室内四索牵引定位与索长求解

Indoor four-cable traction positioning and cable length solution

室内飞机维修四索牵引摄像系统因工作特性定位时系统处于静力平衡状态,不考虑运动时的动力特性,而着重考虑系统内部扰动对索长的影响。为减小悬索索长对定位误差的影响,提高四索牵引系统定位精度,实现悬索可达范围最大化,基于悬链线原理,通过对位置逆解分析,在空间O-XYZ坐标系中推导出悬索水平分力与索长之间的关系式,并建立四索悬链线模型。利用序列二次规划(SQP,sequential quadratic programming)算法优化悬索水平分力,使悬索拉力均匀分布,迭代求解非线性方程组得到最优化索长。通过仿真计算验证了该方法的有效性和可行性,计算过程清晰简便,四索索力分布均匀,避免了索力超限和虚牵现象。

Due to the working nature,the four-cable traction camera system in indoor aircraft maintenance is in static equilibrium when positioning,and the influence of internal disturbance on the cable length is mainly considered regardless of the dynamic characteristics in motion.In order to reduce the positioning error caused by the length of the suspension cable,improve the positioning accuracy of the four-cable traction system and maximize the reach range of the suspension cable,the relationship between the horizontal component of the suspension cable and the cable length is derived in the spatial O-XYZ coordinate system and a four-cable catenary model created based on the catenary principle and through the inverse solution analysis of the position.The SQP(sequential quadratic programming)algorithm is used to optimize the horizontal component of the suspension cable,so that the suspension cable tension is evenly distributed,the nonlinear equations are iteratively established to obtain the optimized suspension cable length.The simulation calculation shows that the algorithm has high accuracy,fast convergence and clear and simple calculation process.The cable force of the four cables is evenly distributed,which avoids the phenomenon of over-limit cable force and virtual traction.