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Abstract
Space electromagnetic formation is characterized mainly by advantages of no propellant consumption, no plume contaminations, continuous reversible and synchronous controllability, and static electromagnetic formation has a broad prospect of application in such fields as optical interferometry. The stability and control issues of dynamics equilibrium are the foundation for static electromagnetic formation. This research focused on the three equilibriums of two-spacecraft aligned with radial, along-track and normal direction, developed the 6-DOF coupled nonlinear dynamic models by the Kane method, and analyzed the open-loop stability, the coupled characteristics and the control requirements for each equilibrium respectively. Finally, an LQR feedback controller was designed and verified to stabilize the equilibriums.
To solve the problem of rigid / non-rigid 3D point set registration, a novel Convex Hull indexed Gaussian mixture model (CH-GMM) is proposed in this paper. The model works by computing a weighted Gaussian mixture model (GMM) response over the convex hull of each point set. Three conditions, proximity, area conservation and projection consistency, are incorporated into the model so as to improve its performance. Given that the convex hull is the tightest convex set of a point set, the combination of Gaussian mixture and convex hull can effectively preserve the topological structure of a point set. Furthermore, computational complexity can be significantly reduced since only the GMM of the convex hull (instead of the whole point set) needs to be calculated. Rigid registration is achieved by seeking the best rigid transformation parameters yielding the most similar CH-GMM responses. Non-rigid deformation is realized by optimizing the coordinates of the control points used by the thin-plate spline model for interpolating the entire point set. Experiments are designed to evaluate a method's robustness to rotational changes between two point sets, positional noise, differences in density and partial overlap. The results demonstrated better robustness and registration accuracy of CH-GMM based method over state-of-the-art methods including iterative closest point, coherent point drift and the GMM method. Besides, the computation of CH-GMM is efficient.
Based on the mechanism of electromagnetic spacecraft, the relative translational “tethered” dynamics model for two-craft electromagnetic formation flight (EMFF) in low earth orbit was developed by using Lagrange theory. The linearized equations for motion and stability analysis of two-craft radial and along-track formation were investigated. To stabilize the formation structure, the feedback control law was studied. The motion programming of electromagnetic formation could be transformed into a standard optimal problem, which could be perfectly solved by the Gauss pseudospectral method. In order to deal with the reconfiguration maneuver of multi-craft electromagnetic formation, the sequence control strategy was proposed. Then the multi-craft problem was transformed into a multi-phase motion planning problem. Thus, the problem of multi-phase optimal control could be solved by Gauss pseudospectral optimization software (GPOPS). The simulation result shows that the methods of dynamics modeling and motion planning proposed in this paper are valid. ©, 2015, Beijing University of Aeronautics and Astronautics (BUAA). All right reserved.
Electromagnetic satellite formation station-tracking is a control problem with input delay and disturbance uncertainties. Taking CW equation as dynamics model, a control law including feed-forward plus feedback is used for the station tracking. The feed-forward control quantity is calculated based on the predetermined trajectory and the CW equation. The feedback control adopts sliding mode variable structure control law with state linear transformation. It is proved that sliding manifolds are reachable and sliding mode movement is independent of disturbance uncertainties. Numerical simulation shows that the position tracking with input delay considered is more accurate than that with input delay ignored.
