基于多目标演化算法的尾座式垂直起降无人 机过渡飞行优化问题研究

      尾座式垂直起降无人机是一种集旋翼无人机和固定翼无人机的优点于一身的无人机，拥有悬停模式和巡航模式，引起了广泛的关注。但是由于它的结构特殊，给过渡飞行控制提出了很高的要求和挑战。故本文对此展开了深入的研究，主要研究内容如下：

       首先，调研了传统方法在尾座式垂直起降无人机过渡飞行控制优化问题上的应用，并分析这些方法的不足；还调研了采用多目标演化算法解决类似的控制优化问题的案例，分析多目标演化算法在控制优化问题上的优势，并确定其应用在本课题上的可行性和优越性；另外，对于基于神经网络的无人机模型辨识方面的文献，也进行了充分的查阅和分析工作。

       其次，本文建立了满足一阶系统假设的纵向三自由度无人机动力学模型，设计了基于NSGA-Ⅲ的多目标演化算法来进行求解。另外，仿真实验中，采用了经典的三个过渡飞行优化目标，即最小化过渡飞行的高度变化，最小化过渡飞行时间和最小化过度飞行的能量消耗，并将基于经典轨迹优化算法的开源软件“OptimTraj”作为对比。实验结果初步的证明了我们的算法的灵活性、高效性和可行性。

       然后，为了进一步的算法验证需求，本文修改并建立了基于Simulink工具箱的六自由度无人机模型，重新整理和设计优化问题。其中，攻角作为尾座式垂直起降无人机的重要参数，影响着无人机的安全性能，故将最小化过渡飞行中无人机的最大攻角加入优化目标中，组成一个四目标优化问题。在仿真实验中，我们探索了不同的解的维度对过渡优化问题的影响，并通过仿真实验结果验证了各优化目标之间的关系。

       最后，本文还在无人机的建模上进行了深入研究，分别建立了基于神经网络的无人机的灰箱模型和黑箱模型。仿真预测结果表明，尽管灰箱模型相比黑箱模型有着更高的预测精确度，但还未达到过渡飞行仿真需求。

