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Finite-time control for electromagnetic satellite formations
Abstract
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.
... Most of the docking mechanisms, whether spacecraft or ORU, realize the docking process through contact collision. Meanwhile, propellants employed in the traditional rendezvous and or model uncertainties [30][31][32]. However, in real-time applications, the sliding surface is not rigorously known, which leads to a high control activity known as chattering [33]. ...
... uncertainties [30][31][32]. However, in real-time applications, the sliding surface is n ously known, which leads to a high control activity known as chattering [33]. ...
Electromagnetic docking technology can realize the flexible docking and safe separation of spacecraft, and presents broad application prospects. However, an electromagnetic force with nonlinearity and uncertainty properties increases the difficulties of the electromagnetic docking control. In this work, the magnetic dipole far-field model of a single coil has been established by simplifying the electromagnetic docking device. Afterward, the electromagnetic force and electromagnetic torque models were obtained during space electromagnetic docking. The space electromagnetic docking dynamics model was established by analyzing the influences of disturbance force and disturbance torque caused by a geomagnetic field. According to the one-dimensional docking reference trajectory, the sliding mode variable structure controllers based on exponential reaching law were proposed and verified. The quasi-sliding mode control method has been adopted to solve the chattering problem in sliding mode variable structure control. The simulation results show that it is necessary to design and add an electromagnetic controller to achieve flexible docking. The sliding mode variable structure controller based on quasi sliding mode can realize one-dimensional electromagnetic flexible docking, and have made good tracking effect on the reference trajectory. Compared with the control method based on exponential reaching law, it can reduce the chattering phenomenon in the control process. The sliding mode variable structure control strategy based on quasi sliding mode presented good robustness. Therefore, it can provide theoretical guidance and control reference for the flexible docking process between electromagnetic satellites.
... For EMFF in low earth orbit, the Earth's strong magnetic field will produce considerable disturbance torque on the satellite, and angular momentum management may be a problem. The polarity reversal method proposed in [14,15] refers to simultaneously changing all satellites' magnetic dipoles' signs. At this time, the direction of the disturbance torque of the geomagnetic field on satellites varies to unload the angular momentum, while the electromagnetic force between satellites remains unchanged. ...
... Achieving high-precision formation control performance in the presence of the above issues is challenging. Some scholars have researched control methods of EMFF, such as adaptive control [7,14], sliding mode control [15,20], linear quadratic regulation (LQR) control [21,22], and robust suboptimal control [12]. Due to the strong nonlinearity and coupling of EMFF dynamics, most controllers need to rely on accurate dynamics models to achieve high-precision control of EMFF. ...
Electromagnetic formation flight uses the electromagnetic interaction between satellites to provide maneuver control for formation satellites, with the advantages of no propellant consumption, long life, and high flexibility. However, high-precision control for electromagnetic formation flight is challenging because of the nonlinear and coupling characteristics of the dynamics, optimal assignment of magnetic dipoles, model uncertainties, and the angular momentum management issues caused by the geomagnetic field. This paper studies the 6-DOF control problem of two-satellite electromagnetic formation flight in low-Earth orbit. A new electromagnetic frame is introduced to promote the decoupling of the translation dynamics model and the electromagnetic model. The electromagnetic model can be expressed as a simple two-dimensional model in this electromagnetic frame. The proposed electromagnetic force envelope diagram can intuitively show the relationship between electromagnetic force and magnetic dipoles, providing practical guidance for dipole assignment. The frequency division multiplexing method is designed for angular momentum management considering the effect of the earth’s magnetic field on the electromagnetic satellites, and the active disturbance rejection control method is used to solve the 6-DOF stability problem with external disturbance and model uncertainties. Numerical simulation verifies the effectiveness of the proposed control method and angular momentum management strategy.
... In [104], the problem of controlling the motion of an electromagnetic formation using the finite time method is investigated. The principle of electromagnetic formation flight (EMFF) uses magnetic fields electrically generated by all satellites, which then allows you to control the relative degrees of freedom. ...
... Zeng and Hu [104] presented an electromagnetic force model and analyzes the effect of the Earth's magnetic field on EMFF satellites. Then, the equations of relative motion and the method for describing the general formation are established. ...
This survey deals with the problem of the group motion of spacecraft, which is rapidly developing and relevant for many applications, in terms of developing the onboard control algorithms to ensure the fulfillment of a given mission. The paper provides a comprehensive overview of spacecraft formation flight control. The bibliography is divided into three main sections: the multiple-input–multiple-output approach, in which the formation is treated as a single entity with multiple inputs and multiple outputs; the leader–follower formation, in which individual spacecraft controllers are linked hierarchically; and a virtual structure formation, in which spacecraft are treated as rigid bodies embedded in a common virtual rigid body. This survey expands a 2004 survey and updates it with recent results.
... The major attractive advantages of such a control form over traditional thrusters are noncontact interaction, no propellant consumption, and continuous controllability. However, many problems remain, such as inherent nonlinearity and coupling in docking dynamics [1], model uncertainties, and unknown external disturbances due to the effects of the Earth's magnetic field [2]- [4]. ...
... where E denotes the input Euler angle to be differentiated; z0, z1, z2 and z3 denote the estimations of E, Ė, Ë and E , respectively; L > 0 denotes the Lipschitz constant; λ0, λ1, λ2 and λ3 are positive parameters; fsat(·) denotes a saturation function [4] defined as ...
This paper presents a novel control method that combines sliding mode controllers, disturbance observers and an exact robust differentiator to solve the underactuated microsatellite electromagnetic docking control problem, in which each docking satellite is equipped with only one single electromagnetic coil. The far-field model of electromagnetic force/torque is given and its model error is analyzed; and a six-degree-offreedom (6-DOF) docking dynamics model using the far-field model is established. The generation method of the desired trajectory and desired attitude in the docking process is presented; and then an improved exact robust differentiator based on the 3rd-order sliding mode is proposed to produce the desired angular velocity and angular acceleration. In the presence of model uncertainties, external disturbances and input constraints, a disturbance observer-based sliding mode control scheme for underactuated microsatellite electromagnetic docking is developed. The whole closed-loop control system contains an inner-loop attitude controller and an outer-loop position controller. Numerical simulation results are presented to validate the effectiveness and the superior properties of the proposed control scheme.
... Because of its speed advantage and flexible maneuverability, the hypersonic vehicle may certainly become a severe threat in the future battlefield; to deal with the threat, the research on the interception of the hypersonic vehicle is already on the agenda. Primarily, the interception of the hypersonic vehicle faces the following issues: (1) when the speed of its target is much faster than the interception missile, the effective attack area of the traditional guidance law greatly shrinks, and it is impossible to accomplish the tail-chase or backward interception; (2) at the high altitude of 25 to 40 km where the hypersonic vehicle flies, the air is relatively thin, the aerodynamic efficiency of an interception missile is low, and there is a limited usable overload for the interceptor; (3) it is difficult to destroy such a hypersonic target with the traditional destructive means such as near explosion fragments, requiring that the interception missile should use knock-on collision as much as possible to attack the target, namely, minimal target missing. As the requirements for guidance accuracy are higher, researchers do massive work to advance the guidance and control theory. ...
