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In order to solve the problem of high complexity and large amount of computation for kinematics of industrial robots, conformal geometric algebra (CGA) is introduced to the construction of kinematics model of industrial robots. In the forward kinematics solving process, the motion expressions of each joint are obtained by using the translation and rotation operators in CGA, and then the pose of the end-effector of the robot is obtained. In the process of solving the inverse kinematics, cross product of the constructed basic geometry is carried out to obtain the position of each joint node, the lines and planes through the joint node are constructed, the inner product is made in the CGA frame to obtain the cosine expression of all joint angles, and then all the solutions of the robot's inverse kinematics are solved. Finally, the MOTOMAN-HP20D 6-DOF industrial robot is used for example calculation, and the accuracy and effectiveness of the algorithm is verified by Matlab/Simulink software, which lays the foundation for the subsequent motion control of the robot.

In order to solve the problem of high complexity and large amount of computation for kinematics of industrial robots, Conformal geometric algebra （CGA） was introduced to the construction of kinematics model of industrial robots. In the forward kinematics solving process, the motion expressions of each joint were obtained by using the translation and rotation operators in CGA, and then the pose of the end-effector of the robot was obtained. In the process of solving the inverse kinematics, cross product of the constructed basic geometry is carried out to obtain the position of each joint node, and then the lines and planes through the joint node are constructed, and the inner product is made in the CGA frame to obtain the cosine expression of all joint angles, and then all the solutions of the robot's inverse kinematics are solved. Finally, the MOTOMAN-HP20D 6-DOF industrial robot was used for example calculation, and the accuracy and effectiveness of the algorithm was verified by Matlab/Simulink, which laid the foundation for the subsequent motion control of the robot.

The airborne array position and orientation measurement system (array POS) is a key device for high-resolution multi-dimensional real-time imaging motion compensation of military reconnaissance mapping. Abnormal values will appear in array POS inertial devices and measurement data in an environment of strong interference, which often leads to a decrease or even divergence in the combination accuracy. The existing detection methods based on innovation characteristics are only sensitive to measurement outliers, which are the abnormal data caused by the strong interference environment. In this paper, an improved innovation robust outliers detection method is proposed, which is valid for both measurement outliers and inertial device outliers. First, the improved outliers detection method based on the innovation of array POS is described. The gain matrix is adaptively adjusted by using the statistical characteristics of innovation. At the same time, the information distribution coefficient is adaptively adjusted by using the filtering performance of the sub filter, which realizes the detection and correction of measurement outliers. Then, the outlier detection method of inertial devices based on extrapolation prediction is added. The predicted value of the inertial device is extrapolated by the fourth-order difference method, and the outliers are recognized and eliminated by the adaptive threshold, which contributes to improving the robustness and accuracy of array POS. STD is selected in this paper to statistic the accuracy of array POS. Compared with the traditional federated Kalman filtering (KFK) methods, the accuracies of position, speed, heading angle and horizontal attitude angle of the left node and right node are all improved when there are outliers in the measurement data. Compared with the fault-tolerant federated combination method based on innovation characteristics, the accuracies of position, speed, heading angle and horizontal attitude angle of the left node and right node are all improved when there are abnormal values in the inertial device data.