中文摘要：

针对末端效应器沿指定曲线运动时的逆向运动学（IK）求解提出了一种二阶数值方法,用末端效应器运动曲线的参数对关节角度运动曲线进行参数化,建立两条曲线之间的直接联系.利用关节角度向量的二阶泰勒展开递推求解末端效应器沿曲线运动时关节角度向量的变化.本方法在计算时引入了末端效应器运动曲线的微分几何属性,因此称为曲线逆向运动学.与传统的一阶类牛顿方法相比,曲线逆向运动学算法精度高,步长可控.对于逆向运动学控制中存在的奇异位形和冗余自由度,现有的算法对曲线逆向运动学算法同样有效,不需要重新设计算法.

英文摘要：

A second-order numerical method was presented for a category of inverse kinematics（IK） problem,in which the end-effector moves along specified curve.By parameterzing joint angle vector with the same parameter of the curve,the joint chain configuration update can be recursively computed by the second-order Taylor expansion of joint angle vector.The method was named as curve inverse kinematics because the differential geometric of the end-effector curve was considered.The second-order method presented was superior in precision and efficiency to conventional quasi-Newton method.Furthermore,the existing improvements of traditional IK method,such as weighted least-norm solution,can be cooperated with curve inverse kinematics harmoniously without any modification.