Laser 3D projection technology is a key technique for achieving fast and accurate positioning of components and enabling digitalized precise assembly. This technology has greatly improved the accuracy and efficiency of production assembly. The prediction accuracy of the mirror deflection voltage in a laser 3D projection system directly affects the projection precision. The prediction accuracy of the mirror deflection voltage in a laser 3D projection system is mainly influenced by the internal parameters of the dual-axis mirror system, including the mirror deflection angle and the perpendicular length of the axis of rotation, denoted as e. In order to reduce the comprehensive nonlinear errors caused by the deviation angle deviation of the laser 3D projection system's galvanometer and the errors in the calibration of the rotation axis's perpendicular line based on the galvanometer deviation angle, and achieve high-precision auxiliary assembly for the laser 3D projection system, this paper presents a laser 3D projection galvanometer deflection voltage prediction model based on the Poisson Remora Optimization Algorithm-Back Propagation (PROA-BP). The model predicts the numerical value of the galvanometer deflection voltage using the unit vector of the laser emission direction as input. By combining the Poisson Remora Optimization Algorithm (PROA) with the Back Propagation (BP) neural network, the PROA-BP model addresses the problem of BP neural networks often getting trapped in local optima. It utilizes the BP neural network to couple and compensate for the nonlinear errors of the laser 3D projection system, thereby improving the accuracy of the galvanometer deflection voltage prediction. Through debugging and comparison, the PROA-BP neural network parameters are determined. The PROA initialization population size is 87, and the BP neural network has one hidden layer with 12 neurons. Training comparisons are conducted between the PROA-BP neural network, PSO-BP neural network, and BP neural network. The Mean Square Error (MSE) and Mean Absolute Error (MAE) of the PROA-BP model are 41.2% and 62.4% of the PSO-BP neural network, and 22.2% and 50.7% of the BP neural network, respectively. This demonstrates that the proposed algorithm yields smaller errors in the prediction of the galvanometer deflection voltage compared to the PSO-BP and BP neural networks, resulting in higher projection positioning accuracy and better fit for the nonlinear errors. Regarding the traditional model for laser 3D projection, and the PROA-BP model for predicting the galvanometer deflection voltage, projection simulations are performed. The Euclidean distance between the theoretical projection points and the actual projection points in the simulation is defined as the projection positioning error. The maximum projection positioning error of the traditional laser 3D projection model is approximately 0.5 mm, while the maximum projection positioning error of the PROA-BP model is approximately 0.35 mm. An experimental verification platform is set up to conduct projection experiments using the PROA-BP model for predicting the galvanometer deflection voltage. The experimental results show that the model achieves a projection positioning accuracy of approximately 0.35 mm, which is approximately 30% higher than the accuracy of the traditional laser 3D projection model. The model effectively couples and compensates for the comprehensive nonlinear errors caused by the deviation angle deviation of the galvanometer and the errors in the calibration of the rotation axis's perpendicular line based on the galvanometer deviation angle. It enables higher-precision auxiliary assembly and is suitable for most laser projection positioning scenarios, providing a new approach for constructing laser 3D projection models.