Satellite Formation Reconfiguration Research Articles

Chain tethered satellite formation reconfiguration: An event-triggered practical prescribed-time control approach

This paper addresses the challenge of rapid reconfiguration control in the chained tethered satellite formation (CTSF) amidst full-state constraints and uncertainties. To tackle this, we propose an innovative event-triggered practical prescribed-time control method grounded in observer theory. Initially, we develop a sliding mode state observer utilizing event triggering to effectively monitor the velocities of adjacent satellites. Subsequently, leveraging the framework of backstepping control, uncertainties are managed by approximating them using fuzzy logic systems. The imposition of full-state constraints is adeptly handled through the barrier Lyapunov function. An event-triggered practical prescribed-time controller (ET-PPTC) is then engineered, drawing on the principles of practical prescribed-time stability. The robustness and stability of the closed-loop control system are rigorously established employing the Lyapunov framework. Finally, through comprehensive numerical simulations, we validate the feasibility and efficacy of the proposed control scheme in facilitating the reconfiguration mission of a four-satellite CTSF.

Relative E/I vector-based optimal and suboptimal control for continuous low thrust formation reconfiguration in circular orbits

This paper addresses the fuel-optimal satellite formation reconfiguration problem with continuous low-thrust control. Based on the relative eccentricity and inclination (E/I) theory, a comprehensive approach to optimal continuous low-thrust reconfiguration in circular or near-circular orbits is proposed. By analyzing the feasible fuel cost lower bound, the reconfiguration scenarios are categorized into four types, and the corresponding optimal or suboptimal control schemes are derived. More specifically, for suboptimal continuous control schemes, the relation between user-defined variables with fuel-cost is derived, providing a clear direction for better fuel cost. Compared with previous work that gives only feasible analytical solutions or obtains optimal solutions with numerical methods, the proposed method provides an efficient approach to optimal continuous low thrust reconfiguration for feasible scenarios and adjustable sub-optimal schemes for unfeasible scenarios. The proposed framework contributes to the practical application in engineering, enabling the design and analysis of more cost-effective space missions. The analysis of fuel cost reveals that the optimal continuous low thrust reconfiguration is limited with scenarios. The overall solutions are simulated and validated in four reconfiguration scenarios.

Fuel-optimal satellite formation reconfiguration method with best passive safety parameters

This paper investigates the problem of satellite formation reconfiguration from the best passive safety parameters while ensuring the minimum fuel cost and desired formation configuration. Based on the relative eccentricity and inclination vectors, a hybrid method is proposed that combines the analytical solution and the genetic algorithm optimization method. It transforms the fuel-optimal conditions into the constraints of optimization model, which theoretically ensures the optimal fuel cost. The proposed hybrid approach is applicable to satellite formation reconfiguration problems with variable relative eccentricity and inclination vectors and passive safety concerns. Compared with the optimal three-impulse strategy and the analytical method in two different reconfiguration scenarios, the proposed method is proven to be more general and has advantages in passive safety performance.

Fuel optimization schemes for formation reconfiguration in satellite formation flying

We study the satellite formation reconfiguration within a fixed orbit transfer time and aim to minimize or balance its fuel consumption. In this study, the formation will end up with an in-plane formation regardless of its initial state. We take consideration of the constraints of relative motion equation, initial and terminal states, collision avoidance, and maximum thrust. We attach an unknown offset in the terminal state of the formation and adapt a convex-programming-based iterative approach to jointly optimize the fuel usage and the offset of the formations. The proposed algorithms clearly outperform benchmarks in all the numerically tested situations with respect to both minimization of the total fuel consumption and minimization of the maximum fuel usages across all the satellites of the formation.

Finite-time synchronization control scheme for underactuated satellite formation reconfiguration

A synchronization control scheme for underactuated satellite formation reconfiguration in circular orbits is proposed in this paper. The main idea of the synchronization scheme is to control the satellite without radial or along-track thrust to track its desired configuration while synchronizing its motion with that of other underactuated satellites to maintain the predefined or time-varying formation. Firstly, a new underactuated control approach is presented for either underactuated case. Based on the inherent coupling of the system states, the finite-time convergence of the system trajectory could be guaranteed by the sliding mode-based underactuated controller. Secondly, to synchronize the reconfiguration motion between followers, the sum of the sliding mode errors of every two neighbor followers is defined as the synchronization control. The Lyapunov-based method proves the finite-time convergence of synchronization control. More importantly, the minimum nonzero eigenvalue of the Laplace matrix can reduce the system state convergence region. Numerical simulations also verify the performance of the proposed underactuated synchronization controller.

