Satellite Formation Control Research Articles

Reinforcement learning-based satellite formation attitude control under multi-constraint

As the complexity of space missions increases, the constraints on satellite attitude control become more stringent, particularly for satellites working in orbit formation. This paper introduces a novel method, based on the categorization and modeling of different constraints, for attitude control of satellite formations under multiple constraints. The method employs the Phased Priority Reinforcement Learning (PPRL) approach, which utilizes Deep Deterministic Policy Gradient (DDPG) technology. Considering the complexity of constraints and the challenge posed by the high control dimensionality due to multi-satellite coordination, the method addresses these challenges through a two-step training strategy. The first step addresses the multi-constraint issue for individual satellites and increases the priority of single-satellite training experience data in the experience replay buffer of the second step to enhance data utilization efficiency. To address the issue of reward sparsity in complex high-dimensional constraint models, a detailed reward mechanism is proposed, incorporating both local and global constraints into the reward function, thereby achieving both efficient and effective attitude control. This approach not only meets dynamic, state, and performance constraints but also demonstrates adaptability and robustness through numerical simulations. Compared to traditional methods, this approach achieves significant improvements in control performance and constraint satisfaction, offering a novel solution pathway for high-dimensional control problems in multi-constraint satellite formations.

Time-Varying Formation Tracking Control of Multi-Leader Multiagent Systems With Sampled-Data

In this paper, the time-varying formation tracking (TVFT) problem of multi-leader multi-agent systems (MASs) under sampled-data control is studied. First, an improved TVFT criterion is derived by employing a general looped-functional and a zero integral functional. Then a new TVFT controller is designed based on our proposed method. Unlike the existing works, the TVFT controller can allow for bigger sampling intervals of multi-leader MASs. The results demonstrate that the states of the followers can form the designated formation and rotate around the convex combination formed by the multiple leaders. In addition, we generalize the results of TVFT to the sampled-data consensus for MASs, a sampled-data consensus controller which can reduce communication consumption is designed. Meanwhile, the values of the allowable maximum sampling intervals (AMSIs) are calculated. Finally, the superiority and availability of the theoretical results are verified by two simulation experiments. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this paper is to address the problem of TVFT for MAS with multiple leaders. It has been applied to several practical engineering systems, e.g., satellite formation control and unmanned air vehicles (UAVs) formation control. Note that information exchange is a prerequisite to ensure safe and stable control of multi-UAV formation. However, continuous-time communication is difficult to be realized in the actual environment, and it will inevitably consume a lot of energy. In addition, sampled-data controller for MAS with a small sampling interval may cause network congestion. Therefore, a sampled-data controller which allows for a bigger sampling interval for MAS is designed to save network resources in this paper. Through simulation experiments, it can be proved that the followers not only track the leaders, but also form the designated formation.

Relative Dynamics and Control of Satellite Formation Flying Representing the Synthetic Aperture Telescope on Geostationary Orbit

Relative Dynamics and Control of Satellite Formation Flying Representing the Synthetic Aperture Telescope on Geostationary Orbit

Collision Avoidance Second Order Sliding Mode Control of Satellite Formation with Air-Floated Platform Semi-Physical Simulation

As the number of satellites in orbit increases, the issue of flight safety in spacecraft formation orbit control has become increasingly prominent. With this in mind, this paper designs a second-order terminal sliding mode controller for spacecraft formation obstacle avoidance based on an artificial potential function (APF). To demonstrate the effectiveness of the controller, this paper first constructs a Lyapunov function to prove its stability and then verifies its theoretical validity through numerical simulation. Finally, a satellite simulator is used for semi-physical simulation to verify the practical effectiveness of the controller proposed in this paper.

Hybrid Event-Triggered Bipartite Consensus Control of Multiagent Systems and Application to Satellite Formation

This work studies event-triggered bipartite consensus problem of multi-agent systems (MAS) with structurally balanced signed graph. A hybrid system approach is proposed to deal with the leaderless and leader-following bipartite consensus problems in a unified framework, and a novel hybrid event-triggering mechanism (ETM) is proposed to reduce the usage of communication resources. By appropriately defining closed-loop states, a unified hybrid model is constructed for both leaderless and leader-following MAS. Then, stability analysis and ETM design results are given under hybrid systems framework. It is worth noting that the designed hybrid ETM is in decentralized form rather than distributed form. Moreover, the lower bound of triggering intervals can be pre-selected, i.e., Zeno-freeness is guaranteed, that is important for control implementation. The proposed method is applied to satellite formation system in simulation results to show the effectiveness. <i>Note to Practitioners</i>&#x2014;This paper considers bipartite consensus control problem of MAS, which can be applied to some practical systems, e.g., bidirectional formation of unmanned air vehicles, since the control objective in these applications can be transformed into bipartite consensus control problem of MAS. Compared with the existing results, a hybrid system approach is proposed for consensus analysis of MAS with or without leader, and a novel event-triggering mechanism is proposed, which is more easier to be implemented, so, the proposed approach is more friendly for control engineers. The obtained results are applied to satellite formation control problem and the effectiveness is verified, and it is expected that the proposed approach can be extended to MAS with more realistic network-induced constraints and applied to more practical engineering systems.

