Attitude synchronization in spacecraft formations: Theoretical and experimental results
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This thesis addresses attitude synchronization in spacecraft formations. In addition to theoretical results the thesis presents the design and implementation of an experimental platform for spacecraft attitude synchronization. The first part of the thesis gives a general introduction to spacecraft formation flying with possible applications and current proposed and scheduled missions, and background information on relevant related work presented in the literature. We also give some necessary mathematical preliminaries, included for the sake of completeness and to give the reader an introduction to the notation and mathematical models required to grasp the theoretical contents. The theoretical results are presented in four separate chapters based on published and submitted conference papers, journal papers and a book chapter. In the final part of the thesis we present the design and implementation of an experimental platform for spacecraft attitude synchronization. The platform is based on two spherical autonomous underwater vehicles, internally actuated by means of reaction wheels. In Chapter 4 we present an adaptive external synchronization scheme for a spacecraft actuated by means of reaction wheels. The controller uses the quaternion parameterization of attitude, and is proven to be globally exponentially stable on S(3)_R3 in the known parameter case and globally convergent when using adaptive feedback. In Chapter 5 we present a 6 degrees of freedom (6-DOF) synchronization scheme for a deep space formation of spacecraft. In the design, which is referred to as a mutual synchronization scheme, feedback interconnections are designed in such a way that the spacecraft track a time varying reference trajectory while at the same time keep a prescribed relative attitude and position. The closed-loop system is proven uniformly locally asymptotically stable, with an area of attraction which covers the complete state-space, except when the spacecraft attains an attitude where the inverse kinematics are undefined. The proof is carried out using Matrosov’s Theorem. The contribution of Chapter 6 is a PID+ backstepping controller, as a solution to the problem of coordinated attitude control in spacecraft formations. The control scheme is based on quaternions and modified Rodriguez parameters as attitude representation of the relative attitude error. Utilizing the invertibility of the modified Rodriguez parameter kinematic differential equation, a globally exponentially stable control law for the relative attitude error dynamics is obtained through the use of integrator augmentation and backstepping. The contribution of Chapter 7 is the design of an observer-controller output feedback scheme for relative spacecraft attitude. The scheme is developed for a leader-follower spacecraft formation, where the leader is assumed to be controlled by an asymptotically stable tracking controller. Furthermore we assume that the follower has knowledge about its own attitude and angular velocity in addition to the relative attitude with respect to the leader. Since we do not know the angular velocity and acceleration of the leader, we design an error observer. The contribution of Chapter 8 is the design of AUVSAT, an experimental platform for relative spacecraft attitude synchronization. We present the mechanical and electrical network design of the vehicles. In addition an overview is given of the control hardware, including sensors, actuators and computers, and software designed to control the vehicle platforms. The contribution of Chapter 9 is the experimental validation of control algorithms for relative attitude synchronization in a two satellite leader-follower formation. We present experimental results for the PID+ backstepping design of Chapter 6 and the output feedback design in Chapter 7.