Abstract: Motion parameterization of complex joint model is the foundation of virtual human motion simulation. The classical parameterization methods of 3D rotation, such as rotation matrix, Euler angle, and quaternion, which bear several drawbacks, cannot resolve the motion parameterization of complex joint model. Based on the improvement of exponential map, a novel motion parameterization method called Dual Exponential Map (DEM) which can depict translation and rotation, linear velocity and angular velocity simultaneously was proposed. The motion description as well as parameters computation capabilities of the DEM were introduced. Finally a simulation on maintenance operation training was implemented. The experimental results illustrate that the DEM method bears powerful capability on derivation, solution to differential and ODEs, optimization control and interpolation.

Key words: Virtual Manufacturing Technology (VMT), joint model, motion parameterization, space description, Dual Quaternion (DQ)

摘要： 复杂关节模型的运动参数化是虚拟人动作仿真的基础，传统的旋转矩阵、欧拉角方法和四元数等参数化方法在运动描述方面存在一定缺陷，都不能很好地解决复杂关节模型的运动参数化问题。对指数映射方法进行改进，提出一种双指数映射(DEM)运动参数化方法，用于同时描述关节模型的平移与旋转、线速度与角速度。首先阐述其在运动描述和参数计算方面的能力，然后进行了维修操作训练仿真实验。研究结果表明了该方法在求导和微分、常微分方程求解、优化控制和插值拟合等方面具有较强的描述功能。

关键词: 虚拟维修技术, 关节模型, 运动参数化, 空间描述, 双四元数