A minimum state multibody/FEM approach for modeling flexible orbiting space systems

In the past the deployment of space structures has widely been analyzed by using multibody formulations. The two leading approaches are usually based on the Newton-Euler (NE) formulation and Euler-Lagrange (EL) formulation. Both of them present advantages and drawbacks. The ideal approach for describing multi-body systems can be represented by a combination between NE and EL formulations. This can be obtained by considering the NE formulation for assembling the equation of motion and then by defining the ODE governing equations with the use of a minimum set of variables. In this paper the authors present a mixed NE/EL formulation suitable for synthesizing optimal control strategies during the deploying maneuvers of robotic arms or solar arrays. The proposed method has two main characteristics: (i) the reference frame, which all the bodies motions are referred to, is a floating reference frame attached to the orbiting base platform body; (ii) it leads to a more organic formulation which makes a shifting from the NE to the EL formulations possible, through the use of a Jacobian matrix. In the present work this mixed formulation is derived to describe a fully elastic multi-body spacecraft. Furthermore the presented formulation, complemented with gravity, gravity gradient and generalized gravitational modal forces, will be used to study the dynamic behavior of an orbiting manipulator with flexible appendages. Finally a Reaction Null/Jacobian Transpose control strategy will be applied to control and deploy the robotic arms to grasp an orbiting flexible spacecraft.