Modeling the formationkeeping control with multibody codes

Formation Flying control involves the computation of relative kinematics and dynamics among a number of orbiting platforms. Formations are not the only space application in which several components operate coordinately at the same time. "Multibody" is the scheme usually adopted to model the robotic arms of the space manipulators or large space platforms as the International Space station, and multibody can be also seen as a set of components orbiting together. A number of software codes have been developed during the years to represent and simulate this scheme, taking into account the differential forces acting on each member. This paper proposes to build on this effort to test a different way for evaluating the control of spacecraft formations. The formation spacecraft will be represented by the joints of the multibody. The links, represented as structural element with infinite stiffness, virtually reproduce the relative constraints in position and attitude among the platforms. The idea is to consider the orientation and the length of the links such that the joints (spacecraft) will actually assume the relative geometry which is the desired state at a given time. The forces and torques to be provided to the real spacecraft belonging to the formation are related to the reaction torques and forces which are provided at the joints in the corresponding multibody representation. These reactions can be easily computed by available multibody codes, and the values found can be applied to a standard orbital propagator to compute the dynamical behavior and to validate the approach. The advantage stays with the quick, easy computation of the inverse kinematics, which is routinely performed by multibody software. The solution should be useful to both the cases of keeping an already acquired configuration, like large distributed antennas virtually built by several spacecraft, as well as to the rigid reorientation of a formation, like in some astronomical missions.