Risley prisms appear to be a promising solution to high-accuracy pointing and tracking. To improve the pointing accuracy of achromatic Risley prisms, an appropriate mathematical model is established, and the forward and inverse solutions are proposed. Focusing on the sources of systematic errors, an optimization method based on a genetic algorithm is proposed to identify the parameters of the physical model, including wedge angles, refractive indexes, and installations. Finally, the experimental platform is established. The pointing accuracy and the size of the blind zone are tested to prove the validity of the method. Experimental results show that the proposed method is effective to reduce the influence of manufacturing, installation, and measurement errors. The optimized pointing accuracy has been improved significantly. Within the maximum deflection angle of 3°, the maximum pointing error is reduced from 33 arcsec to less than 1 arcsec. And the angular dynamic range is found to be greater than 43 dB, able to meet the needs of the majority of applications. In addition, the test of the blind zone shows that the optimized parameters are consistent with the actual system.

Characterized by its compact structure and fast response, the rotational double prisms system is broadly applicable for high-precision pointing and tracking. In particular, closed-loop tracking technology based on an image detector can overcome beam deflection errors caused by prism parameter and target-guiding errors. However, the rotations of each prism affect beam deflection angles in both the x- and y-directions by different amounts in different areas. Therefore, aimed at this problem of the tracking error being coupled to the rotation angle of the two prisms, we proposed a real-time sector selection closed-loop tracking method by inputting error value feedback from the detector and outputting the adjustment values of the prisms. This method can simultaneously close-loop the error signal in two directions and is not limited by the target distance. We established a test platform to verify the proposed method. The test results showed that the proposed method can continuously track moving targets across different areas of a field of view for an extended period. When the maximum moving speed of the target was 0.32 deg / s, the root mean square tracking error of the noncentral area was <1 arcsec. The simulated and experimental results confirmed the effectiveness of this method.

In this paper, a robust control based on disturbance observer is proposed to improve the tracking accuracy of the Risley prism system (RPS). Applying the flexible thin-wall ring mechanism in the RPS causes a series of tracking and pointing challenges. Disturbances such as friction, shaft deformation, and model perturbation significantly deteriorate the tracking and pointing accuracy of the RPS. Two different observer-based control methods are proposed to guarantee the tracking precision of the RPS. Moreover, the disturbance observation and compensation (DOC) performance of the proposed methods is analyzed and compared. Finally, simulation and experiment results indicate that the proposed control methods, especially the DOC-expanded state observer control mode, obtain the best performance for disturbance rejection in the RPS.

In this paper, a cascade double-loop control (DLC) combined with modeling compensation methods is proposed to improve the tracking precision of the multiaperture imaging system (MAIS). The application of the flexible thin-wall ring mechanism in the coupling rotating prism (CRP) system causes a series of tracking and pointing challenges. Disturbances such as friction, shaft deformation, and model perturbation significantly deteriorate the tracking and pointing accuracy of the CRP. Two different modeling compensation methods that are interfaced with classical DLC are proposed to guarantee the tracking precision of the MAIS. Moreover, the disturbance observation and compensation performance of two different modeling compensation methods are analyzed and compared. Finally, simulation and experiment results indicate that the proposed control methods, especially model compensation based on speed close-loop control, obtain the best performance for disturbance rejection in the MAIS.

The Risley prism system offers advantages such as compact structure and excellent dynamic performance, making it suitable for installation on static and motion platforms for target acquisition, aiming, and tracking. This paper presents a strapdown line-of-sight (LOS) stabilization method for the Risley prism system on motion platforms. The method establishes the coordinate transformation between the Risley prism and the motion platform. Real-time platform attitude angles from an inertial measurement unit (IMU) are used to compute the direction cosine matrix, which, combined with the coordinate transformation, determines the target’s actual guided position in the Risley prism’s coordinate. The Risley prism’s rotational angles are then calculated based on the target’s actual guided position to ensure LOS stability and capture the target. After LOS stabilization, an image-based closed-loop tracking cascade control system that integrates a Risley prism and a fast steering mirror with a single image detector (IBCLTCR-F), is used to enable fast and high-precision target tracking. Experimental results demonstrate that the proposed method achieves disturbance rejection of −32.8 dB, −28.8 dB, and −17.3 dB for platform disturbances at 0.05 Hz, 0.2 Hz, and 0.5 Hz, respectively. Furthermore, compared to the Risley prism system, the IBCLTCR-F system improves the dynamic response capability of target tracking in the nonlinear region by a factor of 10 and reduces the tracking error by 70%.

Image-based closed-loop tracking (IBCLT) is an important part of the process of target tracking. The Risley prism system has a unique advantage in improving the target tracking ability because of its compact and lightweight structure. Compared with traditional target tracking equipment, the Risley prism system has two difficulties in the process of IBCLT. First, the Risley prism is a complex coupling system of double input and double output. Second, the Risley prism itself is a nonlinear system. These problems lead to decrease in dynamic response and inconsistent target tracking capabilities. Thus, this paper proposes a method to implement multivariable decoupling and reduce the nonlinear effect. First, the boresight error of IBCLT is decoupled to the azimuth and elevation directions by the rotation matrix error-decoupling (RMED) method. Second, the gains of IBCLT in azimuth and elevation directions are independent variables that comes from two functions of the target elevation angle. The experimental results show that the IBCLT error deviation of different static targets in the field of view is within 0.025 arcsec, which is 70% lower compared with the fixed gain method. Furthermore, the steady-state error deviation of moving targets is controlled within 2.5 arcsec. These experimental results prove the feasibility and effectiveness of the proposed method.