Leader Satellite Research Articles

Guidance and Control Systems for Multi-Satellite Assembly using Decentralized Nonlinear Model Predictive Control

Assembly of multiple satellites enables to replace the functionality of one large satellite by multiple smaller satellites for many applications and missions such as formation flying, multi robot planetary exploration, and satellites warms. In this paper, a novel decentralized guidance and control (G&C) algorithms is developed for multi-satellite assembly in proximity operations based on Non linear Model Predictive Control (NMPC).The two-body relative motion model is utilized in designing the G&C systems. Decentralization avoids the single point of failure (i.e., the leader satellite), which enhances the robustness of the system. The NMPC is utilized because of itsability to handle the output and the input constraints. Collision avoidance is ensured by defining a quadratic constraint equation. Moreover, the optimal thrust vector is computed while considering the control input saturation. The mission is to assemblemultiple satellites into a cubic configuration, where each satellite approaches a cube vertex. Totes the algorithms’ effectiveness and to increase the level of confidence prior flight, the proposed closed-loop G&C system is demonstrated by using MATLAB andtested for a relative motion model with J2 perturbation. The simulation results showsmooth conversion of all satellites to the target while satisfying the input and outputconstraints.

Fully distributed finite-time adaptive robust time-varying formation-containment control for satellite formation

This paper investigates the finite-time time-varying formation-containment control problem for satellite formation flying under discontinuous control protocols based on nonsmooth analysis. The desired consequence is that the follower satellites can converge into a dynamic convex hull in finite time, which is spanned by leader satellites' time-varying formation according to the reference signal. Firstly, to accomplish this objective, a finite-time time-varying formation-containment control strategy is proposed for satellite formation system in present of the bounded disturbances and satellites' accelerations, which are known for each satellite. Then, considering the case that the information of disturbances may not be measured accurately and the accelerations of satellites may not be obtained globally in some practice application scenarios, a fully distributed adaptive control strategy is proposed by introducing the dynamic variables. The adaptive variables can compensate the unknown items and adjust with the evolution of neighbour satellites' states, which makes the controller more flexible. Moreover, the proposed control strategies are able to guarantee a fast dynamic response and also a suppression of disturbance. Finally, the performances of the proposed strategies are demonstrated by numerical simulations.

Satellite affine formation flying with obstacle avoidance

This paper studies the affine formation control problem for a group of flying satellites with the performance of obstacle avoidance. Assuming that leader satellites can detect the locations of obstacles, we first investigate how to plan advisable trajectories for leader satellites such that they can smoothly pass through some specific types of obstacles by tracking the planned trajectories. Secondly, to enable follower satellites pass through the obstacles by following leader satellites' moving trajectories, a relationship between leader satellites' positions and follower satellites' desired positions is established by employing the affine formation approach. Then, a distributed formation control algorithm is proposed, which ensures all follower satellites converge to their desired positions. Moreover, the uncertainties and disturbances are considered in each satellite's motion dynamics, and are compensated by the designed adaptive laws. Finally, simulation examples are provided to validate the effectiveness of the proposed control algorithms.

Satellite Formation Flying Control Using Image Processing

A problem of a formation flying control is observed. As an example a concept of a multysatellite configuration ("space commercial") is described. Space advertisement is realized by groups of specialized free flying and cable-connected satellites, and their combinations. Construction of a space commercial satellite and a set of a control system equipment is presented. Several methods for group configuration are presented: periodic impulse correction of each flying satellite position formation; method of a satellite positioning on nocoplanar orbits. Other methods include combinations of methods mentioned above. Configuration control using onboard video camera with a wide-angle image detector is presented. Characteristics of an optical system are shown. Navigation parameters of a using a received observed videoimage are estimated. A method of a relative position measurement is described. The method detects a video track of a moving ahead satellite on the matrix detector. According to the method lines of the matrix detector are positioned transversely and columns are positioned in parallel with vertical axis of the orbital coordinate system. Course of the slave satellite is proportional to the travel of the centre of the lider satellite mark on the matrix detector columns. Pitch of the slave satellite is proportional to the travel of the centre of the leader satellite mark on the matrix detector lines. A video-display processing algorithm is developed and researched. The algorithm contains procedures of a forming, localization of the leader satellite mark, deviation angle calculation. The algorithm uses structural method, detecting bright spots (image syntactic characteristics). Efficiency of the algorithm depends on the leader satellite mark brightness, size, light-striking, distance.

