欧拉角参数表示下姿态的二阶运动奇异性

由于姿态空间的拓扑结构可知,空间刚体姿态任意三参数表示的奇异性是不可避免的.通过求得关节空间和姿态空间的角速度和角加速度之间的关系,进而得到在12种欧拉角参数表示下,姿态在某些位形空间上都具有二阶运动奇异性.在获得各种欧拉角表示的一阶和二阶奇异位形后,在工程控制中就可以根据实际需要选择适当的欧拉角以避开这些奇异位形,避免驱动机构在输出动量和力矩时造成混乱.

The Second-order Kinematic Singularity of Orientation in Euler Parameters Representation

Because of the topology structure of orientation space, singularity of orientation of rigid body moving in space is unavoidable for any of the three parameters representation. There all exists the second-order kinematic singularity configuration in 12 kinds Euler angles parameters when the relationships of angular velocity and angular acceleration between joint space and configuration space are obtained. After gaining all kinds of the first-order and second-order singularity configuration showed by Euler angles , in the engineering control proper Euler angles are chosen to avoid these singularity configuration according to the actual need . So it can avoid the confusion between the output momentum and the torque for the driving mechanism.