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在研究机器人广义位姿的基础上,依据从基坐标系列任一坐标系的旋转变换可以通过绕基坐标系中的瞬时转动轴的等效旋转来实现的原理,提出用等效角位移矢量来描述机器人姿态以及用姿态旋量及其 Pl(u|¨)cker线坐标来描述机器人的位姿.依据对偶数代数理论中关于三维欧氏空间中的有向直线与三维对偶空间中的点具有一一对应关系的对偶映射原理,在对偶空间中对姿态旋量所映射的点进行规划,从而找到一种机器人位姿轨迹生成和运动分析新方法,文末算例说明上述原理和推导的正确性.
Based on the study of generalized pose of robots and based on the principle that the rotation transformation from any coordinate system in the base coordinate system can be realized by the equivalent rotation of the instantaneous rotation axis in the coordinate system of the base, an equivalent angular displacement vector The robot pose is described and the posture of the robot is described by the posture spin and its Pl (u | ¨) cker line coordinates.According to the theory of even number algebra theory that the directed straight line in 3D Euclidean space and the point in 3D dual space have One-to-one correspondence dual mapping principle, the points mapped by attitude rotation in dual space are planned to find a new method of trajectory generation and motion analysis of robots. The examples show the above principles and the correctness of the derivation .