Electromagnetic formation flying is a novel concept of controlling the relative degrees of freedom of a satellite formation without the expenditure of fuel by using high temperature superconducting wires to create magnetic electromagnetic formation flying Because of inherent nonlinearities and couplings, the dynamics and control problem associated with electromagnetic formation flying are difficult, especially for near Earth operations This paper presents the application of nonlinear adaptive control laws that enable formation maintenance and reconfiguration An approach to control allocation as the solution of an optimization problem is also proposed The accumulation of angular momentum in the presence of Earth's magnetic field is an issue with electromagnetic formation flying and ways of managing it by exploiting the nonlinearity of magnetic dipoles using polarity switching are presented as a solution Closed loop nonlinear simulation results are also presented to demonstrate the feasibility and importance of the control scheme described for electromagnetic formation flying for near Earth operations
A noncanonical Hamiltonian formulation of the Coulomb formation dynamics is used to develop necessary conditions for static Coulomb formations with constant charges. With a static or frozen formation the satellites perform non-Keplerian orbits and maintain constant relative position vectors. As seen by an observer following the center of mass motion, the spacecraft formation would appear to behave equivalently to a rigid body in orbit. Previous research has demonstrated the existence of such static Coulomb formations analytically by employing symmetry simplifying assumptions with linearized relative motion dynamics, or by using numerical genetic search algorithms. These static solutions are used as reference geometries and charges for feedback law developments. This paper presents nonlinear static formation conditions for the circularly restricted problem. Hamiltonian formulations have been used to study equilibrium conditions of rigid bodies in orbit. Analogous techniques are employed to study necessary conditions to achieve a static Coulomb formation. Analytical results using the full and truncated formation gravity potential function are presented. Numerical results illustrate convergence performance improvements of an evolutionary search algorithm where the presented necessary conditions are enforced.
The current paper investigates the electromagnetic formation flight control problem using the finite-time control technique. The electromagnetic force model is presented, and the effects of the Earth's magnetic field on the EMFF satellites are analyzed. The equations of relative motion and general formation description method are then established. A robust sliding mode controller is designed to achieve trajectory tracking in the presence of model uncertainties and external disturbances. The proposed controller, which combines the advantages of linear and terminal sliding mode controls, can guarantee the convergence of tracking errors in finite time rather than in the asymptotic sense. By constructing a particular Lyapunov function, the closed-loop system is proven globally stable and convergent. Numerical simulations of formation maintenance and reconfiguration are then presented to show the effectiveness of the developed controller.
Spacecraft formations typically have to rely upon active control methods to maintain stable configurations. This requirement imposes an associated cost on the satellite through fuel expenditure, actuator mass, and computation time for the controller. This paper proposes using the flux-pinning interaction between a high-temperature superconductor and a magnetic field as a means to reduce these costs by passively stabilizing the dynamics governing the relative motion between spacecraft. A simplified model of a flux-pinned spacecraft formation is developed to provide the framework for future analysis. Linearization of this model about an equilibrium state allows for the development of a state-feedback control law. This framework is then applied to a simplified two-spacecraft formation in a nominally circular orbit about a central body and Controlled to two distinct equilibrium separations.
The linearized dynamics and stability of a two-craft Coulomb tether formation is investigated. With a Coulomb tether the relative distance between two satellites is controlled using electrostatic Coulomb forces. A charge feedback law is introduced to stabilize the relative distance between the satellites to a constant value. Compared to previous Coulomb thrusting research, this is the first feedback control law that stabilizes a particular formation shape. The two craft are connected by an electrostatic tether that is capable of both tensile and compressive forces. As a result, the two-craft formation will essentially act as a long, slender near-rigid body. Interspacecraft Coulomb forces cannot influence the inertial angular momentum of this formation. However, the differential gravitational attraction can be exploited to stabilize the attitude of this Coulomb tether formation about an orbit nadir direction. Stabilizing the separation distance will also stabilize the in-plane rotation angle, whereas the out-of-plane rotational motion remains unaffected. The Coulomb tether has been modeled as a massless, elastic component. The elastic strength of this connection is controlled through a spacecraft charge control law.
The dynamics and stability of a charged two craft formation with nominal fixed separation distance (Coulomb tethers) is studied where the cluster is aligned with either the along-track or orbit normal direction. Unlike the charged two-craft formation scenario aligned along the orbit radial direction, a feedback control law using inter-spacecraft electrostatic Coulomb forces and the differential gravitational accelerations is not sufficient to stabilize the Coulomb tether length and the formation attitude. Therefore, a hybrid feedback control law is presented which combines conventional thrusters and Coulomb forces. The Coulomb force feedback requires measurements of separation distance error and error rate, while the thruster feedback is in terms of Euler angles and their rates. This hybrid feedback control is designed to asymptotically stabilize the satellite formation shape and attitude while avoiding plume impingement issues. The effects of differential solar drag on the formation and the ability of the controller to withstand this disturbance is also studied.