Analytical Solution for Formation Flying Problem near Equatorial-Circular Reference Orbit

The relative motion between multiple satellites is a developed technique with many applications. Formation-flying missions use the relative motion dynamics in their design. In this work, the motion in invariant relative orbits is considered under the effects of second-order zonal harmonics in an equatorial orbit. The Hamiltonian framework is used to formulate the problem. All the possible conditions of the invariant relative motion are obtained with different inclinations of the follower satellite orbits. These second-order conditions warrantee the drift rates keeping two, or more, neighboring orbits from drifting apart. The conditions have been modeled. All the possibilities of choosing mean elements of the leader satellite orbit and differences in momenta between leader and follower satellites’ orbits are presented.

Satellite Formation-Containment Flying Control with Collision Avoidance

This paper investigates the satellite formation-containment flying control problem to handle a scenario where a group of satellite effectively completes deep-space exploration. In such a scenario, the satellite can be divided into two categories, i.e., leader satellite with advanced sensors and follower satellite with general sensors. To make sure all leader satellite keep a desired relative configuration and fly with a constant velocity simultaneously, a cooperative formation control algorithm is proposed for each leader satellite. Then, to actuate all follower satellite converge into the convex hull spanned by the leader satellite for safety or navigation considerations, a distributed containment control algorithm is proposed for each follower satellite. One major contribution of the proposed algorithms lies in its collision-avoidance capacity among all satellite by equipping a close-range omnidirectional relative distance sensor and employing the potential functions methodology. Finally, simulation results are provided to verify the formation-containment performance as well as the collision-avoidance performance of the proposed control algorithms.

Neural network-based distributed adaptive configuration containment control for satellite formations

Considering unknown perturbations and model uncertainties, this paper investigates the configuration containment control for satellite formations based on directed communication topologies. We consider that there are multiple leader satellites with constant relative velocities, while only a subset of follower satellites have access to the leaders. First, a distributed velocity observer is proposed for each follower to obtain velocity information of the leaders. Then, a distributed adaptive configuration containment control algorithm is proposed in which the model nonlinear uncertainties are approximated and compensated through neural networks, while the perturbations and approximation errors are compensated by adaptive gain technique. Furthermore, subject to the chattering caused by sign functions, an improved continuous containment strategy is developed. We use graph theory, Lyapunov theory, and Barbalat lemma to demonstrate that both proposed methods can make all the follower satellites converge to the convex hull spanned by the leader satellites. Numerical examples and comparisons are provided to show the effectiveness and performances of the proposed control strategies.

Distributed finite-time configuration containment control for satellite formation

This paper investigates the distributed finite-time configuration containment control problem for satellite formation with multiple leader satellites under directed communication topology. We consider that only a portion of follower satellites can receive leaders’ information and unknown perturbations and model uncertainties exist in the dynamics models of satellites. By defining the relative configuration error functions and selecting suitable nonsingular terminal sliding mode variables, a fully distributed finite-time configuration containment control scheme is proposed using the matrix properties of graph theory. The Lyapunov method is used to demonstrate the finite-time convergence property of the closed-loop systems. Numerical examples and comparisons with other methods are provided to show the effectiveness and the performance of the proposed control strategy.

Tethered satellite system control using electromagnetic forces and reaction wheels

In this paper a novel non-rotating space tethered configuration is introduced which its relative positions controlled using electromagnetic forces. The attitude dynamics is controlled by three reaction wheels in the body axes. The nonlinear coupled orbital dynamics of a dumbbell tethered satellite formation flight are derived through a constrained Lagrangian approach. These equations are presented in the leader satellite orbital frame. The tether is assumed to be mass-less and straight, and the J2 perturbation is included to the analysis. The forces and the moments of the electromagnetic coils are modeled based on the far-filed model of the magnetic dipoles. A guidance scheme for generating the desired positions as a function of time in Cartesian form is presented. The satellite tethered formation with variable length is controlled utilizing a linear controller. This approach is applied to a specified scenario and it is shown that the nonlinear guidance method and the linear controller can control the nonlinear system of the tethered formation and the results are compared with optimal control approach.

