Spacecraft formation flying: a review and new results on state feedback control (original) (raw)
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Output feedback control of relative translation in a leader-follower spacecraft formation
2006
We present a solution to the problem of tracking relative translation in a leader-follower spacecraft formation using feedback from relative position only. Three controller configurations are presented which enables the follower spacecraft to track a desired reference trajectory relative to the leader. The controller design is performed for different levels of knowledge about the leader spacecraft and its orbit. The first controller assumes perfect knowledge of the leader and its orbital parameters, and renders the equilibrium points of the closed-loop system uniformly globally asymptotically stable (UGAS). The second controller uses the framework of the first to render the closed-loop system uniformly globally practically asymptotically stable (UGPAS), with knowledge of bounds on some orbital parameters, only. That is, the state errors in the closed-loop system are proved to converge from any initial conditions to a ball in close vicinity of the origin in a stable way, and this ball can be diminished arbitrarily by increasing the gains in the control law. The third controller, based on the design of the second, utilizes adaptation to estimate the bounds that were previously assumed to be known. The resulting closed-loop system is proved to be uniformly semiglobally practically asymptotically stable (US-PAS). The last two controllers assume boundedness only of orbital perturbations and the leader control force. Simulation results of a leader-follower spacecraft formation using the proposed controllers are presented.
Linearizing Assumptions and Control Design for Spacecraft Formation Flying Maneuvers
2004
In this paper the validity of neglecting the relative effect of the gravitational force of the Earth on a formation of spacecraft is studied. This relative effect is treated as an unknown disturbance acting on the system and all control laws are designed using a linear model that neglects this effect. A previously designed simple linear feedback controller is tested under different conditions using the linear model and the full nonlinear model that includes the gravitational force. All tests are carried out in the presence of saturation limits. The results show that the linear controller exhibits oscillations in the transient response and poor robustness under certain conditions. It also exhibits a high saturation tendency, thereby leading to increased fuel consumption. This controller also causes a high rise in the velocity errors at ordinary values of the gains. Based on the behavior of this controller, new controllers are proposed that overcome these drawbacks without any need fo...
Autonomous guidance and control of Earth-orbiting formation flying spacecraft: Closing the loop
Acta Astronautica, 2008
Previous work on autonomous formation flying guidance and control identified three key challenges to overcome in order to obtain a fully autonomous guidance and control loop: an accurate but simple model of relative motion about elliptical and perturbed orbits, an efficient way of performing conflicting requirements trade-off with power-limited on-board computers, and finally an optimal or near-optimal control algorithm easy to implement on a flight computer. This paper first summarizes recent developments on each of these subject that help to overcome these challenges, developments which are then used as building blocks for an autonomous formation flying guidance and control system. This system autonomously performs trade-offs between conflicting requirements, i.e. minimization of fuel cost, formation accuracy and equal repartition of the fuel expenditure within the formation. Simulation results show that a complete guidance and control loop can be established using mainly analytical results and with very few numerical optimization which facilitates on-board implementation.
The novel concept of multiple spacecraft formation flying as a substitute for a single large vehicle will enhance future space mission performance. The benefits of a spacecraft formation include more cost effective synthetic aperture radar for observations, "graceful degradation" of the formation, flexibility of the satellites altering their roles, reduction of cost owing to the reduction of mass launched into orbit etc. A significant challenge in the domain of control design is to contrive a formation maintenance controller that will enable the member spacecrafts to maintain a desired relative orbit with minimal propellant expenditure. This thesis examines linear and nonlinear LEO formation control methodologies, one of each type, with the aim of evaluating them from a propellant budget, thrust level and error dynamics standpoint. A Linear Quadratic Regulator has been applied on J 2 -perturbed Clohessy-Wiltshire dynamics. In order to remove the restriction of the applicability of Cartesian local vertical local horizontal frame based control laws to only circular leader orbits, a sliding mode controller acting on a full nonlinear dynamical model has been implemented. This work also studies the effects of leader orbit eccentricity, inclination and formation radius on formation keeping fuel demand and tracking error. Finally, conclusions are drawn regarding the suitability of the control laws considered and various recommendations made.
A Backstepping Sliding Mode Controller Design for Spacecraft Formation Flying
EasyChair Preprints, 2018
In this paper, a backstepping sliding mode controller is developed for tracking control of spacecraft formation flying on elliptical orbits. The controller is designed in accordance with the nonlinear model of relative motion, and combines the advantages of backstepping and sliding mode control techniques. After applying the backstepping method to incorporate the tracking errors and Lyapunov functions, a sliding mode controller is developed to guarantee the Lyapunov stability, handling all nonlinearities, robustness against uncertainties and tracking the desired trajectory. It is supposed that the leader and follower spacecraft are in a low Earth orbit while J2 perturbation and atmospheric drag are considered as external disturbances. The performance of the proposed controller in tracking the desired formation is compared to a sliding mode controller. Simulation results confirm the effectiveness of the proposed controller.