[1] WANG H, LIANG Y, QIU X, et al. Withdrawal: The wind resistance capability of the Egretta tail-sitter VTOL UAV[J]. AIAA Scitech 2021 Forum, 2021.
[2] BETTS J T. Survey of Numerical Methods for Trajectory Optimization[J]. Journal of Guidance Control and Dynamics, 1998, 21: 193-207.
[3] CONWAY B A. A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems[J]. Journal of Optimization Theory and Applications, 2012, 152: 271-306.
[4] DUUN-HENRIKSEN A K, SCHMIDT S, RØGE R M, et al. Model Identification UsingStochastic Differential Equation Grey-Box Models in Diabetes[J]. Journal of Diabetes Science and Technology, 2013, 7: 431-440.
[5] STONE R H. Control architecture for a tail-sitter unmanned air vehicle[J]. 2004 5th Asian Control Conference (IEEE Cat. No.04EX904), 2004, 2: 736-744.
[6] KUBO D, SUZUKI S. Tail-Sitter Vertical Takeoff and Landing Unmanned Aerial Vehicle: Transitional Flight Analysis[J]. Journal of Aircraft, 2008, 45: 292-297.
[7] NALDI R, MARCONI L. Optimal transition maneuver for a class of V/STOL aircrafts[J]. 2009 European Control Conference (ECC), 2009: 1842-1847.
[8] ZHANG W, QUAN Q, ZHANG R, et al. New Transition Method of a Ducted-Fan Unmanned Aerial Vehicle[J]. Journal of Aircraft, 2013, 50: 1131-1140.
[9] VERLING S, WEIBEL B, BOOSFELD M, et al. Full Attitude Control of a VTOL tail-sitter UAV [J]. 2016 IEEE International Conference on Robotics and Automation (ICRA), 2016: 3006-3012.
[10] VERLING S, STASTNY T, BATTIG G, et al. Model-based transition optimization for a VTOL tail-sitter[J]. 2017 IEEE International Conference on Robotics and Automation (ICRA), 2017: 3939-3944.
[11] OOSEDO A, ABIKO S, KONNO A, et al. Optimal transition from hovering to level-flight of a quadrotor tail-sitter UAV[J]. Autonomous Robots, 2017, 41: 1143-1159.
[12] 刘志豪, 闵荣, 方成, 等. 多飞行模式垂直起降无人机过渡飞行控制策略[J]. 上海交通大学学报, 2019, 53(10): 1173-1181.
[13] LI B, SUN J, ZHOU W, et al. Transition Optimization for a VTOL Tail-Sitter UAV[J].IEEE/ASME Transactions on Mechatronics, 2020, 25: 2534-2545.
[14] KELLY M. An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation[J]. SIAM Review, 2017, 59: 849-904.
[15] DOFF-SOTTA M, CANNON M, BACIC M. Fast optimal trajectory generation for a tiltwing VTOL aircraft with application to urban air mobility[J]. 2022 American Control Conference (ACC), 2021: 4036-4041.
[16] KIKUMOTO C, URAKUBO T, SABE K, et al. Back-Transition Control With Large Deceleration for a Dual Propulsion VTOL UAV Based on Its Maneuverability[J]. IEEE Robotics and Automation Letters, 2022, 7: 11697-11704.
[17] WILLIS J B, JOHNSON J, BEARD R W. State-Dependent LQR Control for a Tilt-Rotor UAV [J]. 2020 American Control Conference (ACC), 2020: 4175-4181.
[18] WILLIS J B, BEARD R W. Nonlinear Trajectory Tracking Control for Winged eVTOL UAVs [J]. 2021 American Control Conference (ACC), 2021: 1687-1692.
[19] VASILE M, MINISCI E A, LOCATELLI M. An Inflationary Differential Evolution Algorithm for Space Trajectory Optimization[J]. IEEE Transactions on Evolutionary Computation, 2011, 15: 267-281.
[20] CHAI R, SAVVARIS A, TSOURDOS A, et al. Multi-objective trajectory optimization of Space Manoeuvre Vehicle using adaptive differential evolution and modified game theory[J]. Acta Astronautica, 2017, 136: 273-280.
[21] CHAI R, SAVVARIS A, TSOURDOS A, et al. Solving Multiobjective Constrained Trajectory Optimization Problem by an Extended Evolutionary Algorithm[J]. IEEE Transactions on Cybernetics, 2020, 50: 1630-1643.
[22] DEB K, JAIN H. An Evolutionary Many-Objective Optimization Algorithm Using Reference Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints [J]. IEEE Transactions on Evolutionary Computation, 2014, 18: 577-601.
[23] JAIN H, DEB K. An Evolutionary Many-Objective Optimization Algorithm Using Reference Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach[J]. IEEE Transactions on Evolutionary Computation, 2014, 18: 602-622.
[24] CHAI R, TSOURDOS A, SAVVARIS A, et al. Solving Constrained Trajectory Planning Problems Using Biased Particle Swarm Optimization[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57: 1685-1701.
[25] LIU X, JIANG D, TAO B, et al. Genetic Algorithm-Based Trajectory Optimization for Digital Twin Robots[J]. Frontiers in Bioengineering and Biotechnology, 2022, 9.
[26] SUN Z, REN H, YEN G G, et al. An Evolutionary Algorithm With Constraint Relaxation Strategy for Highly Constrained Multi-objective Optimization[J]. IEEE Transactions on Cybernetics, 2022, 53: 3190-3204.
[27] SHI K, HUANG L, JIANG D, et al. Path Planning Optimization of Intelligent Vehicle Based on Improved Genetic and Ant Colony Hybrid Algorithm[J]. Frontiers in Bioengineering and Biotechnology, 2022, 10.
[28] ALDRICH J. R.A. Fisher and the making of maximum likelihood 1912-1922[J]. Statistical Science, 1997, 12: 162-176.
