Research On Dynamics And Control Of Spacecraft Electromagnetic Formation Flight

Spacecraft formation, a new application for future complicated space missions, represents the frontier and important development trend of aerospace science research. Spacecraft electromagnetic formation flight is proposed by using the magnetic fields electrically generated by magnetic coils equipped on all spacecrafts, and generating electromagnetic force and torque to control the relative trajectory and attitude. This novel technology could effectively address the inherent issues of conventional thruster such as propellant consumption, plume contamination and optical facility interference etc, and offer non-contacting continuous reversible and synchronous controllability. Especially, electromagnetic formation flight allows better control authority and more general application value, which presents several potential space applications such as space-based imaging, space docking and assembly, as well as non-contacting operations. Concentrating on dynamics and control problems of spacecraft electromagnetic formation flight, this paper mainly investigates the dynamics modeling, relative equilibrium analysis, invariant shape design, collective trajectory planning and 6-DOF formation keeping and reconfiguration.(1) Dynamics and relative equilibrium of space craft electromagnetic formation flight. Hypothesizing the spacecraft electromagnets as magnetic dipoles, the far-field electromagnetic force/torque models with its error characteristics are derived by the electromagnetic theory. In view of the different attentions and requirements for dynamics analysis and control, two different approaches are chosen to develop the dynamics model of electromagnetic formation. The relative trajectory and attitude motion dynamics model are derived by the vectorial mechanics approach based on Newton-Euler equations, and main external disturbances models are introduced accordingly. Moreover, treating the electromagnetic formation as a free multi-rigid-body system connected by force element in the concept of multibody dynamics theory, Kane method is applied to developing a generalized 6-DOF dynamic model for the multi-spacecraft electromagnetic formation, and the choice guidelines for such two models are discussed. Then the relative equilibrium for the generalized model is analyzed and the necessary conditions for circularly restricted static electromagnetic formation are derived, which would provide guidance for formation design and keeping control in the future.(2) The tw o-spacecraft static/spinning electromagnetic formation and its stability. Considering the collinear formation, the Kane model can be simplified and three 6-DOF coupled nonlinear dynamics models for the two-spacecraft electromagnetic formation aligned with orbital radial, along-track and normal direction are derived respectively. After analyzing the relative equilibrium, how the electromagnetic force effect and the configuration conditions for each static formation are derived. Then the magnetic moment arrangement modes and their solution strategies are presented, and the coupled characteristics, control requirements, stability and controllability are discussed based on the linear system theory respectively. Additionally, the spinning two-spacecraft formation is studied, which proves that the deep space is the necessary and sufficient conditions for the feasibility of a spinning formation with constant magnetic moments. Naturally, the corresponding configuration condition, coupled characteristics and stability are analyzed and presented.(3) Invariant shapes and stab ility for three-spacecraft electromagnetic formations. Considering the fact that a three-spacecraft formation is either 1-dimension collinear or 2-dimension triangular, so the 6-DOF Kane dynamics models for collinear and general triangular configurations are developed respectively. The superposition and coupling effects of two distinct magnetic dipoles are the key element that potentially complicates the relative equilibrium analysis and magnetic moments design. For the three-spacecraft collinear configuration, the feasible magnetic moment solutions satisfying the electromagnetic torques constraints are examined to be possible in three cases, thus we focus on the along-track and normal relative equilibrium, and derive the magnetic moments, geometry conditions and their complete analytic solutions for static and spinning invariant shapes respectively. For the three-spacecraft triangular configuration, the appropriate isosceles triangular configuration constraint based on angular momentum conservation is examined at first. Due to the non-analyticity of the nonlinear magnetic dipoles, the corresponding families of magnetic moments and shape solutions for some special static/spinning invariant shapes are investigated and presented. Furthermore, numerical simulations based on the linear system theory are carried out to analyze the stability and controllability for various invariant shapes of three-spacecraft electromagnetic formation.(4) Collective trajectory planning for spacecraft formation using inter-satellite electromagnetic force. Starting with the behavior-based strategy, the cohesion, convergence and stability of a formation with behavior model are theoretically proved in both free and constrained environment. According to the conclusions on formation cohesion, a behavioral distributed planning approach based on Equilibrium Shaping with external environment effects considered is developed by designing the desired velocity of each satellite as the sum of several different behavioral velocities, which are used to represent the internal and external interactions of the formation. More importantly, the multi-spacecraft collective trajectory planning problem triggered by integrating the inter-satellite electromagnetic force into such scheme is studied, and the optimized assignment approach for multiple magnetic dipoles solution is presented as well. The trajectory planning problem with sole electromagnetic force actuation and hybrid actuation by electromagnetic forces and thrusters are analyzed respectively, the applicability and the problem of how to utilize the inter-satellite electromagnetic force to provide a better performance, higher efficiency and broader applications for such a complex system are discussed in-depth.(5) 6-DOF keeping and reconfiguration control of electromagnetic formation. Due to the control requirements of strong nonlinearity, uncertainty, coupling and 6-DOF relative motion for electromagnetic formation flight, the formation keeping and reconfiguration control problems of electromagnetic formation are studied respectively. For the 6-DOF formation keeping, the tracking control problem about the relative equilibrium is studied based on the Kane’s integrated model, and the linear feedback controller based on LQR(Linear Quadratic Regulator) and ESO(Extended State Observer) is derived with the parameters tuning methods presented. After analyzing the cyclic pursuit theory and its parameters tuning methods, the integrated guidance and control laws for general two-order dynamics system are derived. For the 6-DOF reconfiguration of electromagnetic formation, two desired fly-around configurations and attitude pointing modes are designed according to different space mission requirements, and the corresponding cyclic pursuit control laws for relative trajectory/attitude motion are derived based on the vectorial mechanics model. Moreover, ESO is integrated to improve the robustness, and the 6-DOF robust decentralized cooperative controllers satisfying different mission requirements for electromagnetic formation configuration are presented. Numerical simulations are carried out to verify the validity of the proposed algorithms at last.In conclusion, the research on dynamics and control problems of spacecraft electromagnetic formation flight, on one hand, proposes the theoretical models and bases of analysis for the in-depth investigation of electromagnetic formation dynamics mechanism; on the other hand, gives the necessary control models and algorithms for the space applications actuated by electromagnetic formation flight. All of these present useful explorations to enrich the theories and applications, and provide a good foundation for further research on electromagnetic formation flight.