guided neural network and GPU-accelerated nonlinear model predictive control for quadcopter. Neural Comput & Applic 35, 393–413 (2023). https://doi.org/10.1007/s00521-022-07783-4

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  • DOI: https://doi.org/10.1007/s00521-022-07783-4

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