[29] MILLIDERE M, CAKIN U, YIGIT T. Generating Aerodynamic Database from Closed Loop Simulated Flight Data[C]//European Conference for Aeronautics and Space Sciences. 2019.
[30] HATAMLEH K S, MA O, PAZ R A. A UAV Model Parameter Identification Method: a Simulation Study[J]. International Journal of Information Acquisition, 2009, 6: 225-238.
[31] EBRAHIMI B, BARZAMINI F. Aircraft System Identification Using Parametric Approaches and Intelligent Modeling[J]. 2021 IEEE Aerospace Conference (50100), 2021: 1-12.
[32] HAO D, ZHANG L, YU J, et al. Modeling of unsteady aerodynamic characteristics at high angles of attack[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2019, 233: 2291-2301.
[33] LINSE D J, STENGEL R F. Identification of aerodynamic coefficients using computational neural networks[C]//1992.
[34] PEYADA N K, GHOSH A K. Aircraft parameter estimation using a new filtering technique based upon a neural network and Gauss-Newton method[J]. The Aeronautical Journal (1968), 2009, 113: 243-252.
[35] CHAUHAN R K, SINGH S. Application of neural networks based method for estimation of aerodynamic derivatives[J]. 2017 7th International Conference on Cloud Computing, Data Science & Engineering-Confluence, 2017: 58-64.
[36] WANG H B, LV B, YANG X J, et al. Research on Unsteady Aerodynamics Modeling Based on Back Propagation Algorithm at High Angle of Attack[J]. Applied Mechanics and Materials, 2013, 392: 170-177.
[37] TAO C, CHEN D, SONGYAN W, et al. Aerodynamic parameter fitting based on BP neural network and hybrid optimization algorithm[J]. Proceeding of the 11th World Congress on Intelligent Control and Automation, 2014: 4961-4964.
[38] BANSAL S, AKAMETALU A K, JIANG F J, et al. Learning quadrotor dynamics using neural network for flight control[J]. 2016 IEEE 55th Conference on Decision and Control (CDC), 2016: 4653-4660.
[39] MOHAJERIN N, WASLANDER S L. Multistep Prediction of Dynamic Systems With Recurrent Neural Networks[J]. IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(11): 3370-3383.
[40] MOHAJERIN N, MOZIFIAN M, WASLANDER S L. Deep Learning a Quadrotor Dynamic Model for Multi-Step Prediction[J]. 2018 IEEE International Conference on Robotics and Automation (ICRA), 2018: 2454-2459.
[41] VERMA H O, PEYADA N K. Parameter estimation of aircraft using extreme learning machine and Gauss-Newton algorithm[J]. The Aeronautical Journal, 2019, 124: 271-295.
[42] VERMA H O, PEYADA N K. Estimation of aerodynamic parameters near stall using maximum likelihood and extreme learning machine-based methods[J]. The Aeronautical Journal, 2020, 125: 489-509.
[43] VERMA H O, PEYADA N K. Estimation of longitudinal aerodynamic parameters using recurrent neural network[J]. The Aeronautical Journal, 2022.
[44] YU P L. Cone convexity, cone extreme points, and nondominated solutions in decision problems with multi-objectives[J]. Journal of Optimization Theory & Applications, 1974, 14(3): 319-377.
[45] KIRKPATRICK S, GELATT C D, VECCHI M. Optimization by Simulated Annealing[J]. Science, 1983, 220: 671-680.
[46] HOLLAND J H. Genetic Algorithms[J]. Scientific American, 1992, 267(1): 66-73.
[47] DORIGO M, MANIEZZO V, COLORNI A. Ant system: optimization by a colony of cooperating agents[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 1996, 26(1): 29-41.
[48] KENNEDY J, EBERHART R C. Particle swarm optimization[J]. Proceedings of ICNN’95-International Conference on Neural Networks, 1995, 4: 1942-1948.
[49] STORN R, PRICE K V. Differential Evolution –A Simple and Efficient Heuristic for global Optimization over Continuous Spaces[J]. Journal of Global Optimization, 1997, 11: 341-359.
[50] DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197.
[51] ZHANG Q, LI H. MOEA/D: A Multi-objective Evolutionary Algorithm Based on Decomposition[J]. IEEE Transactions on Evolutionary Computation, 2007, 11: 712-731.
[52] DAS I, DENNIS J E. Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems[J]. SIAM JOURNAL on CONTROL and OPTIMIZATION, 1998, 8: 631-657.
[53] SUN J, LI B, SHEN L, et al. Dynamic modeling and hardware-in-loop simulation for a tail-sitter unmanned aerial vehicle in hovering flight[C]//AIAA Modeling and Simulation Technologies Conference. 2017.
[54] SUN J, LI B, YUNG WEN C, et al. Design and implementation of a real-time hardware-in-the-loop testing platform for a dual-rotor tail-sitter unmanned aerial vehicle[J]. Mechatronics, 2018.
[55] CRITZOS C C, HEYSON H H, BOSWINKLE R W. Aerodynamic characteristics of NACA0012 airfoil section at angles of attack from 0 degrees to 180 degrees[J]. Technical Report Archive & Image Library, 1955.
[56] DEB K, AGRAWAL R B. Simulated Binary Crossover for Continuous Search Space[J]. Complex Systems, 1995, 9.