Trajectory optimization for rendezvous with bearing-only tracking

Abstract

In this paper the observability of bearing-only tracking is analyzed and the trajectory optimization algorithms to enhance the observability during the rendezvous are presented. Firstly, the relative dynamic model and measurement model are established, and the necessary and sufficient condition for observability when maneuvering is determined using the pseudo linear method. Then, the observability indices, such as the filter covariance matrix trace and the Fisher information matrix (FIM) determinant, are combined with the fuel consumption index to optimize the approaching trajectory. In order to keep the line-of-sight (LOS) aligned with the target and to ensure continuous observation, the attitude of the observer is adjusted synchronously during the rendezvous. Finally, the coordinated control of attitude and orbit for the observer is achieved by optimizing the thrust distribution of the onboard propulsion system. Numerical results demonstrate that the combined optimization of the observability and fuel consumption can generate an optimal control trajectory with high tracking accuracy. The simulation also presents how to choose the optimal relative weight of the two optimization terms, optimal rendezvous time and optimal docking point according to the practical requirements to get the best comprehensive performance of observability and fuel consumption.