Hybrid Modeling Technique Applied to NASA's Magnetospheric MultiScale (MMS) Mission TableSat Generation IB (TableSat IB)

The NASA Magnetospheric MultiScale (MMS) Mission, scheduled for launch in 2014, will use four spacecraft in a tetrahedral formation for its scientific mission to study the interaction of solar winds with Earth’s magnetosphere. Each of the spacecraft is spinstabilized and is equipped with several wire booms, up to 60 m in length. The flexible nature of the MMS spacecraft requires accurate knowledge of the boom and bus dynamics for proper spacecraft (and spacecraft constellation) control. This paper investigates a new hybrid algorithm for obtaining the rigid bus angular rates of a prototype of a spin-stabilized spacecraft with flexible appendages. The method combines Euler’s moment equations to propagate the bus dynamics, while its inertia tensor is updated using a Finite Element Model (FEM) approach to model the flexible appendages. The proposed technique is applied to an MMS spacecraft experimental test bed, MMS TableSat Generation IB. Simulation results show promising results, exhibiting the expected qualitative behavior of boom oscillation. However, standing issues exist and are left for future work. The NASA Magnetospheric MultiScale (MMS) Mission, scheduled for launch in 2014, will use four spacecraft in a tetrahedral formation to collect measurements of and conduct research regarding the interaction of the Sun’s solar winds with the Earth’s magnetosphere. These four s/c are spin-stabilized and must maintain a tetrahedral formation of varying dimensions to obtain 4-D structures (3-D space and time) of plasma magnetic reconnection. In order to accomplish this study each spacecraft is equipped with electric field sensors, which are attached to four 60 m Spin plane Double-Probe (SDP) wire booms and two 12.5 m axial plane Double-Probe (ADP) booms. These flexible booms are of primary focus due to their length and how they affect the overall dynamics of the MMS s/c. As such, there is much interest in analyzing the resulting s/c dynamics and associated flexible boom dynamics under spin rate and nutation control. The University of New Hampshire’s Advanced Controls Lab (ACL) is currently conducting research on the gyroless spin rate and nutation observer-based control, as well as the boom dynamics of the MMS mission s/c. As such, modeling the interaction between the flexible booms and the rigid bus of the MMS spacecraft as well as its overall motion are of interest here. To this end, the UNH ACL has constructed a series of table top experimental test beds (MMS TableSats) for s/c dynamics and control and flexible s/c structure analysis. TableSat I, the first generation of TableSats, is a limited 3-DOF rotation (full spin and limited nutation) prototype (Figure 1). The current goal of this stage of research is to be able to predict the dynamics of the flexible MMS spacecraft using a method that is both accurate and computationally efficient. In so doing, this paper proposes a hybrid technique, using both Finite Element Modeling (FEM) combined with modeling using 3-D rigid body dynamics, to model the overall dynamics of the MMS TableSat IB experimental platform. The final goal is to use the hybrid modeling technique to predict the dynamics of the actual MMS spacecraft during safe mode, science mode, and orbital transfers. There has been significant amount of research performed in this area using multiple techniques. Some of the techniques include modeling the appendages as a series of rigid links connected through ball and socket joints (Multibody Dynamics), using differential element rotations in the beam, and a combination of Multibody Dynamics with the Finite Element Method. 123 The technique proposed in this paper uses Euler’s moment equations to describe the motion of the overall spacecraft (s/c) while also using Finite Element Analysis to account for deflections in the booms. The dynamic Finite Element equations are solved through direct integration using the Central Difference Method. Euler’s moment equations are also solved using the Central Difference integration scheme. Validation of this technique (to be completed for future work) will be obtained using sensor data from the TableSat IB’s array of accelerometers and compared with the simulated model of the TableSat IB prototype.