Optimal satellite formation reconfiguration based on the uncertainty and disturbance estimator

This paper investigates the energy-optimal path generating and robust trajectory tracking of satellite formation reconfiguration. First, to minimize the energy consumption during formation reconfiguration, the problem of finding optimal path and control profile is studied. This problem is solved based on the linear Hill-Clohessy-Wiltshire equations and optimal control theory. Second, considering the nonlinearities and disturbances in the dynamics of satellite relative motion, a robust control law based on an uncertainty and disturbance estimator is designed. The primary advantage of this estimator is the relaxation of the assumption on disturbances, and only frequency range is needed. The asymptotic stability of the closed-loop system formed by a robust feedback controller is analyzed. Finally, numerical simulation results are presented to validate the feasibility of the proposed reconfiguration trajectory optimization approach and control strategy.

Development and Simulation of Motion Control System for Small Satellites Formation

In the paper, the problem of forming and maintaining the small satellites formation in the near-earth projected circular orbits is considered. The satellite formation reconfiguration and formation-keeping control laws are proposed by employing the passivity-based output feedback control. For the complete nonlinear and time-dependent dynamics of the relative motion of a pair of satellites in elliptical orbits, new combined control algorithms, including a consensus protocol, are proposed and analyzed. A comparison of the control modes using the passivity-based output feedback control and the proportional-differential controller with and without the consensus algorithm is given. On the basis of the passification method, the algorithm is obtained ensuring the stable motion of the slave satellite relative to the orbit of the master satellite. To improve the accuracy of the satellites’ positioning, a consensus protocol based on measurements of the relative positions of the satellites is proposed and studied. Computer simulations of the proposed algorithms for options to construct formations are provided for two projected circular orbits of 8 satellites, demonstrating the efficiency of the proposed control schemes. It is shown that the resulting passivity-based output feedback control provides better accuracy than the PD controller. It is also shown that the use of the consensus protocol further increases the positioning accuracy of the satellite constellation.

The fuel consumption analysis for satellite formation reconfiguration based on three-impulsive approach

Currently micro/nano satellites have become the protagonists in most formation flying missions, and there is an urgent demand to propose a reliable approach for quick fuel estimation of multiple-impulsive scheme on-board to achieve formation reconfiguration problems. This paper presents an optimal control approach based on multiple impulses for satellite formation in-plane reconfiguration issue in near circular orbit. Based on initial small deviation in the cylindrical coordinates system, a relative orbit motion expression is investigated, and a time-varying propagate system without perturbation is presented in this paper, which is suitable to calculate the solution of relative orbital maneuver by multiple impulses. The formation reconfiguration problem of this relative orbit motion is considered, and orbital motion equations with initial deviations are presented for relative orbital transfer calculation. Through different combinations of method from normal four-impulsive solution, the optimal three-impulsive method for relative orbital transfer in plane is obtained by analysis solution based on graphical and numerical way. In the end of paper, the effectivity and optimality of method is validated, and fuel consumption is analyzed through simulations of assumptive different formation reconfiguration missions.

Analytical solution of satellite formation impulsive reconfiguration considering passive safety constraints

To handle the potential collision hazards caused by utilizing original fuel optimal impulsive reconfiguration approach, an analytical impulsive satellite formation reconfiguration method in terms of relative eccentricity and inclination vectors (E/I vectors) considering passive safety constraints is proposed. Firstly, the mechanism why original fuel optimal impulsive reconfiguration approach based on relative E/I vectors may cause unsatisfied collision avoidance constraints is analyzed. The unsatisfied scenarios are divided into two cases, namely, the single impulse is too large case and the middle relative E vector is in passive unsafety region case. Secondly, with respect to the unsatisfied collision avoidance scenarios, corresponding analytical impulsive reconfiguration strategies with passive safety constraints are proposed. Finally, the results of the numerical simulations show that the proposed reconfiguration methods can handle the passive safety constraints.

Multi-objective optimal formation reconfiguration with scalarization and stochastic boundaries

Abstract A new method is proposed for multi-objective optimal control of satellite formation reconfiguration. First, necessary optimality conditions of single-objective fuel-optimal reconfiguration are studied. Problem of initial guess of the costate and control discontinuity are addressed by using a new developed stochastic based method. Terminal conditions of Two Point Boundary Value Problem (TPBVP) of the optimal control equations are relaxed using augmented Gaussian. Variances or bandwidths of the terminal conditions are set to decision variables to be optimized. Responses of varied initial costate are modeled and propagated using Riccati equation. Using quadratic convolution of relaxed terminal conditions, objective function of the fuel-optimal problem is reformulated into a quadratic equation, and a gradient based optimizer is used to search the optimal initial guess. In the second part of the paper, optimal control of format flying reconfiguration with two competitive objectives:fuel and time of flight (ToF) is studied. With Pascoletti-Serafini scalarization, the Multi-objective Optimal Control Problem (MOCP) is scalarized into a set of weighted Single-objective Optimal Control Problems (SOCP). Hamiltonian and switch function for the weighted SOCP are developed and constructed. New developed stochastic based approach is then used to search the optimal Pareto solutions. Verification and performances of proposed algorithms are demonstrated through numerical simulations of single-objective and multi-objective optimal control of low-thrust elliptical orbit formation reconfiguration. Potential applications of the algorithms to some other preliminary space mission designs are also discussed.

