Long-term motion prediction and dexterous capturing analysis for tumbling satellites

Accurate motion prediction of free-tumbling satellites is crucial for the success of capture operations. This paper proposes a two-step method to estimate the motion states and parameters of such satellites, thereby enabling precise long-term motion prediction. This paper begins with a measurement of the system's degree of observability, quantified through the Empirical Observability Gramian (EOG). Based on this measurement, a batch processing algorithm is first employed to estimate the satellite's constant parameters offline. Subsequently, an online filtering algorithm, utilizing a minimal state set, fine-tunes these parameters and estimates the motion states in real time. This integrated approach significantly enhances both convergence properties and estimation accuracy, particularly for systems with poor observability. Utilizing the predicted long-term motion of the satellite, a composite evaluation metric is formulated to identify the optimal capture point and moment. The base pose of the space robot is then adjusted to ensure that the optimal capture point lies within the manipulator's dexterous workspace, which is determined through a pre-constructed capability map. The effectiveness of the proposed method is demonstrated through both simulation and experimental results.