... To get finite time convergence, modified SMC like terminal sliding mode control (TSMC) is proposed. In [3] Zeng and Hu combine the advantages of linear and terminal sliding mode controls which guarantee the convergence of tracking errors in finite time. And then, nonsingular terminal sliding mode control (NTSMC) is introduced in the guidance law design. ...
This paper focuses on the integrated guidance and control (IGC) method applied in the interception of maneuvering near space hypersonic vehicles using the homogeneous high order sliding mode (HOSM) approach. The IGC model is derived by combining the target-missile relative motion and dynamic equations. Then, a fourth-order sliding mode controller is implemented in the augmented IGC model. To estimate the high order derivatives of the sliding manifold which is required in the HOSM method, an Arbitrary Order Robust Exact Differentiator is presented. At last, the idea of virtual control is introduced to alleviate the chattering of the control input without using any saturation functions which may lead to a loss of the robustness. And the stability of the closed-loop system with presented fourth-order homogeneous HOSM controller is also proved theoretically. Finally, simulation results are provided and analyzed to demonstrate the effectiveness of the proposed method in three typical engagement scenarios.
... Attaining high-precision formation control performance amidst these complexities presents a significant challenge. Various scholars have delved into control methodologies for EMFF, exploring adaptive control [9,15], sliding mode control [8,16], linear quadratic regulation (LQR) control [17,18], and robust suboptimal control [19]. ...
Satellite formation flying technology currently represents a focal point in space mission research. Traditional spacecraft payload performance and lifespan are often constrained by propellant limitations. Electromagnetic Formation Flying (EMFF), a propellant-free formation flying technique, has garnered widespread attention. Its inherent strong nonlinearity and coupling present challenges for high-precision control within EMFF. This paper presents the relative motion dynamics of a two-satellite EMFF in the port-Hamiltonian framework and constructs an accurate nonlinear model of the dynamics. Utilizing the concept of Interconnection and Damping Assignment and nonlinear disturbance observer, a composite disturbance-rejection passivity-based controller is designed, offering a method for controlling the magnetic dipole strength of formation satellites. Finally, numerical simulations are conducted to demonstrate the viability of the proposed dynamics model and control strategy.
... Finite-time control strategies typically have higher control accuracy, better robustness, and faster convergence to the equilibrium than asymptotic control strategies [19]. Moreover, in many practical applications, the finite-time stabilization makes more sense than asymptotic stabilization, such as in the orbiting state of satellite systems and other applications that focus on the state behavior over a finite period [20], and the trajectory control of spacecraft and other such applications that need to maintain the system's state within a specific time frame without exceeding a predetermined bound [21]. Therefore, the finite-time consensus tracking problem for MASs has attracted much attention [22][23][24]. ...
This paper studies the consensus tracking control for a class of uncertain high-order nonlinear multi-agent systems under an undirected leader-following architecture. A novel distributed finite-time adaptive control framework is proposed based on the barrier function. The distributed cascaded high-gain observers are introduced to solve the problem of robust consensus tracking with unmeasured intermediate states in multi-agent systems based on the proposed control framework. The proposed control schemes guarantee the finite-time consensus of multi-agent systems, which is proven by the finite-time Lyapunov stability and singular perturbation theory. In conclusion, numerical simulations verify the proposed control protocols' effectiveness, and their performance advantages are shown by comparing them with another existing method.
... EMFF have been thoroughly investigated at MIT Space System Laboratory focusing on the effectiveness of EMFF application and feasibility study [25], control algorithms development [26], laboratory testing [27] and inflight demonstration onboard the ISS [28]. A variety of control approaches and algorithms is developed and applied for EMFF including trajectory tracking control during the docking [29], linear quadratic regulator [27,30], optimal control [31], finite-time control [32], adaptive sliding control [33]. One of the main concerns of EMFF application is that the electromagnetic interaction also produce torques that leads to satellite angular momentum build-up. ...
A swarm of ChipSats equipped with miniature magnetorquers is considered, the electromagnetic interaction force is used for relative motion control at extremely short relative distances up to several centimetres. A ChipSat is a satellite printed on 3.5 × 3.5 cm circuit board with a set of sensors, solar panels, onboard computer, and communication system. Assuming the relative motion between each satellite is known, a Lyapunov-based control algorithm is proposed to achieve bounded relative trajectories. A centralized and a decentralized control approaches are implemented. For the centralized approach, a CubeSat is considered as the main satellite after swarm deployment, producing a high value magnetic dipole moment which interacts with the magnetic dipole of the surrounding ChipSats in order to stop relative drift. For the decentralized approach, the ChipSats are linked in interchangeable pairs in order to apply the electromagnetic control force and reduce the relative drift between the satellites to the vicinity of zero. Two different pairing selection methods are proposed in the paper, based on the closest satellite and on the satellite with highest relative drift. Both translational and rotational motion of satellites are considered. The magnetic dipole moments are used for angular velocity damping when orbit control is not required, and a repulsive collision avoidance electromagnetic control is applied when two ChipSats are within dangerously close proximity to each other. The proposed control schemes performance is studied numerically with different algorithm and ChipSats parameters. The influence of these parameters on the swarm separation is obtained using Monte-Carlo simulations.
... It includes the control via electromagnetic field which is produced by the magnetic coils installed on each satellite in formation. This approach was carefully studied in [27]; further studies were carried out in [28][29][30][31][32][33][34]. For this case, the so-called far-field model is derived in [27] 0 21 5 5 5 7 , , , ...
The paper considers various approaches nanosatellites formation flying control , presents dynamic models of the motion of a group of nanosatellites, considers various algorithms for controlling relative angular and translational motions, taking into account the specifics of small satellites and limited inter-satellite communication capabilities. The paper discusses various approaches to the formation flying control, including those using perspective methods that do not require the fuel consumption. With a large number of spacecraft in a group, a new class of space systems appears, defined as a swarm. The main difficulty in implementing a swarm formation flying of satellites is navigation and control of the mutual relative motion of an individual satellite in a swarm, taking into account the fundamental impossibility of having information about the phase state vector of each swarm element. The features of decentralized algorithms for controlling the satellites swarm motion are considered and the dynamics of the swarm is investigated.
... All these applications involve electromagnet-based control and similar dynamics characteristics. Over the past decade, many researches have been conducted on EMFF [8][9][10], and their achievements can serve as a basis for the exploration of electromagnetic docking. However, the essential difference between EMFF and electromagnetic docking is the interaction distance between electromagnetic mechanisms, which leads to different dynamics models and control strategies. ...
This paper presents a novel nonlinear sliding mode control scheme that combines on-line model modification, a nonlinear sliding mode controller, and a disturbance observer to solve the essential problems in spacecraft electromagnetic docking control, such as model uncertainties, unknown external disturbances, and inherent strong nonlinearity and coupling. An improved far-field model of electromagnetic force which is much more accurate than the widely used far-field model is proposed to enable the model parameters to be on-line self-adjusting. Then, the relationship between magnetic moment allocation and energy consumption is derived, and the optimal direction of the magnetic moment vector is obtained. Based on the proposed improved far-field model and the research results of magnetic moment allocation law, a fast-nonsingular terminal mode controller driven by a disturbance observer is designed in the presence of model uncertainties and external disturbances. The proposed control method is guaranteed to be chattering-free and to possess superior properties such as finite-time convergence, high-precision tracking, and strong robustness. Two simulation scenarios are conducted to illustrate the necessity of modifying the far-field model and the effectiveness of the proposed control scheme. The simulation results indicate the realization of electromagnetic soft docking and validate the merits of the proposed control scheme. In the end of this paper, some conclusions are drawn.
