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.