Networking is the future development direction of space laser communication. According to the structural characteristics of optical transceiver in laser communication network, a numerical solution model for the line-of-sight stability of multi-directional mirrors based on Picard algorithm is established. The model can be converted into a numerical iterative program, which can be applied to the optical transceiver coarse tracking intelligent control system. Aiming at the numerical solution error caused by multi-axis joint motion coupling, a method of error compensation based on depth feedforward neural network is designed. The computer simulation results show that the Picard algorithm has high accuracy in the process of single-axis motion calculation. In the multi-axis joint movement, the application of depth feedforward neural network improves the accuracy of Picard algorithm.