基于李群的水下航体动力学建模及最优控制

系统仿真学报 ›› 2016, Vol. 28 ›› Issue (5): 1150-1157.

基于李群的水下航体动力学建模及最优控制

白龙¹, 董志峰¹, 戈新生²

1.中国矿业大学(北京)机电与信息工程学院,北京 100083;
2.北京信息科技大学机电工程学院,北京 100192

收稿日期:2015-05-15 修回日期:2015-08-17 发布日期:2020-07-03
作者简介:白龙(1988-),男,山东兖州,博士,研究方向为水下航体的动力学与控制建模;董志峰(1957-),男,吉林通化,博士,教授,博导,研究方向为机械系统动力学;戈新生(1957-),男,安徽合肥,博士,教授,博导,研究方向为动力学与控制。
基金资助:
国家自然科学基金(11472058)

Lie Group Modeling and Optimal Control of Underwater Vehicle

Bai Long¹, Dong Zhifeng¹, Ge Xinsheng²

1. School of Mechanical Electronic &Information Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China;
2. Mechanical & Electrical Engineering school, Beijing Information Science &Technology University, Beijing 100192, China

Received:2015-05-15 Revised:2015-08-17 Published:2020-07-03

摘要/Abstract

摘要： 研究了水下航体的李群建模法和高斯伪谱能量最优控制。先将水下航体简化为自由刚体,针对水下航体的大姿态转动角度存在的奇异性问题,引入李群和李代数,结合变分法和拉格朗日法,得到刚体动力学方程,将传统水动力表达式进行变换,得到基于李群的水下航体动力学方程。利用高斯伪谱法,将水下航体连续空间最优控制问题转化为非线性规划,在此基础上采用MATLAB进行求解。通过对水下航体进行能量最优控制的仿真结果的分析可知,所采用的最优控制方法较好的满足了约束条件,算法的求解精度较高,对初值的依赖性较小,所设计的计算方法可行。

关键词: 水下航体, 李群, 变分法, 能量最优, 伪谱法

Abstract: The Lie group modeling method and gauss pseudo-spectral energy optimal control of the underwater vehicle are in research. Simplifying the underwater vehicle to be a free rigid body, in view of the possible large attitude angle maneuvering of the underwater vehicle, importing the concept of lie group and lie algebra, combining with the variation method and Lagrange method, the dynamics equation of the rigid body was derived, translating the tradition expression of the hydrodynamic force to obtain the dynamics equation of the underwater vehicle base on the lie group. With the Gauss pseudo-spectral method, the continue space optimal control problem of the underwater vehicle was translated into the nonlinear programming solved with MATLAB. According to the simulation of the energy optimal control of the underwater vehicle under the constraints of boundary values, path and control, the optimal control method can satisfy the constraint conditions, the method has a high accuracy, has a low dependency to the initial value, and the calculation method is feasible.

Key words: underwater vehicle, Lie group, variational method, energy optimum, pseudo-spectral method

中图分类号:

TP391.9

白龙, 董志峰, 戈新生. 基于李群的水下航体动力学建模及最优控制[J]. 系统仿真学报, 2016, 28(5): 1150-1157.

Bai Long, Dong Zhifeng, Ge Xinsheng. Lie Group Modeling and Optimal Control of Underwater Vehicle[J]. Journal of System Simulation, 2016, 28(5): 1150-1157.

参考文献

[1] 边宇枢, 高志慧, 贠超. 6自由度水下机器人动力学分析与运动控制[J]. 机械工程学报, 2007, 43(7): 87-92.
[2] 孙尧, 赵新华. 水下超高速航行体的动力学建模及控制问题研究[J]. 哈尔滨工程大学学报, 2008, 29(2): 144-150.
[3] 白涛, 孙尧, 莫宏伟. 水下高速运动体空间运动的建模与仿真[J]. 系统仿真学报, 2008, 20(22): 6109-6113.
[4] 吴琪, 李晔. 基于四元数的欠驱动AUV的镇定控制设计[J]. 智能系统学报, 2014, 9(2): 186-191.
[5] 唐国元, 徐正武, 黄道敏, 等. 基于姿态控制力矩陀螺的水下航形体运动建模方法研究[J]. 中国造船, 2014, 55(2): 18-27.
[6] Nalin A Chaturvedi, Taeyoung Lee.Nonlinear Dynamics of the 3D pendulum[J]. Nonlinear Science (S0938-8974), 2011, 21(1): 3-32.
[7] Lee Taeyoung, McClamroch, N Harris. A Lie group variational integrator for the attitude dynamics of a rigid body with application to the 3D pendulum[C]// Proceedings of the IEEE International Conference on Control Applications (S1085-1992). USA: IEEE, 2005: 962-967.
[8] Taeyoung Lee, Melvin Leok, N HarrisMcClamroch. Dynamics of connected rigid bodies in a perfect fluid[C]// 2009 American Control Conference (S0743-1619). NEW YORK, NY 10017 USA : IEEE,345 E 47TH ST, 2009: 408-413.
[9] Nikolaj Nordkvist, Amit K Sanyal.A Lie group variational integrator for rigid body motion in SE(3) with applications to underwater vehicle dynamics[C]// 49^th IEEE Conference on Decision and Control (S0191-2216). USA: IEEE, 2010: 5414-5419.
[10] Jie Li.Geometric Pseudo-spectral Method on Lie Group with application to 3D Pendulum[C]// Proceedings of 3rd International Conference on Material Science and Information Technology (S1662-8985), STAFA-ZURICH, SWITZERLAND , Trans Tech Publications, Ltd, 2013, 3021-3029.
[11] Jie Li, Xiangjiang Xiao.Discrete Mechanics Modeling and Real-time Optimal Control Method Based on Lie Group Variational Integrator[C]// 2013 Chinese Automation Congress (S4799-0333). NEW YORK, NY 10017 USA : IEEE,345 E 47TH ST , 2013: 930-937.
[12] 徐少兵, 李升波, 成波. 最优控制问题的Legendre伪谱法求解及其应用[J]. 控制与决策, 2014, 29(12): 2113-2120.
[13] 孙勇, 张卯瑞. 求解含复杂约束非线性最优控制问题的改进Gauss伪谱法[J]. 自动化学报, 2013, 39(5): 672-678.
[14] 张友安, 王丽英. 基于伪谱法的自由采样实时最优反馈控制及应用[J]. 控制理论与应用, 2012, 29(9): 1151-1156.
[15] 刘英杰, 赵又群. 基于Gauss伪谱法的紧急避让汽车操纵逆动力学[J]. 机械工程学报, 2012, 48(22): 127-132.
[16] 童科伟, 周建平. Legendre-Gauss 拟谱法求解最优控制问题[J]. 航空学报, 2008, 29(6): 1531-1537.