Cross-Coupled Dynamics Modeling,Analysis And Ground Testing For On-Orbit Assembled Spacecraft Proximity Relative Motion

High-efficiency and low-cost on-orbit structural assembly technology has been a hot research topic in recent years.In order to improve the efficiency of on-orbit assembly missions,the size of the assembly module is designed to be as large as possible to reduce assembly frequency.In the process of transporting such large-scale modules to form a pre-assembled configuration by using space free-flying robots,the influence of the rigid-flexible coupling effect on the relative motion cannot be ignored;and the relative motion between spacecrafts is also affected by the attitude-orbit coupling effect.Then,the relative motion of the module transportation process is affected by the attitude-orbit coupling,the rigid-flexible coupling and the intrinsic relationship between the above two.The complex coupling effects directly affect the relative motion description accuracy of the module transportation process.However,current investigations on attitude-orbit coupling dynamics and rigid-flexible coupling dynamics have been carried out independently,and the influence of the cross-coupling effect between attitudeorbit coupling and rigid-flexible coupling on relative motion is not considered.Therefore,it is of great significance to carry out research on the cross-coupled relative dynamics modeling,analysis and ground testing of on-orbit assembled spacecraft.(1)The Newton-Euler equations based on dual algebra are extended from rigid-body spacecraft to rigid-flex coupled spacecraft in terms of components along the body-fixed coordinate system of the assembled spacecraft.The dual velocity screw,dual momentum,dual rigid-flex coupling coefficients and dual modal coordinates of the flexible modules are derived.The interaction among flexible vibration,relative attitude,relative position,and the dynamic cross-coupling effect caused by this interaction are investigated.The dual screw calculation methods of the space rigid-flex coupling system are provided.The specific expression form of the cross-coupling elements are proposed.(2)Aiming at the problem of describing the relative motion between two rigid-flex coupled spacecrafts in on-orbit assembly missions,a crosscoupling relative dynamics modeling method based on dual quaternion is proposed.On this basis,the relative cross-coulping dynamics models of the centroid point and the non-centroid point in terms of components along the centroid relative coordinate system are derived,respectively.The influence of cross-coupling effects on relative motion is analyzed.(3)Aiming at the problem of describing relative motion between two rigid-flex coupled spacecrafts with time-varying centroid and time-varying configuration,a cross-coupling relative dynamics modeling method considering time-varying factors is proposed.On this basis,the centroid timevarying and configuration time-varying relative cross-coupling dynamic models in terms of components along the arbitrary relative coordinate system are derived,respectively.The key influencing factors of cross-coupling effect are analyzed.(4)The ground test system of the three-degree-of-freedom motion of the rigid-flex spacecraft is designed and constructed.On this basis,the test method of the correctness of the cross-coupling dynamic model is proposed.The research shows that the cross-coupling relative dynamics model constructed in this paper in terms of components along the body-fixed coordinate system has the following application value:it is suitable for the relative motion description between two rigid-flex coupled spacecrafts of the mission scenario where the measurement quantity of the highprecision relative measurement sensor between spacecraft is used as the system state quantity.The main advantages of the model are:(1)It adopts the integrated representation form of dual screw,which is compact and concise in mathematical expression;(2)In the physical sense,the cross-coupling dynamics model can explain the phenomenon of complex coupled nonlinear relative motion with reference to the relative coordinate system.The description problem of the relative motion between two rigid-flex spacecrafts in terms of components along the body-fixed coordinate system is solved;(3)In engineering applications,the cross-coupling dynamics model can directly match the mounted coordinate system of the measurement sensor and actuator to reduce the calculation amount and system error caused by coordinate transformation.Model analysis and ground tests show that:(1)The relative trajectory between two rigidflex spacecrafts in terms of components along the body-fixed coordinate system is affected by the cross-coupling effect,and the impact is significantly greater than the module docking accuracy requirements.(2)Attitude maneuvering and relative reference selection are the main influencing factor of the cross-coupling effect in the module transportation process.The influence of the cross-coupling effect on the relative motion trajectory becomes more significant with the increase of the relative angle maneuvering range,and the distance from the origin of the relative coordinate system to the center of mass.