Fast cooperative trajectory optimization and test verification for close-range satellite formation using Finite Fourier Series method

The process of formation reconfiguration for close-range satellite formation should take into account the risk of collisions between satellites. To this end, this paper presents a method to rapidly generate low-thrust collision-avoidance trajectories in the formation reconfiguration using Finite Fourier Series (FFS). The FFS method can rapidly generate the collision-avoidance three-dimensional trajectory. The results obtained by the FFS method are used as an initial guess in the Gauss Pseudospectral Method (GPM) solver to verify the applicability of the results. Compared with the GPM method, the FFS method needs very little computing time to obtain the results with very little difference in performance index. To verify the effectiveness, the proposed method is tested and validated by a formation control testbed. Three satellite simulators in the testbed are used to simulate two-dimensional satellite formation reconfiguration. The simulation and experimental results show that the FFS method can rapidly generate trajectories and effectively reduce the risk of collision between satellites. This fast trajectory generation method has great significance for on-line, constantly satellite formation reconfiguration.

A guidance approach to satellite formation reconfiguration based on convex optimization and genetic algorithms

This paper presents a new approach for autonomous reconfiguration of distributed space systems, which ensures safe guidance of spacecraft formations towards the desired patterns while optimizing the total propellant consumption. The orbital transfer is reduced to the form of a convex optimization problem to guarantee rapid computation of control laws. Hence, tasks are iteratively assigned to the component platforms to detect the best reconfiguration strategy. The path-planning is entrusted to a reference satellite of the cluster, that coordinates the remaining ones by means of a procedure based on genetic algorithms. Two methods are proposed, depending on the organizational architecture of the spacecraft formation. In the first one, the maneuver is completely planned by the reference satellite, that determines final tasks and control actions for the whole cluster. As an alternative to such a fully-centralized approach, a distributed version of the algorithm is proposed: tasks are sorted by the reference satellite and transfer orbits are computed by exploiting the computational resources of the whole cluster. Whatever the considered framework, both the planners ensure a safe transition of the formation towards the target geometry. Simulation results show that, when relative distances are of the order of hundreds of meters, a mean delta-v per satellite of the order of 0.1 m/s is required to reconfigure LEO clusters within one orbital period.

Dynamic optimal output feedback control of satellite formation reconfiguration based on an LMI approach

This study presents a dynamic quadratic-optimal (DQO) output feedback controller for satellite formation reconfiguration based on a linear matrix inequality (LMI) approach. A relative motion model involving communication topology of formation flying on a circular reference orbit is established through graph theory. As the design of a static quadratic-optimal (SQO) output feedback controller was determined to be infeasible, emphasis is placed on designing a DQO output feedback controller. Introducing an impulse function enables us to transform the original DQO output feedback control (DQO-OFC) problem into an optimal L2-norm problem, which can be solved in the standard frame of an LMI approach. It is infeasible to employ a conventional substitution method to treat a nonlinear term with a quadratic form. Thus, an elimination method is adopted in order to address nonlinear terms in the matrix inequalities to obtain a set of equivalent LMIs. Additional control quantities are developed in order to retain the formation configuration in a non-zero state. Simulation results demonstrate validity and functionality of the proposed DQO output feedback controller.

Optimal satellite formation reconfiguration using co-evolutionary particle swarm optimization in deep space

This paper proposes a method that plans energy-optimal trajectories for multi-satellite formation reconfiguration in deep space environment. A novel co-evolutionary particle swarm optimization algorithm is stated to solve the nonlinear programming problem, so that the computational complexity of calculating the gradient information could be avoided. One swarm represents one satellite, and through communication with other swarms during the evolution, collisions between satellites can be avoided. In addition, a dynamic depth first search algorithm is proposed to solve the redundant search problem of a co-evolutionary particle swarm optimization method, with which the computation time can be shorten a lot. In order to make the actual trajectories optimal and collision-free with disturbance, a re-planning strategy is deduced for formation reconfiguration maneuver.

