Target-tracking control technology is extensively employed in several fields, including aerospace, satellite remote sensing, and laser communication. The Risley-prism system enables the direction of the beam to be altered or the visual axis to be adjusted by controlling the rotation angle of the prism. Compared with alternative mechanical beam-pointing mechanisms, such as gimbal and fast steering mirror mechanisms, the target tracking control system based on Risley-prisms exhibits several advantageous characteristics. These features include a compact structure, high reliability, and high pointing accuracy, which collectively provide the system with a wide range of potential applications. In the case of a traditional beam-pointing mechanism, the relationship between the pose adjustment of the actuator and target motion trajectory is characterized by intuitive linearity. However, there is a nonlinear relationship and strong coupling between the prism rotation angle and visual axis orientation of the Risley prism system, which makes it challenging to accurately determine the prism rotation angle via analytical means. Furthermore, conventional numerical methods have limitations in terms of accuracy and efficiency, which impede the advancement of research and practical applications of the Risley-prism system in target-tracking scenarios. In this study, we report a target-tracking method based on the Risley-prism system using a virtual system, whereby the spatial direction of the outgoing beam of the actual Risley-prism system is mapped. Our basic approach and discoveries provide useful insights into the design of pointing and tracking control systems based on Risley-prisms for time-varying optical targets.

A particle swarm-optimized target tracking method based on a virtual system was employed in this study. First, based on the nonparaxial ray-tracing method, a virtual Risley-prism system was constructed to map the spatial direction of the outgoing beam of the actual Risley-prism system. Subsequently, by combining the virtual system model projected by the actual two-prism system with the particle swarm algorithm, multiple possible prism rotation angles (particles) and their corresponding virtual pointing targets were calculated in parallel. Subsequently, if the estimation error between the outgoing beam-pointing of the virtual Risley-prism system and the target to be tracked was less than the actual error, then the actual prism rotation angle was replaced by the estimated prism rotation angle and applied to the actual Risley-prism system. In the next step, the prism rotation angle that best matches the target to be pointed at and tracked was selected based on the interoperability and information-sharing mechanism of the particle swarm algorithm. In addition, the prism angles of the experimental prototype Risley-prism system were adjusted to realize dynamic target tracking.

The prepared Risley-prism system based on the virtual system with the RPSO algorithm presents comparable performance for static target pointing in numerous simulations, and the final convergence accuracy of the proposed RPSO-based Risley-prism system approaches 5?10 mm (Fig. 6). In addition, when tracking a moving target, the RPSO-based Risley-prism system can converge to the global optimum more quickly than can the PSO-based method, exhibiting a faster convergence speed and higher convergence accuracy (Fig. 8). The results of the simulation analysis show the effect of particle population size on virtual system-based target tracking methods: larger particle populations lead to faster convergence but increased computation (Fig. 9). In the simulation of continuously tracking target points, the estimation error of the virtual system and real error of the Risley-prism system can still converge, indicating that the proposed algorithm still has a stable tracking effect when tracking continuously changing dynamic targets (Fig. 10). The pixel deviation distribution of the 60 target pointing tests demonstrates the excellent performance of the proposed method: the mean pointing error and standard deviation are 9.43 and 10.14 pixel, respectively (Fig. 13). In the static target pointing experiments, the proposed method demonstrates better pointing performance. The fitted circle radius of the pointing error distribution of the proposed method is smaller than that of the two-step method, and the average pointing error, root mean square error, and maximum pointing error of the proposed method are all smaller than those of the two-step method. During the dynamic tracking experiments, the Risley-prism system sequentially achieved the tracking of three targets with a final pixel error of approximately 13.04 pixel, thus demonstrating the excellent performance of the proposed target-tracking method in the application of continuous target tracking. The performance difference in dynamic target pointing tracking shows that the performance of the proposed RPSO-based algorithm is superior to that of the two-step method. The average tracking errors (in pixel) and the root-mean-square (RMS) tracking errors of the two algorithms are as follows: 10.64 pixel and 11.22 pixel (two-step method) and 8.113 pixel and 9.429 pixel (proposed method), respectively.

This study successfully develops a new Risley-prism system-based target tracking method by introducing a combination of particle swarm optimization and a virtual system into an actual Risley-prism system. The particle swarm method is used to adjust the Risley prism angle and achieve target tracking in the Risley-prism system. To maintain a certain degree of correlation between the virtual and actual systems, a virtual target is constructed based on the deviation of the center of the camera field-of-view from the center of the actual target to be tracked in the x- and y-directions. The error feedback information used to estimate the prism angle in the virtual system is consistent with the tracking error fed back from the actual system, and the prism angle is calculated based on the dynamic changes of the target to be tracked. The simulation and experimental results demonstrate the feasibility of the method for achieving target tracking. In the static target experiments, the average pointing error and standard deviation are 9.43 pixel and 10.14 pixel, respectively, whereas in the dynamic target tracking experiments, the average tracking error is approximately 16 pixel at the three key positions. The proposed method provides a promising method for realizing the target pointing and dynamic target tracking of rotating Risley-prism systems with a wide range of applications.