The stability of dual PSD based calibration system without its relative location to 3D forming of carbon fiber

The trajectory accuracy of the carbon fiber 3D forming robots is one of the key factors to ensure the quality of forming. It is well known that carbon fiber 3D forming robots have high repeatability but low accuracy. Compared to conventionally used calibration methods, dual PSD based methods provide a more efficient way to accurately calibrate the joint offsets of industrial robots. But the stability of dual PSD calibration system requires a strict proof in mathematics when the relationship between the robot base frame and the PSD frame is unknown. In this paper, by using an adaptive algorithm based on Lyapunov function, we can estimate the unknown parameters online without the parameters of the relationship. It is proved that the laser spots were stable to the desired positions on the dual PSD plane. The performance is confirmed by the simulations at last. The carbon fiber 3D forming robots positioning accuracy can reach 0.0222mm when the method proposed in this paper is used successfully. In this case, the quality of the forming can be assured.  Carbon fiber is a new type of industrial material and has been applied in many fields. The carbon fiber 3D forming robots can print various precise parts, so its' accuracy is of critical importance. The high precision automatic calibration system is a hot research topic to improve the precision of 3D forming robot localization. Dual PSD based robot calibration system has been proposed in reference  Due to that the position of the dual PSD in the robot's task space is unknown, the study on the stability of the unknown system is the primary problem of the calibration method. For the study on the stability of robot system, models and control approaches based on dual PSD have been proposed by Yunyi Jia, Chengzhi Su, et al.  and the simulation experiments have been carried out. Zhihui Deng, Yunyi Jia, et al.  have designed the dual PSD based adaptive alignment algorithm and have given a conclusion that the system is stable by simulation. Yantao Shen, Guoliang Xiang, et al.  have adopted visual servo control on a planar robot when the transformation matrix between the CCD camera frame and the robot base frame is unknown and have proved the stability of the system by Lyapunov method. In literature  Yantao Shen, Ning Xi, et al. have proposed the adaptive algorithm when the position of the PSD array is unknown in the robot task space, eventually have reached the conclusion that the laser spots were stable to the desired positions. For the stability of the system, in the literature [2 4] the corresponding control algorithms have been proposed, and the simulation results have been demostrated, however, the theoretical proof has not been discussed. In literature [5, 6] the discussion of the system stability was only on planar robots. There is no theoretical proof about the stability of the space robot calibration system based on dual PSD. The Lyapunov function based adaptive estimation law is designed and the large scale asymptotic stability of the calibration method have been proved in this paper, which lays a theoretical foundation for the study of the calibration system. International Symposium on Mechanical Engineering and Material Science (ISMEMS 2016)