A Minimum State Multibody/FEM Approach for Modelling Flexible Orbiting Space Systems

In the past the deployment of space structures has widely been analysed 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 should be represented by a combination between the NE and EL formulations. This can be obtained by taking the NE formulation for assembling the equation of motion into account and then by defining the ODE governing equations by using 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 behaviour 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