螺旋矢量的优化算法设计

Design of optimization algorithm for screw vector

对偶四元数是统一描述一般性刚体运动的最简洁和最有效的数学工具,它的更新计算需要利用没有冗余约束的螺旋矢量来实现。螺旋矢量微分方程与旋转矢量微分方程具有相同的结构形式,借鉴后者的优化求解方法,设计了螺旋矢量的优化算法求解方案。选取经典螺旋运动作为运动环境,分析不可交换性误差产生的原因,在定义了误差准则的基础上,推导了螺旋矢量优化求解过程,求出了各子样优化算法的系数。结果表明,螺旋矢量优化算法系数的对偶部为零,实部与相应子样数旋转矢量优化算法的系数相同,验证了公认观点的正确性。

The update calculation of dual quaternion, a most concise and efficient tool to describe general motion of a rigid body, should be implemented by using screw vector which has no redundant constraints. The solving program of optimization algorithm for screw vector referring to the optimizing method of rotation vector is presented. Under the classical screw motion selected for optimizing environment, the cause of noncommutativity error is ana- lyzed and the error criterion for optimization is defined. Based on the error criterion, the optimizing process for solving screw vector is developed and consequently optimal coefficients for cases of the number of sample being less than or equal to 4 are obtained. The results show coefficients in the screw vector optimization algorithm just are identical to coefficients in the rotation vector optimization algorithm with the same number of sample. This conclusion verifies correctness of the generally accepted view.