Autonomous Orbit Determination for Quasi-Periodic Orbit about the Translunar Libration Point
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The quasi-periodic orbit about the translunar libration point can be used to establish a continuous communication link between the Earth and the far side of the Moon.In this paper,Sun-Earth-Moon autonomous navigation is implemented and investigated in the translunar libration point problem.Firstly,a new navigation dynamic model is proposed.Furthermore,due to the unstable nature of the translunar libration orbit,three sensor configuration cases for Sun-Earth-Moon autonomous navigation are studied.Simulation results of autonomous navigation are obtained by the iterative Least Squares Filtering.The nonlinear identifiability analysis is used to evaluate the identifiability and find an appropriate and robust sensor configuration for translunar libration probe.Finally,Simulations show that the sensor configuration of using directional data from the spacecraft to the Sun,the Earth and the Moon and one Doppler measurement can satisfy both the economical index and reliability.Keywords:
Libration (molecule)
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A Non-Linear Approach to Spacecraft Formation Control in the Vicinity of a Collinear Libration Point
An expanding interest in mission design strategies that exploit libration point regions demands the continued development of enhanced, efficient, control algorithms for station-keeping and formation maintenance. This paper discusses the development of a non-linear, formation maintenance, control algorithm for trajectories in the vicinity of a libration point. However, the formulation holds for any trajectory governed by the equations of motion for the restricted three body problem. The control law guarantees exponential convergence, based on a Lyaponov analysis. FreeFlyer and MATLAB provide the simulation environment for controller performance evaluation. The simulation, modeled after the MAXIM Pathfinder mission, maintains the relative position of a follower spacecraft with respect to a leader spacecraft, stationed near the L2 libration point in the Sun-Earth system. Evaluation metrics are fuel usage and tracking accuracy.
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Dynamic Optimization of Multi-Spacecraft Relative Navigation Configurations in the Earth-Moon System
In this paper, the notion of relative navigation introduced by Hill, Lo and Born is analyzed for a large class of periodic orbits in the Earth-Moon three-body problem, due to its potential in supporting Moon exploration efforts. In particular, a navigation metric is introduced and used as a cost function to optimize over a class of periodic orbits. While the problem could be solve locally as an optimal control problem, a dynamical based approach that allows for a global/systematic view of the problem is proposed. First, the simpler problem of multiple spacecraft placement on a given periodic orbit is solved before the notion of continuation and bifurcation analysis is used to expand the range of solutions thus obtained.
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Abstract Libration-point missions have been very useful and successful. Due to the unstable natures of most of these orbits, the long-time stationkeeping demands frequent maneuvers and precise orbit determinations. Earth-based tracking will have to undertake much more responsibilities with the increasing number of libration missions. An autonomous navigation system could offer a better way to decrease the need for Earth-based tracking. Nevertheless, when an autonomous navigation system is applied, there are three important factors affecting autonomous navigation accuracy, i.e., the accuracy of initial conditions, the accuracy of measurements, and the accuracy of onboard dynamics for propagation. This paper focuses on analyzing the influence from the third factor and finding an appropriate navigation dynamics, which can satisfy the requirement of estimation accuracy but not cause too much burden for onboard computation. When considering the restricted three-body model and the bicircular restricted four-body model as navigation dynamics, the astringency is not shown during the simulations. Meanwhile, when considering the influences of the Sun’s direct and indirect perturbations and the eccentricity of the Moon’s orbit, a new navigation dynamic model with the standard ephemerides is proposed. The simulation shows the feasibility of the proposed model.
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This paper studies the problem of autonomous rendezvous in the libration point orbit without relative velocity measurement information. The proposed rendezvous algorithm consists of the finite-time-convergent differentiator and the finite-time prescribed performance controller. Wherein, the differentiator is used to compute the unknown relative velocity between the target and the chaser spacecraft. The novel differentiator-based finite-time prescribed performance controller ensures that the rendezvous error converges to an arbitrarily small prescribed region in finite time in spite of the presence of additive bounded disturbances. Furthermore, the prescribed convergence rate can be also achieved simultaneously. The associated stability proof is constructive and accomplished by the development of a Lyapunov function candidate. Numerical simulations on a final rendezvous approach example are provided to demonstrate the effectiveness and robustness of the proposed control algorithm.
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Lissajous curve
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Dynamics of the Earth-Moon system is more complex than the Sun-Earth system when a high-fidelity ephemeris model is adopted, which makes the long-term stationkeeping of the Earth-Moon libration orbits a challenging problem. This paper applies the LQR and the target point methods to this problem, and proposes a method for the coarse selection of control parameters. One typical Lissajous orbit around the L2 point is taken as the nominal orbit for simulation. Results show that both methods are able to maintain the spacecraft in the close vicinity of the reference orbit, and the average yearly cost is below 1.5m/s with the current capability of the tracking accuracy. Compared with the LQR, target point method has a simpler form, and its control efficiency and robustness is higher as well.
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This paper analyzes the problem of precise autonomous orbit control of a spacecraft in a low Earth orbit. Autonomous onboard orbit control means that the spacecraft maintains its ground track close to a reference trajectory, without operator intervention. The problem is formulated as a specific case of two spacecraft in formation in which one, the reference, is virtual and affected only by the Earth’s gravitational field. A new parametrization, the relative Earth-fixed elements, is introduced to describe the relative motion of the two spacecraft’s subsatellite points on the Earth surface. These relative elements enable the translation of absolute-into-relative orbit-control requirements and the straightforward use of modern control-theory techniques for orbit control. As a demonstration, linear and quadratic optimum regulators are designed and compared, by means of numerical simulations, with an analytical autonomous orbit-control algorithm that has been validated in flight. The differences of the numerical and analytical control methods are identified and discussed.
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Halo orbit
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A decentralized control framework is investigated for applicability of formation flying control in libration orbits. The decentralized approach, being non-hierarchical, processes only direct measurement data, in parallel with the other spacecraft. Control is accomplished via linearization about a reference libration orbit with standard control using a Linear Quadratic Regulator (LQR) or the GSFC control algorithm. Both are linearized about the current state estimate as with the extended Kalman filter. Based on this preliminary work, the decentralized approach appears to be feasible for upcoming libration missions using distributed spacecraft.
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