... In recent years, some authors have extensively discussed the finite time stability and control methods of dynamic systems [1], and the finite time is called the settling time or the time of convergence. Different from the problem of infinite time control for dynamic systems [2][3][4][5], in some engineering fields, such as consensus of satellite formation flight, control of spacecraft attitude and control of permanent magnet synchronous motor etc [6][7][8], the finite time convergence of dynamic systems is more meaningful than the convergence of infinite time of dynamic systems. Unfortunately, the finite time control is mainly dependent on the initial state of the dynamic system. ...
This paper discusses synchronization of time-varying delayed neural networks by fixed-time control. Firstly, several new fixed-time stability theorems of dynamic system are discussed, and the estimation of the convergence time are also gained. Compared with some existing results, the convergence time given in this paper can be less conservative and more accurate. Secondly, as one of the important applications of fixed-time stability, several novel sufficient criteria are derived such that two time-varying neural networks can be synchronized within a fixed-time. Finally, simulation result is presented to show the effectiveness of the theoretical result.
... To handle the external disturbance and system uncertainty, some other sliding-mode-based controllers have also been presented in Refs. [31,32]. Unfortunately, they can only achieve uniform ultimate boundedness, that is, the system states will converge to an acceptable neighborhood of origin. ...
This paper proposes a novel feedback control law for spacecraft to deal with attitude constraint, input saturation, and stochastic disturbance during the attitude reorientation maneuver process. Applying the parameter selection method to improving the existence conditions for the repulsive potential function, the universality of the potential-function-based algorithm is enhanced. Moreover, utilizing the auxiliary system driven by the difference between saturated torque and command torque, a backstepping control law, which satisfies the input saturation constraint and guarantees the spacecraft stability, is presented. Unlike some methods that passively rely on the inherent characteristic of the existing controller to stabilize the adverse effects of external stochastic disturbance, this paper puts forward a nonlinear disturbance observer to compensate the disturbance in real-time, which achieves a better performance of robustness. The simulation results validate the effectiveness, reliability, and universality of the proposed control law.
... Sliding mode can be designed and is unrelated to the object parameter and disturbance. It has the advantages of quick response, insensitiveness to parameter change and disturbance, no need of on-line identification of parameters, and simple physical implementation (Huang, 1997;Zeng and Hu, 2012;Hu and Zeng, 2011). Thus it is widely used in practical engineering, especially in the fields of motor and power system control, robot control, aircraft control and satellite attitude control, etc. ...
Rescue of satellite with attitude fault is of great value. Satellite with improper injection attitude may lose contact with ground as the antenna points to the wrong direction, or encounter energy problems as solar arrays are not facing the sun. Improper uploaded command may set the attitude out of control, exemplified by Japanese Hitomi spacecraft. In engineering practice, traditional physical contact approaches have been applied, yet with a potential risk of collision and a lack of versatility since the mechanical systems are mission-specific. This paper puts forward a touchless attitude correction approach, in which three satellites are considered, one having constant dipole and two having magnetic coils to control attitude of the first. Particular correction configurations are designed and analyzed to maintain the target’s orbit during the attitude correction process. A reference coordinate system is introduced to simplify the control process and avoid the singular value problem of Euler angles. Based on the spherical triangle basic relations, the accurate varying geomagnetic field is considered in the attitude dynamic mode. Sliding mode control method is utilized to design the correction law. Finally, numerical simulation is conducted to verify the theoretical derivation. It can be safely concluded that the no-contact attitude correction approach for the satellite with uniaxial constant magnetic moment is feasible and potentially applicable to on-orbit operations.
... Ahn et al. [29] considered an iterative learning control scheme to ensure the trajectory-keeping between the leader and follower-satellites. Zeng and Hu [30] developed a finite-time control method for the electromagnetic satellite formations. Morgan and Chung [31] presented a real-time optimal control algorithm for a linearized model of a swarm of satellites. ...
In this paper, we address the formation flying problem of underactuated nanosatellites by concurrent attitude-position control. Lack of space in nanosatellites hinders us from having omnidirectional motion capabilities. Hence, a practical model for nanosatellites is to employ a one-directional propulsion system together with the reaction wheels. To achieve the formation flying of such nanosatellites, we develop a strategy based on the simultaneous control of attitude and position. The proposed formation flying method consists of three sublevels: first for each underactuated nanosatellite, a virtual fully actuated system is considered and a finite-time translational control method together with a disturbance estimator is developed for the fully actuated system. Subsequently, an adaptive finite-time attitude tracking is proposed to align the thruster of each underactuated nanosatellite with the obtained translational input of the corresponding virtual fully actuated system. Finally, by using the attitude and the obtained virtual input, the thrust for each underactuated nanosatellite is computed. Unlike the existing methods that are merely limited to control of fully actuated satellites, the proposed method presents a robust concurrent formation flying control for a group of underactuated nanosatellites, and accounts for disturbances such as air drag. A rigorous mathematical formulation and the stability analysis of the system are provided. Simulation results are presented to illustrate the performance of the proposed method.
... Elias et al. (2007) demonstrated that two-satellite formation flying is fully controllable using three orthogonal coils and reaction wheels and designed a linear optimal controller using linearized dynamics. Ahsun et al. (2010) presented a nonlinear adaptive control law and Zeng and Hu (2012) have investigated a finite time control for the general N-satellites EMFF in LEO. Cai et al. (2013) have studied the optimal and sliding-mode control of two satellites EMFF. ...
This paper investigates the control of tethered satellite formation actuated by electromagnetic dipoles and reaction wheels using the robust sliding mode control technique. Generating electromagnetic forces and moments by electric current coils provides an attractive control actuation alternative for tethered satellite system due to the advantages of no propellant consumption and no obligatory rotational motion. Based on a dumbbell model of tethered satellite in which the flexibility and mass of the tether is neglected, the equations of motion in Cartesian coordinate are derived. In this model, the J2 perturbation is taken into account. The far-field and mid-field models of electromagnetic forces and moments of two satellites on each other and the effect of the Earth’s magnetic field are presented. A robust sliding mode controller is designed for precise trajectory tracking purposes and to deal with the electromagnetic force and moment uncertainties and external disturbances due to the Earth’s gravitational and magnetic fields inaccuracy. Numerical simulation results are presented to validate the effectiveness of the developed controller and its superiority over the linear controller.
... The satellite characteristics and control parameters are itemized in Table 1. These parameters are for a typical satellite formation taken from [8,35]. The linear controller gains and the optimal control parameters are presented in Tables 2 and 3, respectively, which are selected using the nonlinear simulation results to obtain appropriate responses of the system. ...
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.
... Although Natarajan and Schaub [8] analyzed the dynamics and stability of a two-spacecraft hybrid control, they have not presented the completed dynamic models actuated by this hybrid control. Additionally, the relative motion keeping and reconfiguration capabilities of inter-craft electromagnetic force and electrostatic force have been much exploited [8][9][10][11][12][13][14][15]. ...
