基于四元数表示法的机器人基坐标系标定方法

Calibration method of robot base frame by quaternion form

在多机器人协同、运动学参数辨识和机器人离线编程等作业任务下,需要标定出机器人基坐标系在世界坐标系中的精确位姿.提出和实施了一种利用四元数表示法进行机器人基坐标系精确标定的方法.利用指数积公式,建立机器人的运动学模型.利用外部测量设备,测量出5个不共面的工具中心点,并记录对应的机器人关节位形.以基坐标系位姿对应的旋转矩阵元素为变量,建立不相容方程组,并求出基坐标系位姿的初步齐次矩阵.由于测量误差和截断误差,初步齐次矩阵的旋转矩阵部分不能满足单位正交阵的性质.利用四元数的几何约束条件,建立罚函数形式的目标方程,将初步齐次矩阵进行正交化修正.通过一系列的实际机器人的标定试验,验证了该标定方法的正确性,并提高了机器人末端的定位精度.

The accuracy pose of robot base frame with respect to the world frame needs to be calibrated under the task of multi-arm cooperation, identification of kinematics parameter and off-line program of robot. An accurately calibration method of robot base frame using quaternion form was proposed and applied. The ki- nematic model of robot was established by the product-of-exponential formula. 5 tool center points （TCPs） , which were not coplanar, were measured with the external measuring device, and the corresponding robot joint configurations were also recorded. By considering the elements of rotational matrix corresponding to the base frame pose as the variables, a group of incompatible equations was set up, and the initial homogeneous matrix of the base frame pose was also obtained. However, due to the errors of measuring and truncation, the rota- tional matrix part of initial homogeneous matrix cannot satisfy the regulation of unit orthogonal matrix. Using the geometrical constraints of a quaternion, an objective equation by the form of penalty function was estab- lished, and the initial homogeneous matrix was orthogonalized. By a set of practical calibration experiments of robot, the validity of calibration method was verified, which improved the accuracy of the location of robot end.