摘要
为研究船舶运动模拟器运动学正解的数值解法,建立其运动平台的数学模型,将运动学正解问题转化为非线性方程组的无约束最优化问题。分别采用数值迭代算法中的牛顿法、逆Broyden秩1法、BroydenFletcher-Shanno(BFS)秩2法及Broyden-Fletcher-Goldfarb-Shanno(BFGS)法进行求解,运用MATLAB编程并采用同一数值模型对这4种算法进行对比分析。分析结果表明:4种算法在工作空间内都收敛且数值稳定,BFS秩2法的迭代效率最高,BFGS法可用于奇异场合。通过仿真试验对各算法进行适当的修改,优化各算法的迭代效率并增加其对初值的鲁棒性,为位姿正解应用于实时控制场合提供理论指导。
In order to investigate the numerical methods for solving direct kinematics problems of the ship motion simulator, a mathematical model of the motion platform is established and the kinematics problems are transformed to the unconstrained optimization problem of the nonlinear equations. The Newton method, single rank inverse Broyden, rank-two BFS and BFGS method are used to solve the problem respectively and the MATLAB program is used to verify and compare the algo- rithms with the same numerical model. The analysis results show that all the algorithms are convergent and stable in the workspace, while rank-two BFS shows the highest efficiency. The BFGS method can be used in singular cases. Through ex- periments, all the algorithms are modified and optimized for better iterative efficiency and the robustness to initial valuses.
出处
《中国航海》
CSCD
北大核心
2017年第1期106-109,134,共5页
Navigation of China