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

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

Robust multiplexed piecewise affine MPC-based decentralized control of multi-satellite formations using aerodynamic forces

Aerodynamic forces are well suited to be exploited for Low Earth Orbit satellite formation control. However, some critical gaps still exist in control schemes suitable for multi-satellite formation applications, especially when facing atmospheric environmental uncertainties. This paper proposes a scalable and flexible decentralized control scheme for the multi-satellite formation using only aerodynamic forces. This scheme adopts a strategy of updating the control inputs alternatively and is applicable to various formation configurations with different architectures without increasing the computational complexity and communication pressure of each satellite. Aerodynamic forces are changed by reorienting the satellite, and the linear formation control model with pointing angles as inputs is obtained by the PWA (piecewise affine) approximation method. A decentralized control scheme is proposed in which each satellite only has to communicate with its neighboring satellites and update its own inputs. This control scheme allows various generalizations of formation architectures, such as one that includes local chief satellites. To deal with model uncertainties, an improved MPC algorithm named Robust PWA-MMPC is developed using the constraint tightening approach, and then its feasibility and stability issues are analyzed. Hard-in-the-loop simulations are carried out for formation maintenance and reconfiguration, in which aerodynamic force uncertainties are considered.

Modeling and Control of Satellite Formations: A Survey

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.

General attitude cooperative control of satellite formation by set stabilization

This paper investigates the problem of general attitude cooperative control for different satellite formation structures from a new perspective of set theory. A virtual single-integral nonlinear node dynamic system is first presented. Then the general satellite attitude cooperative controller can be designed based on the virtual node dynamic system and consensus theory. The stability of the closed-loop system with respect to the goal set is analyzed by integral input to state stable method. Subsequently, two different scenarios, leaderless and leader-following satellite formation structures, are introduced by the general attitude cooperative control scheme. Corresponding simulations of these two scenarios verify the obtained theoretical results.

Adaptive terminal sliding mode control for satellite formation flying system with external disturbance and actuator misalignment

Adaptive terminal sliding mode control for satellite formation flying system with external disturbance and actuator misalignment

Coordinative coupled attitude and orbit control for satellite formation with multiple uncertainties and actuator saturation

This paper studies the coordinative coupled attitude and orbit control system (AOCS) of a satellite formation composed of one microsatellite and two 3U CubeSats. It is described as a highly nonlinear and coupled system subject to actuator saturation and multiple uncertainties including parametric perturbations and external disturbances. To address this issue, the centralized architecture and leader-following method are adopted in the formation firstly. The closed-loop system of each satellite member is divided into orbit and attitude control loops respectively. The coupling relationship between orbit and attitude is introduced as a constraint of the control law. Then a robust controller consisting of a nominal controller, a robust compensator and an advanced proportional–derivative (APD) controller is proposed to achieve high-accuracy formation control. The robust compensator is constructed from an auxiliary system and a finite-time observer to compensate the influence of an equivalent lumped disturbance. The APD controller is developed to achieve desired performances under actuator saturation. Stability analysis indicates that both relative position errors and attitude tracking errors can converge asymptotically. Finally, numerical simulations are carried out to verify the effectiveness of proposed control law in both relatively-stationary and fly-around scenarios.

Reconfiguration control of satellite formation using online quasi-linearization iteration and symplectic discretization

This paper focuses on the reconfiguration control problem of formation flying spacecraft via low-thrust continuous propulsion. A nonlinear receding horizon control (NRHC) scheme for performance optimization and constraint enforcement is presented. The nonlinear optimal control (NOC) problem underlying the receding horizon control scheme is transcribed into a sequence of linear optimal control (LOC) problems by exploiting an online quasi-linearization strategy. Hence, only a LOC must be solved in each sampling interval, thereby significantly reducing the computational cost. It differs from conventional receding horizon control schemes that require solving a NOC problem in each sampling interval. Moreover, the numerical solution of the LOC problem is obtained using a structure-preserving symplectic algorithm that is capable of maintaining a high degree of accuracy while simultaneously improving computation efficiency. Finally, a numerical case study is presented to illustrate the effectiveness and superiority of the proposed control approach.

