Equations of Motion of Free-Floating Spacecraft-Manipulator Systems: An Engineer's Tutorial

Abstract

The paper provides a step-by-step tutorial on the Generalized Jacobian Matrix (GJM) approach for modeling and simulation of spacecraft-manipulator systems. The General Jacobian Matrix approach describes the motion of the end-effector of an underactuated manipulator system solely by the manipulator joint rotations, with the attitude and position of the base-spacecraft resulting from the manipulator motion. The coupling of the manipulator motion with the base-spacecraft are thus expressed in a generalized inertia matrix and a GJM. The focus of the paper lies on the complete analytic derivation of the generalized equations of motion of a free-floating spacecraft-manipulator system. This includes symbolic analytic expressions for all inertia property matrices of the system, including their time derivatives and joint-angle derivatives, as well as an expression for the generalized Jacobian of a generic point on any link of the spacecraft-manipulator system. The kinematics structure of the spacecraft-manipulator system is described both in terms of direction-cosine matrices and unit quaternions. An additional important contribution of this paper is to propose a new and more detailed definition for the modes of maneuvering of a spacecraft-manipulator. In particular, the two commonly used categories free-flying and free-floating are expanded by the introduction of five categories, namely floating, rotation-floating, rotation-flying, translation-flying, and flying. A fully-symbolic and a partially-symbolic option for the implementation of a numerical simulation model based on the proposed analytic approach are introduced and exemplary simulation results for a planar four-link spacecraft-manipulator system and a spatial six-link spacecraft manipulator system are presented.

Kinematic Indices of rotation-floating space robots for on-orbit servicing

“…The coupled dynamics of a spacecraft-manipulator system have been extensively studied in the available literature [15] [16]. To address the issue of control of rotation-floating robots, we propose to extend the free-floating dynamic model detailed in [5] by adding the states of the kinetic moment exchange actuators. By using the Lagragian approach, we just need to express the kinetic energy of the attitude actuator and add the term obtained by derivation of its kinetic energy according to the system state and time.…”

“…In this paper, one serial manipulator with n-DOF is mounted on the satellite. However, multiple manipulators and manipulator with complex kinematic could be considered as well [5]. Consequently, Lagrange equation derivation of (3) leads to the following dynamics equation of motion for spacecraft with n r reaction wheel:…”

“…Based on this decomposition of the spacecraft base inertia matrix H 0 , this relation can be inversed in analytic way by using a the Banachiewicz inversion formula [17] which yields to the following expression of H −1 0 as detailed in [5]:…”

“…More recently Wilde and al. proposed in [5] to distinct three additional modes to fully covering all possible spacecraft maneuvers: rotation flying and translation flying modes which are sub-modes of the free-flying and require reaction-jet thrusters. These actuators allow to actively control the angular and/or linear momentum of the system but consume fuel and their using shorten the lifespan of the spacecraft.…”

Quaternion-Based Constrained Dynamics Modeling of a Space Manipulator with Flexible Arms for Servicing Tasks

“…Servicing dedicated spacecraft equipped with robotic manipulators, which we refer to later as the space manipulators become more widely used in variety of applications like on-orbit servicing, asteroid mining, active space debris removal and space mining. Examples of such missions can be found in [1] and references there. Servicing spacecraft equipped with the space manipulator is a complex dynamic system embedded into disciplines of mechanics and aerospace engineering.…”