基于微分平坦理论的飞行器轨迹规划方法研究
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摘要
作为任务规划技术的重要内容,轨迹规划技术有利于提高飞机的飞行品质以满足既定任务要求,能够有效提高作战飞机对地打击的成功率。飞行器轨迹规划可以抽象为一个包含微分方程、代数方程和不等式约束条件下求解泛函极值的最优控制问题,直接求解的难度很大。
论文为了降低问题的复杂度,针对轨迹规划中的动力学微分方程这一非完整性约束,引入了微分平坦理论,提出了一种分层递阶规划求解方法——在基于B样条的样板航迹规划的基础上,根据微分平坦理论将最优控制问题转化为非线性规划进行求解,保证了生成轨迹的可执行性。论文的主要研究内容如下:
1、问题分析与建模。对飞行器对地打击任务进行了深入分析,总结了轨迹规划中所涉及的各种约束条件,并提出了相应的指标,在此基础上,对轨迹规划进行了最优控制形式的一般化描述,建立了以过载和滚转角为控制量的动力学模型、威胁模型等作为轨迹规划的约束条件,为进一步研究轨迹规划方法奠定了基础。
2、样板航迹规划技术研究。通过对飞行器对地打击任务中惯常采用的战术机动进行分析,从中提炼出一系列基本动作和空对地打击的一般模式(即战术模板)。论文选取两种典型的对地打击战术模板,进行了基本动作分解和参数化模型描述。在此基础上,研究了基于B样条的样板航迹规划,提出了一个能满足终端约束的避障航迹规划算法,从而为后续的轨迹生成提供了技术支撑。
3、基于微分平坦理论的轨迹生成研究。针对具有非完整性约束的飞行器轨迹规划问题,设计了基于微分平坦理论的轨迹生成步骤。并对飞行器的动力学和运动学模型进行了平坦属性的判定,确定了平坦输出。在基于B样条的样板航迹规划的基础上,使用B样条参数化平坦输出,将最优控制问题转化为一般非线性规划问题,保证了生成轨迹的可执行性,同时降低了问题求解难度。
通过在项目中的应用,该方法能满足平台本身的非完整性约束、战术终端约束等各种约束条件,并科学地将飞行器对地打击任务中战术和技术进行有机结合,较好地解决了飞行器对地打击任务中轨迹规划问题。
Trajectory planning, as an integral part of the mission planning technology, can help to improve the aircrafts' flying qualities to meet the established mission requirements, and effectively enhance the success rate of combat aircraft attacking. Being an optimal control problem, aircraft trajectory planning is restrained by differential equations, algebraic equations and inequalities, and it aims to find the functional extremum. Consequently, the immediate solution is difficult to imagine.
In order to reduce the complexity of the problem, the thesis introduces the differential flatness theory to serve the dynamical equations, the nonholonomic constraint, and proposes a hierarchical programming approach. With the basis of template route planning based of B-spline curve, the optimal control problem were changed into a general nonlinear programming problem and got the solution in the framework of the differential flatness theory, which guaranteed the enforceability of the generated trajectory. The main contents are as follows:
1. Problem analysis and modeling. With the analysis of the aircraft combat mission and the summary of the constraints of the trajectory planning involved, the thesis proposed the objective functions of the trajectory planning. On this basis, the trajectory planning problem was modeled as a general nonlinear programming one, comprising the aircraft dynamic model, described by the overload and roll angle as the decision variables, and the threat model, etc., which constituted the constraints of the trajectory planning, and laid the foundation for further study of the method of trajectory planning.
2. Template route planning technology. Having analyzed the commonly-used tactical motivation of the aircraft combat missions against the ground, the paper extracted a series of basic maneuver and the general pattern of air-to-ground combat (i.e. tactical template). Two typical tactical templates were selected to execute the maneuver decomposing and numerical value description. Then the template route planning based on the B-spline curve was studied, and a collision free route planning algorithm was put forward, which could satisfy the terminal constraints and provide the technical support for the following trajectory generation.
3. Trajectory generation based on the Differential Flatness Theory. The aircraft trajectory planning with nonholonomic constraints was discussed and the trajectory generating procedures, based on differential flat trajectory, were presented. In addition, the flat output was determined by judging the flatness of the aircraft dynamics and the kinematics model. Based upon its template path planning, B-spline curve was used as the flat output in a parametric way, transforming the optimal control problem into a general nonlinear programming problem, which ensured the generating trajectory enforceable, and reduced the difficulty of the problem solution.
Through the application in the project, this method is able to satisfy the nonholonomic constraints of the aircraft, terminal constraints and other constraints, and combine the tactical and the techniques intelligently. As a result, it may solve the problem of aircraft trajectory planning effectively in the air-to-ground attacking mission.
