Singularity-avoidance Trajectory Generation for Roll-pitch Gimbals Using Kinematic Thresholds and Reference Dynamics

This study presents a new singularity-avoidance trajectory generation algorithm for roll–pitch gimbal seekers. Two kinematically derived thresholds, namely the minimum allowable pitch angle and the trajectory offset, were introduced to classify local target motion and determine the appropriate control strategy between predictive roll angular rate shaping and roll angle alignment in conjunction with pitch angle optimization. The second order reference dynamics was incorporated to eliminate discontinuities that typically arise during mode transitions, ensuring smooth and stable command generation for the gimbal controller. To evaluate the algorithm under various simulated target conditions, target trajectories with varying speeds, minimum approach angles, and turning behaviors were generated using both outward- and inward-bending hyperbolic motion. The proposed method consistently maintained target lock without field-of-view violation across all scenarios, including those involving rapid direction changes near the singularity. These results demonstrate that the algorithm improves tracking stability and general applicability under the considered simulation conditions, suggesting its potential for practical implementation in roll–pitch seeker systems.