Bounds on maximal and minimal distances for coplanar satellite relative motion under given initial conditions

Maximal and minimal distances are the key parameters for a typical leader–follower satellite formation. For the mission designers, the definition of the initial relative orbital elements that are constrained by extreme distances is a difficult but meaningful problem. In this paper, the analytic distance bounds for the coplanar relative motion are obtained. These solutions are accurate for those periodic close formations in which the follower and leader satellite have equal semi-major axis. Besides, the assumption that the leader satellite has a circular orbit is adopted. Five kinds of special positions that are located on a single axis and generated the given extremum distances are derived and discussed. The simulation results are also provided to corroborate the analytic developments.

Multiple spacecraft formation reconfiguration using solar radiation pressure

In this paper the use of solar radiation pressure for spacecraft formation reconfiguration at the L2 Sun–Earth/Moon collinear libration point is presented. The system consisting of a leader and three follower spacecraft is considered. The leader spacecraft is assumed to be in a fixed halo trajectory and the follower spacecraft position relative to the leader satellite is controlled using two angles and area; these are varied based on a variable structure model reference adaptive control technique to achieve the desired formation reconfiguration. This approach ensures that all follower spacecraft complete the required maneuver in the same time. An intertially fixed circular trajectory, which is suitable for interferometer missions, is used in this paper. The stability of the proposed controller is established using Lyapunov theory. The performance of the proposed controller is tested through numerical simulation of the governing nonlinear equations of motion and is applied for formation initialization, resizing, retargeting, and rotation. The numerical results demonstrate the effectiveness of the proposed control technique for spacecraft formation reconfiguration using solar radiation pressure at the L2 libration point. Furthermore, control inputs on the order of 15degrees and 2m2 for area change are sufficient to execute the maneuvers.

Explicit Control Force and Torque Determination for Satellite Formation-Keeping with Attitude Requirements

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 -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.

Tuning functions-based output feedback adaptive spacecraft formation flying despite disturbances

This article presents a non-linear adaptive satellite formation control system based on the tuning functions design method using output feedback. A leader spacecraft is orbiting in an elliptic orbit, and a follower satellite is in motion around it. It is assumed that unknown periodic disturbance forces as well as random disturbances are acting on the follower spacecraft, and its mass is not known. Furthermore, only the relative position of the follower satellite, with respect to the leader satellite, is measured for feedback. The objective is to design an adaptive controller so that the follower spacecraft remains in a specific formation with respect to the leader spacecraft. For the purpose of design, first a simplified model including only periodic disturbance inputs is considered, and a canonical representation of the non-linear relative dynamics is obtained. Based on this canonical form, filters are designed to obtain the estimate of the relative velocity of the follower spacecraft and an output feedback adaptive law is derived for the relative position trajectory control. Based on the Lyapunov approach, it is shown that the closed-loop system is globally uniformly stable, and that the adaptive law accomplishes global asymptotic tracking of the reference trajectory in the presence of periodic disturbances. For robustness with respect to random forces in the model, a modified form of the adaptation law using σ-modification is synthesized. Simulation results are presented, which show that the designed output feedback control system achieves precise formation control, despite the periodic and random disturbance forces and parameter uncertainty in the model.

Spacecraft formation-keeping using a closed-form orbit propagator and optimization technique

In this paper, a simple method for modeling the relative orbital motion of multiple spacecraft and their formation-keeping control strategy is presented. Power series and trigonometric functions are used to express the relative orbital motion between the member spacecraft. Their coefficients are obtained using least square regression such that the difference between the exact numerically integrated position vector and the approximate vector obtained from the closed-form propagator is minimized. Then, this closed-form orbit propagator and optimization technique is used to plan a series of impulsive maneuvers which maintain the formation configuration within a specified limit. As an example, formation-keeping of four spacecraft is investigated. The motion projected onto the local horizontal plane (along- and cross-track plane) is a circle with the leader satellite located at its center and follower satellites positioned circumferentially. The radial distance between the leader and the followers, and the relative phase angles between the followers are controlled. Results from the nonlinear simulation are presented.

Satellite formation flying using variable structure model reference adaptive control

In this paper a variable structure model reference adaptive control technique for spacecraft formation flying is proposed. The system consisting of a leader and a follower satellite is considered. The stability of the proposed controller is established using a Lyapunov function. Also, the robustness of the control law to non-linearities and external disturbances is presented. A reference model suitable for formation reconfiguration is then established. The performance of the proposed controller is tested through numerical simulation of the governing non-linear equations of motion and is applied for both formation keeping and formation reconfiguration. The effect of the control parameters on tracking performance and fuel consumption is examined. The effects of initial state errors, leader satellite eccentricity, constant perturbation, and differential J2 are also considered. The numerical results demonstrate the effectiveness of the proposed control technique for satellite formation flying. In the case of the formation reconfiguration, the proposed controller outperforms the adaptive sliding mode control.

