Satellite Formation Flying

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This paper presents a new, simple, and exact solution to the formation keeping of satellites when the relative distance between the satellites is so large that the linearized relative equations of motion no longer hold. We employ a recently proposed approach, the Udwadia-Kalaba approach, which makes it possible to explicitly obtain the desired control function without making any approximations related to the nonlinearities in the underlying dynamics. We use an inertial frame of reference to describe the motion of a satellite and since no approximations are made, the results obtained apply to situations even when the distance between the satellites is arbitrarily large. The paper deals with a projected circular formation, but the methodology in this paper can be applied to any desired configuration or orbital requirements. Numerical simulations confirm the brevity and the accuracy of the analytical solution to the dynamical control problem developed herein.

This paper presents an analytic solution to the optimal reconfiguration problem of satellite formation flying in J2 orbital perturbation. Continuous and variable low-thrust accelerations are represented by the Fourier series, and initial and final boundary conditions are used to establish the constraints on the thrust functions. The thrust functions are implemented by optimal Fourier coefficients that minimize the cost during the maneuver. The analytic solution composed of these Fourier coefficients are simply represented in a closed form, and no approximation is needed. Numerical simulations are conducted to visualize and compare the results obtained in this paper with those of previous papers with no perturbations. The analytic solution developed in this paper is more accurate in that the general behavior of the optimal control history and reconfiguration trajectories are easily calculated even in the presence of the J2 potential disturbance. The analytic solution is useful for designing a reconfiguration controller for satellite formation flying under J2 orbital perturbation.

A simple analytical approach for formation-keeping of satellites in the presence of both orbital and attitude requirements is developed. A leader satellite is assumed to be in a J2-perturbed circular reference orbit and each follower satellite is required to stay in its prescribed, desired orbit with respect to the leader satellite, and at the same time, to point to an arbitrarily chosen specific spot in space that may be time-varying. Nonlinear relative dynamics is considered in its entirety without any approximations, and nonlinear controllers are designed to exactly satisfy the desired orbital and attitude mission requirements for the formation. The analytical approach leads to a separation principle that points out when orbital control is completely unaffected by attitude control. In the presence of sensor measurement noise that leads to incorrect initial conditions at the start of the control maneuver the approach asymptotically satisfies both the orbital and attitude control requirements, at any desired rate of convergence
depending on mission requirements. The effect of small unmodelled dynamics is also considered. A numerical example demonstrates the simplicity of the approach, its ease of implementation, accuracy of results, and its robustness to both sensor measurement errors and unmodelled dynamics.

In order to face numerous challenges in the autonomous control of relative position in space, this work proposes an introduction and critical comparison of three different approaches to adaptive control. Uncertainties coming from unknown orbital perturbations and system errors, together with the need of a high precision control, i.e. during docking maneuvers, make adaptive algorithms particularly attractive. Adaptive control allows real-time estimation of unknown parameters such as drag coefficient, thrust misalignment and magnitude error, spacecraft mass variation, and their inclusion in the control law. Apart from parameters estimation, this paper describes three ways of dealing with system nonlinearities: backstepping algorithm, sliding mode technique and the use of a fuzzy method. A final comparison between the three control techniques is provided, including comments regarding the respective applicability on actual space missions.

The current paper presents simple and general analytic solutions to the optimal reconfiguration of multiple satellites governed by a variety of linear dynamic equations. The calculus of variations is used to analytically find optimal trajectories and controls. Unlike what has been determined from previous research, the inverse of the fundamental matrix associated with the dynamic equations is not required for the general solution in the current study if a basic feature in the state equations is met. This feature is very common due to the fact that most relative motion equations are represented in the LVLH frame. The method suggested not only reduces the amount of calculations required, but also allows predicting the explicit form of optimal solutions in advance without having to solve the problem. It is illustrated that the optimal thrust vector is a function of the fundamental matrix of the given state equations, and other quantities, such as the cost function and the state vector during the reconfiguration, can be concisely represented as well. The analytic solutions developed in the current paper can be applied to most reconfiguration problems in linearized relative motions. Numerical simulations confirm the brevity and accuracy of the general analytic solutions developed in the current paper.

The “sonic region” of the Sun corona remains extremely difficult to observe with spatial resolution and sensitivity sufficient to understand the fine scale phenomena that govern the quiescent solar corona, as well as phenomena that lead to coronal mass ejections (CMEs), which influence space weather. Improvement on this front requires eclipse-like conditions over long observation times. The space-borne coronagraphs flown so far provided a continuous coverage of the external parts of the corona but their over-occulting system did not permit to analyse the part of the white-light corona where the main coronal mass is concentrated. The proposed PROBA-3 Coronagraph System, also known as ASPIICS (Association of Spacecraft for Polarimetric and Imaging Investigation of the Corona of the Sun), with its novel design, will be the first space coronagraph to cover the range of radial distances between ~1.08 and 3 solar radii where the magnetic field plays a crucial role in the coronal dynamics, thus providing continuous observational conditions very close to those during a total solar eclipse. PROBA-3 is first a mission devoted to the in-orbit demonstration of precise formation flying techniques and technologies for future European missions, which will fly ASPIICS as primary payload. The instrument is distributed over two satellites flying in formation (approx. 150m apart) to form a giant coronagraph capable of producing a nearly perfect eclipse allowing observing the sun corona closer to the rim than ever before. The coronagraph instrument is developed by a large European consortium including about 20 partners from 7 countries under the auspices of the European Space Agency. This paper is reviewing the recent improvements and design updates of the ASPIICS instrument as it is stepping into the detailed design phase.

In this paper the vibration suppression of a flexible structure using fuzzy controller with bonded piezoelements is investigated. A flexible beam with PZT piezoceramics as sensor and actuators is fabricated at the Advanced Dynamic and Control Systems lab (ADCSL). A dynamic model of the smart structure is derived from an experimental system ID. On the other hand using finite element method (FEM), a theoretical model of the structure is obtained which is in good agreement with the experimental model. A fuzzy control system is then designed and implemented for vibration suppression of the smart beam subjected to the impulse excitation and resonance disturbances. Results show the effectiveness of the fuzzy controller and its advantage over conventional controllers.

The current paper presents application of a new analytic solution in general relative motion to spacecraft formation flying in an elliptic orbit. The calculus of variations is used to analytically find optimal trajectories and controls for the given problem. The inverse of the fundamental matrix associated with the dynamic equations is not
required for the solution in the current study. It is verified that the optimal thrust vector is a function of the fundamental matrix of the given state equations. The cost function and the state vector during the reconfiguration can be analytically obtained as well.
The results predict the form of optimal solutions in advance without having to solve the problem. Numerical simulation shows the brevity and the accuracy of the general analytic solutions developed in the current paper.

The current paper presents and examines a general analytical solution to the optimal reconfiguration problem of satellite formation flying in an arbitrary elliptic orbit. The proposed approach does not use any simplifying assumptions regarding the eccentricity of the reference orbit. For the fuel optimal reconfiguration problem, continuous and variable low-thrust accelerations can be represented by the Fourier series and summed into closed-form solutions. Initial and final boundary conditions are used to establish the constraints on the thrust functions. The analytical solution can be implicated by the Fourier coefficients that minimize propellant usage during the maneuver. This solution is found that compares favorably with numerical simulations. Also, this analytical solution is very useful for designing a reconfiguration controller for satellite formation flying in a general elliptic orbit.