In this paper, the dynamics analysis, inertial propulsion force allocation, and magnetic moment solution for multispacecraft electromagnetic orbit correction, which are especially valuable with potential applications to disabled spacecraft deorbit missions, are investigated. The dynamics analysis of the coupled absolute orbit motion correction and spacecraft relative motion keeping, the allocation of the inertial propulsion force, and the coordination design between inertial propulsion force and intercraft electromagnetic force are challenging and have not been resolved. This paper first analyzes the actuation and coordination problems of these coupled forces, and it derives the relative motion dynamic models of spacecraft with respect to the mass center of spacecraft cluster and one spacecraft with respect to the other. Then, taking a three-craft cluster, for example, the magnetic moment solutions for collinear and triangular static equilibria are given, which are possible rigid configurations for orbit correction. Based on these configurations, the orbit correction performance is analyzed and evaluated. Finally, the numerical simulation of a geostationary orbit collinear configuration is carried out that, combined with the theoretical deduction, validated the feasibility of dynamics and solutions for the multispacecraft orbit electromagnetic correction.
This paper investigates event-triggered time-varying grouping formation (TVGF) problem for generic linear homogeneous multi-agent systems under directed graphs. A distributed adaptive event-triggered TVGF algorithm is proposed to ensure that the goal of TVGF can be achieved and the communication frequency between agents is reduced. Compared with previous formation control methods, the algorithm presented in this paper can complete the group formation task while saving communication energy. In addition, the algorithm’s dependence on global network information is also eliminated by using adaptive techniques. Finally, the availability of the proposed control law is established by numerical simulation.
The electromagnetic force generated by the interaction of electromagnetic coils can be used to replace the conventional propellant consumption mode in close relative motion control, thereby promoting the application of formation flight technology for long-term and continuous space missions. Herein, a hysteresis-switching logic-based switching linear parameter varying (LPV) controller synthesis technique with guaranteed performance for electromagnetic formation flying on a highly elliptical orbit is proposed. First, considering that the relative dynamics model of an elliptical orbit is characterized by time-varying uncertainty, the LPV model is described. By introducing switching LPV controllers among different scheduled parameter subsets, conservativeness can be reduced. Second, the system modeling error, the uncertainty caused by a simplified electromagnetic coil model, and external disturbance are considered to derive switching LPV controller synthesis conditions based on the guaranteed H∞ performance. Derivation analysis shows that the proposed switching LPV controller not only ensures the robustness of the system against uncertainties, but also realizes the control input constraints. Finally, numerical simulations and comparative analyses are performed to demonstrate the effectiveness and advantages of the proposed control method.
In this paper, the simplified electromagnetic force/torque model and coupled orbit-attitude dynamics modeling in spacecraft electromagnetic docking are investigated, and an improved sliding mode control scheme based on planned trajectory is proposed. In this scenario, the docking two spacecraft are equipped with four energized solenoids with iron cores fixed in the body frame, and small- angle hypothesis is used to derive the simplified electromagnetic force/torque model, based on which the coupled orbit-attitude dynamics equation is established. With trajectory planning of relative orbit and attitude, where the tracking process of coupled orbit-attitude is divided into three successive parts with predefined time using three characteristic time instants, a sliding mode control strategy is proposed to solve the tracking problem. Simulation results illustrate the simplification rationality of electromagnetic force/torque model, and the good tracking performance of coupled orbit-attitude tracking controller at predefined time.
As a novel approach to control the relative motion of a satellite formation, electromagnetic formation flight (EMFF) has some prominent advantages, such as no propellant consumption and no plume contamination, and has a broad prospect of application in such fields as on-orbit detection and optical interferometry. The current paper investigates the optimal control for the reconfiguration of a two-satellite electromagnetic formation using the nonlinear quadratic optimal control technique. Specifically, the effects of the Earth’s magnetic field on the EMFF satellites are analyzed, and then the nonlinear translational dynamic model of a two-satellite electromagnetic formation is derived by utilizing the analytical mechanics theory. Considering the high nonlinearity and coupling in the dynamic model and the actuator saturation, a closed-loop robust suboptimal control strategy based on the indirect robust control scheme and the θ-D technique is proposed with robust stability and optimality. To ensure a further reduction of control input, the designed suboptimal controller is modified by applying the Tracking-Differentiator. The feasibility of the derived translational dynamics and proposed control strategy for the robust reconfiguration mission is validated through theoretical analysis and numerical simulations.
Purpose
The purpose of this paper is to develop a theoretical design for the attitude control of electromagnetic formation flying (EMFF) satellites, present a nonlinear controller for the relative translational control of EMFF satellites and propose a novel method for the allocation of electromagnetic dipoles.
Design/methodology/approach
The feedback attitude control law, magnetic unloading algorithm and large angle manoeuvre algorithm are presented. Then, a terminal sliding mode controller for the relative translation control is put forward and the convergence is proved. Finally, the control allocation problem of electromagnetic dipoles is formulated as an optimization issue, and a hybrid particle swarm optimization (PSO) – sequential quadratic programming (SQP) algorithm to optimize the free dipoles. Three numerical simulations are carried out and results are compared.
Findings
The proposed attitude controller is effective for the sun-tracking process of EMFF satellites, and the magnetic unloading algorithm is valid. The formation-keeping scenario simulation demonstrates the effectiveness of the terminal sliding model controller and electromagnetic dipole calculation method.
Practical implications
The proposed method can be applied to solve the attitude and relative translation control problem of EMFF satellites in low earth orbits.
Originality/value
The paper analyses the attitude control problem of EMFF satellites systematically and proposes an innovative way for relative translational control and electromagnetic dipole allocation.
Electromagnetic formation flight (EMFF) denotes a method of formation flight control in which a cluster of spacecraft are equipped with controllable magnetic dipoles for coordination of their relative positions using interdipole forces. We present a method for finding a minimum-power dipole solution for a given set of desired interdipole forces. We approach this nonlinear constrained optimization problem using sequential quadratic programming, which requires a Jacobian relating changes in the dipoles to changes in forces, as well as the gradient and Hessian of a Lagrangian function. We derive compact analytic solutions for all three of these quantities, using linear-algebraic representations and vector calculus, which can be implemented numerically with a small set of simple functions. Our approach does not rely on arbitrary parameterizations as have prior approaches, and the structure enables further analysis of numerical conditioning and convergence. We conduct numerical simulations, using a number of configurations relevant to EMFF, to verify the method and characterize its performance when numerical routines are randomly initialized, which can serve as a benchmark against which future improvements can be quantified. The method presented may have other uses beyond EMFF, including being applied to new classes of modular magnetic systems.
Electromagnetic formation flight utilizes electromagnetic forces to control the relative positions of satellites, and offers a promising alternative to a traditional propellant-based spacecraft formation flying due to no fuel expenditure. Since available electromagnetic forces generated on board are small, their efficient use is a challenging issue in the presence of saturation. This paper proposes a novel adaptive reaching law based sliding mode control for the trajectory tracking of electromagnetic formation flight with actuator saturation. The adaptive reaching law is characterized by a modulation function which combines a saturated term with a non-switching term. The saturated term makes the sliding variable converge as fast as possible under input saturation, while the non-switching term is used to guarantee a terminal tracking performance and remove chattering. Thus, the introduced modulation function enables a smooth transition of the reaching law between two terms and an adaptive decrease rate of sliding variable. The proposed control can achieve a fast convergence and offers the robustness against external disturbance with input saturation. Simulation results are given to demonstrate the performance of the presented method.
