3D trajectory reconstruction of moving points based on asynchronous cameras

Photomechanics is a crucial branch of solid mechanics. The localization of point targets constitutes a fundamental problem in optical experimental mechanics, with extensive applications in various missions of unmanned aerial vehicles. Localizing moving targets is crucial for analyzing their motion characteristics and dynamic properties. Reconstructing the trajectories of points from asynchronous cameras is a significant challenge. It encompasses two coupled sub-problems: Trajectory reconstruction and camera synchronization. Present methods typically address only one of these sub-problems individually. This paper proposes a 3D trajectory reconstruction method for point targets based on asynchronous cameras, simultaneously solving both sub-problems. Firstly, we extend the trajectory intersection method to asynchronous cameras to resolve the limitation of traditional triangulation that requires camera synchronization. Secondly, we develop models for camera temporal information and target motion, based on imaging mechanisms and target dynamics characteristics. The parameters are optimized simultaneously to achieve trajectory reconstruction without accurate time parameters. Thirdly, we optimize the camera rotations alongside the camera time information and target motion parameters, using tighter and more continuous constraints on moving points. The reconstruction accuracy is significantly improved, especially when the camera rotations are inaccurate. Finally, the simulated and real-world experimental results demonstrate the feasibility and accuracy of the proposed method. The real-world results indicate that the proposed algorithm achieved a localization error of 112.95 m at an observation distance range of 15–20 km.