Research on the Path Optimization of Satellite Formation Reconfiguration Based on Gauss Pseudospectral Method

Aim to the path programme problem of satellite formation reconfiguration under low thrust, optimization is simulated based on Gauss Pseudospectral Method (GPM). The simulation result demonstrates that the GPM can effectively solve the the path optimization problem.

Cooperative Control for Satellite Formation Reconfiguration via Cyclic Pursuit Strategy

This paper investigates a methodology for group coordination and cooperative control of satellites with the aim to achieve formation reconfiguration such as radius enlargement and phase angle adjustment. The proposed approach separates the control law into two distinct stages: planar movement control and orthogonal displacement suppression. The in plane approach is based on a cyclic pursuit strategy, where satellite i pursues satellite i +1. For phase angle adjustment, a control law that makes use of beacons guidance is synthesized to maintain the circling centre stationary. In the orthogonal direction, a linear feed back control on displacement and velocity is used. Simulation of two missions with low thrust are provided, which high light the over all effectiveness of the proposed approach.

Optimal Satellite Formation Reconfiguration Based on Closed-Loop Brain Storm Optimization

In recent years, satellite formation flying has become an increasingly hot topic for both the astronomy and earth science communities due to its potential merits compared with a single monolithic spacecraft system. This paper proposes a novel approach based on closed-loop brain storm optimization (CLBSO) algorithms to address the optimal formation reconfiguration of multiple satellites using two-impulse control. The optimal satellite formation reconfiguration is formulated as an optimization problem with the constraints of overall fuel cost minimization, final configuration, and collision avoidance. Three versions of CLBSOs are developed by replacing the creating operator in basic brain storm optimization (BSO) with closed-loop strategies, which facilitate search characteristic capture and enhance the optimization performance by taking advantage of feedback information in the search process. Numerical simulations are carried out using particle swarm optimization (PSO), basic BSO, and the three versions of CLBSOs. Comparison results show that all versions of CLBSOs outperform PSO and the original BSO in terms of final results and convergence speed. In addition, CLBSO reduces the computation burden and shortens CPU time to a certain extent in contrast with basic BSO. Furthermore, among the three CLBSO algorithms, the one using the strategy of difference with the best gains the best overall performance, which is inspired by the updating rule in PSO that each particle tends to move towards the individual with the best fitness.

Optimal satellite formation reconfiguration actuated by inter-satellite electromagnetic forces

The inter-satellite electromagnetic forces generated by the magnetic dipoles on neighboring satellites provide an attractive control actuation alternative for satellite formation flight due to the prominent advantages of no propellant consumption or plume contamination. However, the internal force nature as well as the inherent high nonlinearity and coupling of electromagnetic forces bring unique dynamic characteristics and challenges. This paper investigates the nonlinear translational dynamics, trajectory planning and control of formation reconfiguration actuated by inter-satellite electromagnetic forces. The nonlinear translational dynamic model is derived by utilizing analytical mechanics theory; and analysis on the dynamic characteristics is put forward. Optimal reconfiguration trajectories of electromagnetic force actuated formation are studied by applying optimal control theory and the Gauss pseudospectral method. Considering the high nonlinearity and uncertainty in the dynamic model, an inner-and-outer loop combined control strategy based on feedback linearization theory and adaptive terminal sliding mode control is proposed with finite-time convergence capability and good robust performance. Theoretical analysis and numerical simulation results are presented to validate the feasibility of the proposed translational model, reconfiguration trajectory optimization approach and control strategy.

Collision Avoidance Algorithm for Satellite Formation Reconfiguration under the Linearized Central Gravitational Fields

A collision-free formation reconfiguration trajectory subject to the linearized Hill's dynamics of relative motion is analytically developed by extending an algorithm for gravity-free space. Based on the initial solution without collision avoidance constraints, the final solution to minimize the designated performance index and avoid collision is found, based on a gradient method. Simple simulations confirm that satellites reconfigure their positions along the safe trajectories, while trying to spend minimum energies. The algorithm is applicable to wide range of formation flying under the Hill's dynamics.

Optimal satellite formation reconfiguration strategy based on relative orbital elements

This paper presents an analytical fuel-optimal impulsive formation reconfiguration strategy in terms of relative orbital elements (especially using the geometrically intuitive form called relative eccentricity and inclination vectors [E/I vectors]). The relative motion and orbit transfer problem is reparameterized in the form of relative orbit elements. Given a set of transfer conditions, the optimal impulsive strategy for a single satellite maneuver is formulated. Based on the analytical solution of a single satellite transfer, the proposed method is further extended to reconfiguration maneuvers for satellites flying in formation, which accounts for the optimization that relates to the satellites reassignment problem in the reconfiguration stage. Simulations are conducted to demonstrate the validity of the proposed approaches for both single satellite and formation flying reconfiguration scenarios.