J 2 invariant relative orbits via differential correction algorithm

This paper describes a practical method for finding the invariant orbits in J 2 relative dynamics. Working with the Hamiltonian model of the relative motion including the J 2 perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth’s orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between J 2 invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte–Carlo simulation.

Satellite formation flying using along-track thrust

The formation flying of satellites using thrust in along-track direction is explored in the present paper. The system comprising of a leader and a follower satellite is considered and a linear controller is developed to achieve a desired formation. The performance of the proposed controller is tested using numerical simulation of the governing nonlinear system equations of motion considering several factors including variations in initial conditions, formation size, presence of disturbance forces, and orbital eccentricity of the leader satellite. It is found that the controller using only along-track thrust can provide bounded relative position errors with the maximum control acceleration, in m / s 2 , of 0.0718 times the product of square of the orbital rate of the leader satellite and the along-track error. The proposed controller was successful in establishing circular as well as projected circular formations of leader and follower satellites within relative position errors of ± 10 m .

Approximate analysis for relative motion of satellite formation flying in elliptical orbits

This paper studies the relative motion of satellite formation flying in arbitrary elliptical orbits with no perturbation. The trajectories of the leader and follower satellites are projected onto the celestial sphere. These two projections and celestial equator intersect each other to form a spherical triangle, in which the vertex angles and arc-distances are used to describe the relative motion equations. This method is entitled the reference orbital element approach. Here the dimensionless distance is defined as the ratio of the maximal distance between the leader and follower satellites to the semi-major axis of the leader satellite. In close formations, this dimensionless distance, as well as some vertex angles and arc-distances of this spherical triangle, and the orbital element differences are small quantities. A series of order-of-magnitude analyses about these quantities are conducted. Consequently, the relative motion equations are approximated by expansions truncated to the second order, i.e. square of the dimensionless distance. In order to study the problem of periodicity of relative motion, the semi-major axis of the follower is expanded as Taylor series around that of the leader, by regarding relative position and velocity as small quantities. Using this expansion, it is proved that the periodicity condition derived from Lawden’s equations is equivalent to the condition that the Taylor series of order one is zero. The first-order relative motion equations, simplified from the second-order ones, possess the same forms as the periodic solutions of Lawden’s equations. It is presented that the latter are further first-order approximations to the former; and moreover, compared with the latter more suitable to research spacecraft rendezvous and docking, the former are more suitable to research relative orbit configurations. The first-order relative motion equations are expanded as trigonometric series with eccentric anomaly as the angle variable. Except the terms of order one, the trigonometric series’ amplitudes are geometric series, and corresponding phases are constant both in the radial and in-track directions. When the trajectory of the in-plane relative motion is similar to an ellipse, a method to seek this ellipse is presented. The advantage of this method is shown by an example.

An orbital design method for satellite formation flying

An orbital design method of the formation initialization based on the relative orbital element method is presented. It firstly constructed the relative motion equation of the satellite formation flying in terms of the leader and followers’ orbital elements. Then the equation was simplified when the orbit eccentricity of the leader satellite was small. And according to the satellites’ mission, a general design method for the relative trajectory was proposed. The advantage of this method is that one can get a very simple analytical formula of each follower satellite’s orbital elements when the orbital eccentricity of the leader satellite is zero. The simulation results show that the method is effective.

Solution set on the natural satellite formation orbits under first-order earth's non-spherical perturbation

Using the reference orbital element approach, the precise governing equations for the relative motion of formation flight are formulated. A number of ideal formations with respect to an elliptic orbit can be designed based on the relative motion analysis from the equations. The features of the oscillating reference orbital elements are studied by using the perturbation theory. The changes in the relative orbit under perturbation are divided into three categories, termed scale enlargement, drift and distortion respectively. By properly choosing the initial mean orbital elements for the leader and follower satellites, the deviations from originally regular formation orbit caused by the perturbation can be suppressed. Thereby the natural formation is set up. It behaves either like non-disturbed or need little control to maintain. The presented reference orbital element approach highlights the kinematics properties of the relative motion and is convenient to incorporate the results of perturbation analysis on orbital elements. This method of formation design has advantages over other methods in seeking natural formation and in initializing formation.