Electromagnetic formation flight leverages electromagnetic force to control the relative position of satellites. This new propulsion technique offers a promising alternative to traditional propellant-based spacecraft formation flying since it does not consume fuel. Due to the restriction of maximum current in coils, the available inter-satellite electromagnetic force is small, and its efficient use is an important issue. In this paper, a modified far-field model is proposed to gain better accuracy of electromagnetic force approximation. Based on this model, an adaptive terminal sliding mode control is proposed to achieve fast trajectory tracking. The given method can guarantee the finite-time convergence of tracking error in the presence of bounded disturbance, input uncertainty, and saturation. Numerical simulation results demonstrate the performance and robustness of the proposed control.
The satellite formation flying involved in electromagnetic forces is studied in this paper. A 6-DOF relative motion model taking into account the inherent electromagnetic coupling is established to achieve synchronous control of both the relative translation and rotation in the array. Based on this model, the coupling effects can be fully utilized so as to treat the electromagnetic torque part of the control moment rather than the disturbance. Considering the reconfiguration of electromagnetic formation flying as an optimal control problem with regard to relative translation, angular momentum management and control output, it is transformed into a constrained non-linear program through the Legendre pseudospectral method. A novel high-precision numerical computation method is developed against the strong nonlinearity and coupling of the system. Feasible trajectories for both the general and the specific planar formation reconfiguration are generated to verify the validity of the proposed dynamic model and optimization algorithm.
Optimal reconfigurations of two-craft electromagnetic formation in low earth circular orbit are discussed. Equations of motion for two-spacecraft electromagnetic formation are derived according to the motion of tethered satellite. Three optimality criteria considered are minimum time, minimum acceleration, and minimum control acceleration. Two examples are presented to demonstrate the feasibility with different DOFs. The two-point-boundary-value problem is numerically solved via Gauss pseudo-spectral methods. A general framework of calculating control currents in electromagnetic coils according to the required control forces is presented. Analytical solutions of control currents for the case of two-craft are derived considering energy consumption equilibrium.
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.
This paper presents the concept of electromagnetic satellite formation flight (EMFF), a novel propulsion mode of controlling the relative motion of satellite formation without propellant consumption. The alternative actuation system utilizes electromagnetic force, generated by the interaction of electromagnets around component spacecrafts, to transform the configuration. The linear equation of relative motion and stable analytical solution for circle reference orbit are then established. The optimal reconfiguration problem of a two-spacecraft electromagnetic formation in low earth circular orbit is solved using optimal control techniques. The objective of the reconfiguration is to maneuver the formation between two stable elliptic configurations based on CW equation. The optimality criteria considered is minimum time. Gauss pseudospectral method is applied to convert the problem into nonlinear programming (NLP) which can be solved by sequential quadratic programming (SQP). Numerical simulation indicates that the Gauss pseudospectral method can effectively converge to optimal solution, and it can be applied to other non-contact forces satellite formation. It also proves that the electromagnetic actuation technology is feasible for satellite formation reconfiguration.
Electromagnetic formation is a novel method of propellantless formation, which enables synchronous control of both relative translation and rotation in the array. To fully utilize the inherent electromagnetic coupling effects, an integrated relative dynamic model is established. Considering the reconfiguration of electromagnetic formation as an optimal control problem with regard to relative translation and angular momentum management, it is transformed into a constrained non-linear programming problem through the Legendre pseudospectral method. Facing the system’s strong nonlinearity and coupling, a novel high-precision numerical computation method is developed. Feasible trajectories for a specific planar transformation and a more general case of reconfiguration are generated to verify the proposed dynamic model and optimization algorithm.
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 dipoles. Micro-electromagnetic formation flying, which is an alternative to electromagnetic formation flying in terms of reduced complexity, uses conventional conductors to replace the high-temperature superconducting coils in electromagnetic formation flying, shortening the separation distances between the electromagnets. This paper investigates the use of micro-electromagnetic formation flying for providing relative position control for unperturbed station-keeping in a multi-satellite array along the cross-track direction that can be used in cross-track interferometric synthetic aperture radar applications. Considering that conventional conductors produce small separation distances between electromagnets, comparatively large baselines can be achieved by positioning multiple satellites consecutively in an array. The existence of equilibrium positions of the satellites is demonstrated. The station-keeping efficiency of the formation satellites is studied. It is found that the electromagnetic dipoles on neighboring satellites should be equal in magnitude and opposite in direction to obtain the maximum station-keeping efficiency of the formation; correspondingly, the equilibrium positions of the satellites along the cross-track direction are symmetrical about the center of mass of the formation. A method for maximizing the station-keeping efficiency of the formation using micro-electromagnetic formation flying is also presented, using feasible designs for small satellite formations as examples.
Aimed at the electromagnetic formation flying (EMFF) ground testbed, an optimal linear quadric regulator (LQR) and sliding mode controller (SMC) are both proposed in this paper. Firstly, the highly nonlinear characteristics of the electromagnetic force and torque are analyzed. Then, the nonlinear dynamics equations are linearized, the controllability of the linearized system is analyzed, the optimal linear quadric regulator is then presented. Moreover, a sliding mode controller is also presented. Finally, the numerical simulation is carried out to compare LQR and SMC, and demonstrate the robustness of SMC. The results show that the SMC is more effective than LQR, which pave the way for electromagnetic formation flying ground simulation.
This paper deals with the optimal tracking and synchronized control of leader–follower spacecraft formation flying, considering motion with 6 degree-of-freedom (6-DOF). The relative position and relative attitude between spacecrafts are required to track a desired time-dependent trajectory. Modeling of 6-DOF formation spacecraft is introduced firstly, applying dual quaternion in describing the coupled relative motion. A nonlinear suboptimal synchronized tracking controller is then proposed to perform two tasks: (1) to ensure globally asymptotic convergence of the translational and rotational tracking errors with parametric uncertainties and external disturbances considered, and (2) to minimize the predefined performance indices. In the proposed controller, the optimal control and the sliding mode control (SMC) operate in a complementary manner. A control Lyapunov function (CLF) is constructed to solve the nonlinear optimal control problem, whereas SMC is established to ensure robustness and achieve accurate control. A detailed stability analysis and proofs of the resulting closed-loop system using a Lyapunov framework are also included. Finally, illustrative numerical simulations and comparisons are presented to demonstrate the validity and advantages of the proposed controller.
In this work, using the finite time sliding mode control, the design of attitude tracking control of a rigid spacecraft has been discussed. The proposed control law has been designed by using the novel fast terminal sliding mode surface with a reaching law. The proposed control law , avoids the singularity possibility, and offers the faster convergence speed in the reaching phase and in the sliding phase. In addition, the applied control input is continuous in nature. The finite time stability has been proved using the Lyapunov theory. In last, to show the effectiveness of the proposed control method, simulations have been conducted under the conditions of mass inertia uncertainty and external disturbances, and the results, in comparison with the existing methods have been demonstrated .