Control for Satellites Formation Flying
Journal of Aerospace Engineering, 2007
In this paper, a controller is designed for a satellite formation flying system around the Earth based on an uncertainty model derived from a nonlinear relative position equation. In this model, nonzero eccentricity and varying semimajor axis are included as parametric uncertainties. J 2 perturbation, atmospheric drag, and actuation and sensor noise are bounded by functional uncertainties. The controller design based on the nominal mission ͑an 800 km altitude circular reference orbit͒ is capable of achieving desired performance, is robust to uncertainties, and satisfies fuel consumption requirements even in a challenge nonnominal mission ͑a 0.1 eccentricity and 7,978 km semimajor axis elliptic reference orbit͒ with the same control gain. In this nonnominal mission, the designed controller is able to keep formation with almost the same level of the ⌬V budget ͑43.86 m/s/year͒ as used in the nominal mission ͑39.65 m/s/year͒. For comparison, linear quadratic regulator ͑LQR͒ and sliding mode controllers ͑SMC͒ are developed and extensively tuned to get the same ⌬V consumption as that of the designed controller for the nominal mission. However, as shown in the simulation, the designed linear robust controller ͑LQR͒ and nonlinear robust controller ͑SMC͒ have a serious ⌬V consumption penalty ͑1.72 km/ s / year for SMC͒ or are unstable ͑for LQR͒ in the nonnominal mission.
Asymptotic Tracking Control for Spacecraft Formation Flying with Decentralized Collision Avoidance
This paper presents a tracking control scheme for spacecraft formation flying with a decentralized collisionavoidance scheme, using a virtual leader state trajectory. The configuration space for a spacecraft is the Lie group SE3, which is the set of positions and orientations in three-dimensional Euclidean space. A virtual leader trajectory, in the form of attitude and orbital motion of a virtual satellite, is generated offline. Each spacecraft tracks a desired relative configuration with respect to the virtual leader in an autonomous manner, to achieve the desired formation. The relative configuration between a spacecraft and the virtual leader is described in terms of exponential coordinates on SE3. A continuous-time feedback tracking control scheme is designed using these exponential coordinates and the relative velocities. A Lyapunov analysis guarantees that the spacecraft asymptotically converge to their desired state trajectories. This tracking control scheme is combined with a decentralized collision-avoidance control scheme generated from artificial potentials for each spacecraft, which includes information of relative positions of other spacecraft within communications range. Asymptotic convergence to the desired trajectory with this combined control law is demonstrated using a Lyapunov analysis. Numerical simulation results verify the successful application of this tracking control scheme to a formation maneuver with decentralized collision avoidance.
Closed Relative Trajectories for Formation Flying with Single-Input Control
2012
We study the problem of formation shape control under the constraints on the thrust direction. Formations composed of small satellites are usually subject to serious limitations for power consumption, mass, and volume of the attitude and orbit control system AOCS . If the purpose of the formation flying mission does not require precise tracking of a given relative trajectory, AOCS of satellites may be substantially simplified; however, the capacity of AOCS to ensure a bounded or even periodic relative motion has to be studied first. We consider a formation of two satellites; the deputy one is equipped with a passive attitude control system that provides oneaxis stabilization and a propulsion system that consists of one or two thrusters oriented along the stabilized axis. The relative motion of the satellites is modeled by the Schweighart-Sedwick linear equations taking into account the effect of J 2 perturbations. We prove that both in the case of passive magnetic attitude stabilization and spin stabilization for all initial relative positions and velocities of satellites there exists a control guaranteeing their periodic relative motion.
Nonlinear dynamics and output feedback control of multiple spacecraft in elliptical orbits
Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000
This paper considers the problem of relative position control for multiple spacecraft formation flying. Specifically, the nonlinear dynamics describing the motion of a follower spacecraft relative to a leader spacecraft are developed for the case where the leader spacecraft is in an elliptical orbit. Next, a Lyapunov-based, nonlinear, output feedback control law is designed which guarantees global uniform ultimate boundedness of the position and velocity tracking errors in the presence of unknown, spacecraft masses and disturbance force parameters. Simulation results are provided to illustrate the performance of the output feedback control design methodology for formation maintenance in ideal, naturally attractive, orbits.