基于李群的水下航体动力学建模及最优控制  

Lie Group Modeling and Optimal Control of Underwater Vehicle

作　　者：白龙[1] 董志峰[1] 戈新生[2] 

机构地区：[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

出　　处：《系统仿真学报》2016年第5期1150-1157,共8页Journal of System Simulation

基　　金：国家自然科学基金(11472058)

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。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.

关 键 词：水下航体 李群 变分法 能量最优 伪谱法 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]