An alternative actuation system for fractionated spacecraft is to use electromagnetic force without the expenditure of fuel. This paper investigates the novel application of virtual rendezvous and docking for fractionated spacecraft with concepts such as wireless power transfer in mind. Firstly, the magnetic force model and relative motion dynamics are introduced. Then, the feedback control law for circular motion of electromagnetic system is presented, and the control scheme for virtual rendezvous and docking is also proposed. Finally, the numerical simulations are carried out. Simulation results verify that the proposed approach is feasible and effective.
The magnitude of hinge moment is a prominent problem for rapid dive maneuver of hypersonic glide vehicles. A robust optimal integrated guidance law considering constraints of hinge moment and terminal impact angle is proposed with excellent performance. Based on the analogy relationship of hinge moment and normal aerodynamic load, the constraint of hinge moment is transformed to normal load constraint; and the optimal guidance law under nominal conditions is derived utilizing optimal control theory. A terminal sliding mode control based guidance modification is designed to eliminate the inevitable departure brought by uncertainties in finite time; and the hyperbolic tangent function is introduced to reduce the high-frequency chatting. The theoretical analysis and simulation results are conducted to illustrate the capability of the proposed integrated guidance law for hypersonic glide vehicle.
This paper addresses the tracking control problem of six-degree-of-freedom (6DOF) leader-follower satellite formation flying. First using dual quaternion, 6DOF relative motion model of formation satellite is introduced. Then, a 6DOF quasi-optimal integral sliding mode controller is proposed to guarantee the globally asymptotic convergence of translational and rotational tracking errors despite the presence of parametric uncertainties and external disturbances. In the presented controller, control Lyapunov function isused to construct an optimal controller to minimize two predefined performance indices. A detailed stability analysis of the resulting closed-loop system using a Lyapunov framework is also included. Finally, numerical simulations are presented to illustrate the validity and effectiveness of the proposed controller.
Satellite formation keeping through inter-satellite electromagnetic force provides an attractive alternative for future space missions due to its distinct advantages of no propellant consumption or plume contamination as compared to conventional approaches. However, the internal force nature as well as the high nonlinearity and coupling of electromagnetic force brings new control challenges for this novel technique. In this paper, analysis on the dynamics characteristics and special control issues in the presence of electromagnetic force is carried out on the basis of the derived relatively translational dynamics. Considering the model uncertainties, external disturbances and sensor noise, a combined nonlinear control scheme involving feed-forward and feedback control components is proposed for electromagnetic-force-based formation keeping. The feed-forward component is directly obtained through desired configuration and dynamics under nominal conditions while the feedback component is realized utilizing active disturbance rejection control methodology with some reasonable improvement. Numerical simulation is presented to verify the feasibility and validity of the combined control scheme.
An alternative actuation system for formation flight spacecraft uses electromagnetic force generated by an electromagnetic dipole in concert with reaction wheels to control the position and attitude of each satellite relative to each other. This novel concept is called electromagnetic formation flight. All the actuators in the system are powered by solar energy and the formation flight propulsion system does not depend on consumables. To demonstrate electromagnetic formation flight a proof-of-concept ground testbed is developed. This paper describes the design of the testbed vehicles and the first known closed-loop control of electromagnetic formation flight vehicles. Demonstrations involving position hold and trajectory following maneuvers show that standard control approaches can be used to control the motion of a formation flying testbed using unique electromagnet actuation system.
This paper presents a global non-singular terminal sliding mode controller for rigid manipulators. A new terminal sliding mode manifold is first proposed for the second-order system to enable the elimination of the singularity problem associated with conventional terminal sliding mode control. The time taken to reach the equilibrium point from any initial state is guaranteed to be finite time. The proposed terminal sliding mode controller is then applied to the control of n-link rigid manipulators. Simulation results are presented to validate the analysis.
Examines finite-time stability of homogeneous systems. The main
result is that a homogeneous system is finite-time stable if and only if
it is asymptotically stable and has a negative degree of homogeneity
In this paper, a robust multi-input/multi-output (MIMO) terminal
sliding mode control technique is developed for n-link rigid robotic
manipulators. It is shown that an MIMO terminal switching plane variable
vector is first defined, and the relationship between the terminal
switching plane variable vector and system error dynamics is
established. By using the MIMO terminal sliding mode technique and a few
structural properties of rigid robotic manipulators, a robust controller
can then be designed so that the output tracking error can converge to
zero in a finite time, and strong robustness with respect to large
uncertain dynamics can be guaranteed. It is also shown that the high
gain of the terminal sliding mode controllers can be significantly
reduced with respect to the one of the linear sliding mode controller
where the sampling interval is nonzero
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.
A sliding mode control method based on finite-time control technology is designed for the spacecraft attitude tracking control system in the presence of uncertain term. The tracking error system can not only be controlled to the sliding manifold from any initial state in finite-time but also converge to zero along the sliding manifold in finite-time. Rigorous mathematical proof is also given. In order to avoid the chattering problem, the sign function in control law is substituted by a new saturation function. Numerical simulation results are presented to validate the effectiveness of the system.
This article studies spacecraft attitude control problem to achieve global fast tracking for ground target. The expected spacecraft attitude parameters and a Lagrange-like model of spacecraft attitude motion are presented, respectively, and then a robust sliding mode controller based on this model and Euler parameters is designed to achieve tracking in the presence of model uncertainties and external disturbances. The proposed controller can guarantee global fast stability of the closed-loop systems and convergence of tracking errors by employing global fast-sliding mode model, which combines the advantages of linear and terminal sliding mode controls. The theoretical proof of stability and convergence is given subsequently. Numerical simulations are finally presented to demonstrate the performance of the developed controller.
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
This paper focuses on the design of a safe control method minimizing the collision hazard for satellites flying on near-circular orbits. The geometry of formation configuration is described based on the relative orbital elements, which is particularly efficient for relative orbit control design and proximity analyses. Formulas of the parameters of the ellipse in the cross-track plane are proposed and the parameters of the safe formation configuration which remains out of the avoidance region are described by the rotating angle of the ellipse in the cross-track plane. The energy needed for the collision avoidance control is expressed by the initial and the target in-plane formation configuration, which is optimized by the Newton method. A collision avoidance control method is also presented for formation initialization and formation reconfiguration operations. Finally, the maneuver control is planned by the initial and the optimized target formation configuration. The simulation results clearly indicate the simplicity and effectiveness of the presented method. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
The collinear equilibrium three-craft-formation charge feedback control problem is investigated. Given a charged-equilibrium collinear configuration of spacecraft flying in deep space, a nonlinear charge feedback control algorithm is developed to stabilize the formation to the desired shape and size. The Coulomb forces are assumed to be acting along the line-of-sight directions between the bodies and thus do not provide general vehicle position controllability. A study of the charged collinear three-craft formation shows that there exists an infinite number of equilibrium charge solutions for any collinear configuration. Given a real value of one spacecraft charge, the required equilibrium charges of the remaining two vehicles are solved analytically. A Lyapunov-based nonlinear control algorithm is developed to stabilize the configuration to the equilibrium state using only the spacecraft charges as the control states. Real charge solutions are ensured by using the one-dimensional solution null-space. Numerical simulations illustrate the new charge feedback control performance. In contrast to earlier efforts, collinear configurations are stabilized even in the presence of very large initial position errors.
