We introduce rotation addition and motion addition. In this way, motions replace unit dual quaternions to represent rigid body movements in the 3D space. The infinitesimal unit is no longer needed. By means of motion addition, we formulate two classical problems in robot research, i.e., the hand-eye calibration problem and the simultaneous localization and mapping (SLAM) problem as motion optimization problems, which are actually real unconstrained optimization problems. In particular, it avoids to go through the unit dual quaternion operations.

翻译：我们引入了旋转添加和运动添加。 这样一来, 动议可以取代单元双四, 以代表 3D 空间的僵硬身体运动。 无限的微小单位不再需要了 。 通过运动添加, 我们提出了机器人研究的两个典型问题, 即手眼校准问题, 以及同时定位和绘图问题, 它们是运动优化问题, 这些其实是真正不受限制的优化问题 。 特别是, 它避免了通过单元的双四重操作 。