论文为了降低问题的复杂度,针对轨迹规划中的动力学微分方程这一非完整性约束,引入了微分平坦理论,提出了一种分层递阶规划求解方法——在基于B样条的样板航迹规划的基础上,根据微分平坦理论将最优控制问题转化为非线性规划进行求解,保证了生成轨迹的可执行性。论文的主要研究内容如下:
1、问题分析与建模。对飞行器对地打击任务进行了深入分析,总结了轨迹规划中所涉及的各种约束条件,并提出了相应的指标,在此基础上,对轨迹规划进行了最优控制形式的一般化描述,建立了以过载和滚转角为控制量的动力学模型、威胁模型等作为轨迹规划的约束条件,为进一步研究轨迹规划方法奠定了基础。
2、样板航迹规划技术研究。通过对飞行器对地打击任务中惯常采用的战术机动进行分析,从中提炼出一系列基本动作和空对地打击的一般模式(即战术模板)。论文选取两种典型的对地打击战术模板,进行了基本动作分解和参数化模型描述。在此基础上,研究了基于B样条的样板航迹规划,提出了一个能满足终端约束的避障航迹规划算法,从而为后续的轨迹生成提供了技术支撑。
3、基于微分平坦理论的轨迹生成研究。针对具有非完整性约束的飞行器轨迹规划问题,设计了基于微分平坦理论的轨迹生成步骤。并对飞行器的动力学和运动学模型进行了平坦属性的判定,确定了平坦输出。在基于B样条的样板航迹规划的基础上,使用B样条参数化平坦输出,将最优控制问题转化为一般非线性规划问题,保证了生成轨迹的可执行性,同时降低了问题求解难度。
通过在项目中的应用,该方法能满足平台本身的非完整性约束、战术终端约束等各种约束条件,并科学地将飞行器对地打击任务中战术和技术进行有机结合,较好地解决了飞行器对地打击任务中轨迹规划问题。
Trajectory planning, as an integral part of the mission planning technology, can help to improve the aircrafts' flying qualities to meet the established mission requirements, and effectively enhance the success rate of combat aircraft attacking. Being an optimal control problem, aircraft trajectory planning is restrained by differential equations, algebraic equations and inequalities, and it aims to find the functional extremum. Consequently, the immediate solution is difficult to imagine.
In order to reduce the complexity of the problem, the thesis introduces the differential flatness theory to serve the dynamical equations, the nonholonomic constraint, and proposes a hierarchical programming approach. With the basis of template route planning based of B-spline curve, the optimal control problem were changed into a general nonlinear programming problem and got the solution in the framework of the differential flatness theory, which guaranteed the enforceability of the generated trajectory. The main contents are as follows:
1. Problem analysis and modeling. With the analysis of the aircraft combat mission and the summary of the constraints of the trajectory planning involved, the thesis proposed the objective functions of the trajectory planning. On this basis, the trajectory planning problem was modeled as a general nonlinear programming one, comprising the aircraft dynamic model, described by the overload and roll angle as the decision variables, and the threat model, etc., which constituted the constraints of the trajectory planning, and laid the foundation for further study of the method of trajectory planning.
2. Template route planning technology. Having analyzed the commonly-used tactical motivation of the aircraft combat missions against the ground, the paper extracted a series of basic maneuver and the general pattern of air-to-ground combat (i.e. tactical template). Two typical tactical templates were selected to execute the maneuver decomposing and numerical value description. Then the template route planning based on the B-spline curve was studied, and a collision free route planning algorithm was put forward, which could satisfy the terminal constraints and provide the technical support for the following trajectory generation.
3. Trajectory generation based on the Differential Flatness Theory. The aircraft trajectory planning with nonholonomic constraints was discussed and the trajectory generating procedures, based on differential flat trajectory, were presented. In addition, the flat output was determined by judging the flatness of the aircraft dynamics and the kinematics model. Based upon its template path planning, B-spline curve was used as the flat output in a parametric way, transforming the optimal control problem into a general nonlinear programming problem, which ensured the generating trajectory enforceable, and reduced the difficulty of the problem solution.
Through the application in the project, this method is able to satisfy the nonholonomic constraints of the aircraft, terminal constraints and other constraints, and combine the tactical and the techniques intelligently. As a result, it may solve the problem of aircraft trajectory planning effectively in the air-to-ground attacking mission.
引文
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[2] H. Choset, K. Lynch, S. Hutchinson, et al. Principles of Robot Motion: Theory, Algorithms, and Implementation[M]. Boston: The MIT Press, 2005.
[3] R. Siegwart, I. Nourbakhsh. Introduction to Autonomous Mobile Robots[M]. Boston: The MIT Press, 2004.
[4] H. Seywald. Trajectory Optimization Based on Differential Inclusion[J]. Journal of Guidance, Control, and Dynamics, 1994, 17(3): 480~487.
[5] T. Betts. Survey of Numerical Methods for Trajectory Optimization[J]. Journal of Guidance, Control, and Dynamics, 1998, 21(2): 193~207.
[6]税清才,方振平.非线性数学规划在飞行力学中的应用[J].飞行力学, 1995, 13(3): 29~36.
[7] Robert Bibeau, David Rubenstein. Trajectory Optimization for a Fixed-Trim Reentry Vehicle Using Direct Collocation and Nonlinear Programming[C]. // Proceeding of AIAA Guidance, Navigation and Control Conference and Exhibit, Denver, CO. 2000.
[8] Nirmal Baran Hui, Dilip Kumar Pratihar. A Comparative Study on Some Navigation Schemes of a Real Robot Tackling Moving Obstacles[J]. Robotics and Computer-Integrated Manufacturing, 2009, (25): 810~828.
[9] A. Elfes. Using Occupancy Grids for Mobile Robot Perception and Navigation[J]. Computer, 1989, 22(6): 46~57.
[10] L. Huang. Velocity Planning for a Mobile Robot to Track a Moving Target—a Potential Field Approach[J]. Robotics and Autonomous Systems 2009, (57): 55~63.
[11] R. Volpe, P. Khosla. Manipulator Control with Super-Quadric Artificial Potential Functions: Theory and Experiments[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1990, 20(8): 1423~1436.
[12] Yunong Zhang, Zhiguo Tan, Ke Chen, et al. Repetitive Motion of Redundant Robots Planned by Three Kinds of Recurrent Neural Networks and Illustrated with a Four-Link Planar Manipulator's Straight-Line Example[J]. Robotics and Autonomous Systems, 2009, (57): 645 ~ 651.
[13] Ioannis Nikolos, Kimon Valavanis, Nikos Tsourveloudis, et al. Evolutionary Algorithm Based Offline/Online Path Planner for UAV Navigation[J]. IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, 2003, 33(6): 898~812.
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