Finite-time control theory has attracted much attention in recent years, since finite-time stable systems usually possess better robustness and disturbance rejection properties. First of all, the origin for finite-time control method is discussed, and the frequently-used criteria for finite-time control systems is listed. Then the present research development for finite-time control systems is summarized. Finally, the future outlook on finite-time control is discussed.
The use of propellant to maintain the relative orientation of multiple spacecraft in a sparse aperture telescope such as NASA's Terrestrial Planet Finder (TPF) poses several issues. These include fuel depletion, optical contamination, plume impingement, thermal emission, and vibration excitation. An alternative is to eliminate the need for propellant, except for orbit transfer, and replace it with electromagnetic control. Relative separation, relative attitude, and inertial rotation of the array can all be controlled by creating electromagnetic dipoles on each spacecraft, in concert with reaction wheels, and varying their strengths and orientations. Whereas this does not require the existence of any naturally occurring magnetic fields, such as the Earth's, such fields can be exploited. Optimized designs are discussed for a generic system and a feasible design is shown to exist for a five-spacecraft, 75-m baseline TPF interferometer.
In this paper, we consider the equations of motion of a two-spacecraft formation flying array that uses electromagnets as relative position actuators. The relative positions of the spacecraft are controlled by the forces generated between the electromagnets on the two spacecraft, and the attitudes of the spacecraft are controlled using reaction wheels. The nonlinear equations of motion for this system are linearized about a nominal operating trajectory, taken to be a steady-state spin maneuver used for deep-space interferometric observation. The linearized equations are analyzed for stability and controllability. Although the open-loop system proves to be unstable, a controllability analysis indicates that the system is fully controllable with the given suite of actuators, and is therefore stabilizable. An optimal linear feedback controller is then designed, and the closed-loop dynamics are simulated. The simulations demonstrate that the closed-loop system is indeed stable, and that linear control is a very promising technique for electromagnetic formation flight systems, despite the nonlinearity of the dynamics.
This paper considers the control of entire-formation maneuvering in low-thrust Earth-orbiting spacecraft formation flying (SFF). A coordinated control scheme based on the leader-follower approach is developed to achieve formation maneuvers while keeping the internal formation intact. To implement the control scheme, a low-level sliding mode control (SMC) based on nonlinear dynamics is provided. Using a Lyapunov-based control design and stability analysis technique, we prove that the closed-loop system is globally asymptotically stable. Numerical simulations show the advantage of the controller for fuel cost reductions, tracking accuracy, and effectiveness in ensuring entire-formation maneuvering. An exact nonlinear model with modeled disturbances (J2 disturbance and bounded uncertainties) is used for dynamic simulation.
Satellite formation flight is a much-anticipated technology for future space-science missions, such as high-resolution space-based telescopes. A potentially enabling technology under development allows clusters of spacecraft to maneuver without the use of propellant, instead using electromagnetic control of the relative degrees of freedom within the cluster. This electromagnetic formation-flight technology offers potentially limitless mission life, in exchange for a highly coupled, nonlinear control problem. Several methods have been explored to address this problem, and some have achieved considerable success at its optimal, or at least locally optimal, solution. This paper does not produce optimal trajectories for unconstrained maneuvers, but instead provides a method for determining all of the feasible control solutions that will produce a specified maneuver. An example is provided for the case of three spacecraft rotating in a planar, equilateral triangle configuration, while the plane of rotation is simultaneously changing direction, as might be encountered while retargeting a separated spacecraft interferometer. The approach may be used on its own to find feasible, albeit suboptimal, solutions, or in conjunction with an optimal-control solution, to probe its optimality, find alternative solutions, or plan for contingencies. The current research deals solely with free-space translational solutions, without consideration of torques that are developed or the resulting buildup or removal of angular momentum. Extension of the current approach to address these issues is the subject of a follow-on paper.
An alternative actuation system for formation flight spacecraft uses electromagnetic force generated by an electromagnetic dipole in concert with reaction wheels to control the position and attitude of each satellite relative to each other. This novel concept is called electromagnetic formation flight. All the actuators in the system are powered by solar energy and the formation flight propulsion system does not depend on consumables. To demonstrate electromagnetic formation flight a proof-of-concept ground testbed is developed. This paper describes the design of the testbed vehicles and the first known closed-loop control of electromagnetic formation flight vehicles. Demonstrations involving position hold and trajectory following maneuvers show that standard control approaches can be used to control the motion of a formation flying testbed using unique electromagnet actuation system.
The synthesis of optimal controls for second-order linear systems with a saturable scalar input is considered. A non-quadratic cost functional is introduced which, as in the case of quadratic cost, can give rise to singular solutions ; the associated optimal controls are explicitly characterized and, in contrast to the case of quadratic cost, act over a finite time interval only. For a double integrator system it is shown that, under certain conditions, the optimal control is identical to the minimum-time solution.
Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using Hölder continuous Lyapunov functions. In this paper, we extend the finite-time stability theory to revisit time-invariant dynamical systems and to address time-varying dynamical systems. Specifically, we develop a Lyapunov-based stability and control design framework for finite-time stability as well as finite-time tracking for time-varying nonlinear dynamical systems. Furthermore, we use the vector Lyapunov function approach to study finite-time stabilization of compact sets for large-scale dynamical systems. Copyright © 2008 John Wiley & Sons, Ltd.
This paper investigates the spacecraft attitude tracking control problem. Two robust sliding mode controllers based on the quaternion and Lagrange-like model are proposed to solve this problem both in the absence of model uncertainties and external disturbances as well as in the presence of these. The controllers can guarantee the convergence of attitude tracking errors in finite time rather than in the asymptotic sense, where time tends to infinity. By constructing a particular Lyapunov function, the convergences of the proposed controllers for the closed-loop systems are proven theoretically. To alleviate the chattering phenomenon while at the same time guaranteeing the finite convergence during the process of attitude tracking, a new function is introduced into the controller. Numerical simulations are finally provided to illustrate the performance of the proposed controllers.
This paper considers the problem of relative motion control for spacecraft formation flying (SFF). Using terminal sliding mode technique, a relative position/velocity tracking control based on the nonlinear model is developed. The presented controller enables rapid formation reconfiguration with feasible fuel cost and strong robustness in the presence of uncertain but bounded disturbances. A nonlinear model with J<sub>2</sub> disturbance and bounded uncertainties is used for dynamic simulation.
A real-time testing system for the realistic demonstration of the Guidance, Navigation and Control (GNC) system for the distributed spacecraft in Low Earth orbit (LEO) is presented in this paper. The developed processor-in-the-loop simulation system has led to the full testing and validation of the GNC flight code to be ported to a VxWorks environment in a PowerPC8245 board, representative of the onboard computer. The developed system is built under a distributed architecture which consists of industrial control computers, embedded computers, wire and wireless Ethernet, PCI-CAN devices and plasma displayer. The system allows elaborate validations of formation flying functionalities and performance for the full operation phases. The test results of autonomous formation keeping and formation reconfiguration provide good evidence to support performance and quality of the coordination control algorithms.
In this paper, we develop a new finite-time formation control framework for multi-agent systems with a large population of members. In this framework, we divide the formation information into two independent parts, namely, the global information and the local information. The global formation information decides the geometric pattern of the desired formation. Furthermore, it is assumed that only a small number of agents, which are responsible for the navigation of the whole team, can obtain the global formation information, and the other agents regulate their positions by the local information in a distributed manner. This approach can greatly reduce the data exchange and can easily realize various kinds of complex formations. As a theoretical preparation, we first propose a class of nonlinear consensus protocols, which ensures that the related states of all agents will reach an agreement in a finite time under suitable conditions. And then we apply these consensus protocols to the formation control, including time-invariant formation, time-varying formation and trajectory tracking, respectively. It is shown that all agents will maintain the expected formation in a finite time. Finally, several simulations are worked out to illustrate the effectiveness of our theoretical results.
The alternative to using propellant for actuation of formation flying satellites is for each spacecraft to produce their own electromagnetic field that others in the formation can react against. This technique can be achieved by creating a steerable magnetic dipole and is called Electromagnetic Formation Flight (EMFF). EMFF can be implemented on a spacecraft by driving current through three orthogonal electromagnetic coils to create a steerable magnetic dipole in three dimensions. This paper investigates the applicability of EMFF as a means for attitude and translation control of multiple spacecraft maneuvering in close proximity. One example scenario is using two EMFF satellites as an inspector system to examine a non-EMFF satellite that is nearby. The results of the analysis show the design of the proximity guidance, navigation, and control laws that allow for rapid inspection scenarios. The primary role of EMFF is to impart forces and torques to maintain a satellite array. In addition, potential secondary roles of EMFF were investigated using EMFF in a multi-role sense. These included power transmission, passive, offensive capabilities, and use of the HTS coils as torque coils for geostationary satellites. The results of this paper show that EMFF is a promising propellantless formation flight technology.
A continuous finite-time control scheme for rigid robotic manipulators is proposed using a new form of terminal sliding modes. The robustness of the controller is established using the Lyapunov stability theory. Theoretical analysis and simulation results show that faster and high-precision tracking performance is obtained compared with the conventional continuous sliding mode control method.
A nonlinear relative position control algorithm is designed for spacecraft precise formation flying. Taking into account the effect of J2 gravitational perturbations and atmospheric drag, the relative motion dynamic equation of the formation flying is developed in a quasi-linear parameter-varying (QLPV) form without approximation. Base on this QLPV model, polynomial eigenstructure assignment (PEA) is applied to design the controller. The resulting PEA controller is a function of system state and parameters, and produces a closed-loop system with invariant performance over a wide range of conditions. Numerical simulation results show that the performance can fulfill precise formation flying requirements.
This brief proposes a robust control algorithm for stabilization of a three-axis stabilized flexible spacecraft in the presence of parametric uncertainty, external disturbances and control input nonlinearity/dead-zone. The designed controller based on adaptive variable structure output feedback control satisfies the global reaching condition of sliding mode and ensures that the system state globally converges to the sliding mode. A modified version of the proposed control law is also designed for adapting the unknown upper bounds of the lumped uncertainties and perturbations. The stability of the system under the modified control law is established. Numerical simulations show that the precise attitude pointing and vibration suppression can be accomplished using the derived robust or adaptive controller.
Conventional guidance laws are designed based on Lyapunov theorems on asymptotic stability or exponential stability. They will guide the line-of-sight angular rate to converge to zero or its small neighborhood, however, only as time approaches infinity. In this paper, new guidance laws with finite convergent time are proposed. The guidance laws are obtained based on new sufficient conditions derived in this paper for the finite time convergence of the line-of-sight angular rate. It is proved that, with the guidance laws, the line-of-sight angular rate will converge to zero or a small neighborhood of zero before the final time of the guidance process. Furthermore, such guidance laws will ensure finite time convergence and finite time stability in both the planar and three-dimensional environments. Simulation results show that the guidance laws are highly effective.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2005. Includes bibliographical references (p. 325-327). Electromagnetic Formation Flight (EMFF) describes the concept of using electromagnets (coupled with reaction wheels) to provide all of the necessary forces and torques needed to maintain a satellite's relative position and attitude in a formation of satellites. With EMFF, this formation can be controlled without the use of traditional thrusters. This thesis demonstrates the feasibility of the EMFF system. First three different models for the forces and torques produced by the electromagnets are created, and the equations of motion are developed and described. The equations of motion are determined to be polynomial functions of each satellite's magnetic dipole (which is directly related to the current in the electromagnets). Methods for solving the equations of motion are presented along with examples showing that any desired maneuver can be performed as long as the formation's center of mass is not required to change. An effect of Newton's third law causes torques to be applied to the individual vehicles in a direction opposite to the formation's angular acceleration. Reaction wheels are used to absorb the angular momentum. Next, the thesis describes methods for distributing the angular momentum evenly among the satellites. Finally, the additional challenges of operating in low Earth orbit are addressed. These include operating in the Earth's gravitational field (including the J₂ disturbance), and operating in the Earth's magnetic field. The latter is a mixed blessing due to the large disturbance torques produced from the Earth's magnetic field. However, it is shown in this thesis that it is possible to control and utilize these disturbance torques. (cont.) In fact, the torques from the Earth's magnetic field can be used to remove excess angular momentum built up on the satellite reaction wheels. Overall, this thesis proves that EMFF can be used to control the relative position and attitude of satellites flying in formation. by Samuel Adam Schweighart. Ph.D.
Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Holder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability. It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related. Consequently, converse Lyapunov results can only assure the existence of continuous Lyapunov functions. Finally, the sensitivity of finite-time-stable systems to perturbations is investigated.
This paper studies properties of homogeneous systems in a geometric, coordinate-free setting. A key contribution of this paper is a result relating regularity properties of a homogeneous function to its degree of homogeneity and the local behavior of the dilation near the origin. This result makes it possible to extend previous results on homogeneous systems to the geometric framework. As an application of our results, we consider finite-time stability of homogeneous systems. The main result that links homogeneity and finite-time stability is that a homogeneous system is finite-time stable if and only if it is asymptotically stable and has a negative degree of homogeneity. We also show that the assumption of homogeneity leads to stronger properties for finite-time stable systems. Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/45918/1/498_2005_Article_151.pdf
In this paper, we revisit the classical problem of attitude stabilization for a rigid spacecraft. A global set stabilizing scheme with finite-time technique is proposed. We show that the states of the closed loop system will be stabilized to an equilibrium set in finite time. Using adding a power integrator method, we prove that the closed loop system satisfies the global set stability. We also show that the control method in this paper is more natural and energy efficient. Numerical simulation results show the effectiveness of the method.
In this note, global finite time stabilization is investigated for a class of nonlinear systems in p normal form with parametric uncertainties. To achieve finite-time stabilization, a constructive control design approach is proposed by following backstepping methodology, and an adaptive finite-time control law is obtained in the form of continuous time-invariant feedback.
A class of bounded continuous time-invariant finite-time
stabilizing feedback laws is given for the double integrator. Lyapunov
theory is used to prove finite-time convergence. For the rotational
double integrator, these controllers are modified to obtain
finite-time-stabilizing feedback that avoid
“unwinding”
The US/UK World Magnetic Model for
- S Maus
- S Macmillan
- S Mclean
S. Maus, S. Macmillan, S. McLean, et al., The US/UK World Magnetic Model for 2010–2015, NOAA Technical Report NESDIS/NGDC.