Autonomous Precision Control of Satellite Formation Flight under Unknown Time-Varying Model and Environmental Uncertainties

This paper presents a new methodology for autonomous precision control of satellite formations in the presence of uncertainties and external disturbances. The methodology is developed in two steps. First, using a nominal system model that provides the best assessment of real-life uncertainties, a nonlinear controller that satisfies the formation configuration requirements is developed without making any linearizations/approximations. This closed-form control strategy is inspired by results from analytical dynamics and uses the fundamental equation of constrained motion. In the second step, an adaptive continuous robust controller is developed to compensate for model uncertainties and field disturbances to which the satellite formation may be subjected. This controller is based on a generalization of the concept of sliding mode control, and produces no chattering. The control gain is automatically updated in real time and the norm of the trajectory error is guaranteed to lie within user-provided desired bounds without a priori knowledge of the uncertainty/disturbance bounds. Since the control force is explicitly obtained, the approach is not computationally intensive, thereby making the approach ideal for on-orbit autonomous real-time satellite formation control. Numerical simulations demonstrate the effectiveness of the proposed control methodology, in which a desired formation configuration is required to be precisely and autonomously maintained despite large initial trajectory errors in the presence of uncertain satellite mass and environmental disturbances.

Decentralized active sensor fault tolerance in attitude control of satellite formation flying

SummaryThis article presents a decentralized framework of active fault tolerant control for attitude synchronization in satellite formation flying. By employing a nonlinear observer and a static approximator, the fault in both the angular velocity and orientation sensors can be diagnosed whether the sensor belongs to the satellite or its neighbors. The convergence of the observer is guaranteed by utilizing Lyapunov's direct method and Barbalat's lemma. The proposed approach is based on unknown input and requires only the angular velocity and orientation of the states in a decentralized architecture. Moreover, by designing a sensor fault tolerant controller, the tracking synchronization among the satellites' attitudes with individual set‐points is guaranteed and the uniformly ultimate boundedness of the synchronization/tracking errors is provided. The simulation results are presented to illustrate the performance of the developed algorithm.

Propulsionless planar phasing of multiple satellites using deep reinforcement learning

This work creates a framework for solving highly non-linear satellite formation control problems by using model-free policy optimisation deep reinforcement learning (DRL) methods. This work considers, believed to be for the first time, DRL methods, such as advantage actor-critic method (A2C) and proximal policy optimisation (PPO), to solve the example satellite formation problem of propellantless planar phasing of multiple satellites. Three degree-of-freedom simulations, including a novel surrogate propagation model, are used to train the deep reinforcement learning agents. During training, the agents actuated their motion through cross-sectional area changes which altered the environmental accelerations acting on them. The DRL framework designed in this work successfully coordinated three spacecraft to achieve a propellantless planar phasing manoeuvre. This work has created a DRL framework that can be used to solve complex satellite formation flying problems, such as planar phasing of multiple satellites and in doing so provides key insights into achieving optimal and robust formation control using reinforcement learning.

Event‐triggered coordinated attitude control for satellite formation under switching topology

Event‐triggered coordinated attitude control problem for satellite formation under switching topology is investigated in this article. First, triggering function with state error is designed to adjust update period of controller. Event is triggered, state information is sampled, and controller is updated if and only if triggering condition is satisfied, while controller in nontriggering time uses state information of triggering time. Then, in the existence of model uncertainties, distributed adaptive attitude controller based on event‐triggered strategy is proposed for satellite formation with leader‐follower architecture. Under directed switching graph, formation system is proved to be asymptotical convergence by Lyapunov stability theory, and inter‐event time interval is given to avoid Zeno behavior. At last, simulation results show that the proposed event‐triggered adaptive attitude controller can reduce execution frequency of control tasks, as well as ensure control performance of cluster system.

Satellite formation flying control using an innovative technique subject to electromagnetic acceleration

The electrostatic charge became a possible method to control both orbital and attitude motion without fuel consumption or reduce the fuel cost. This study needs to install an ion collector on the satellite to increase the level of charging as artificial charging. In this paper, we developed a linearised satellite relative motion and a combination of Lorentz forces provided by modulating spacecraft's electrostatic charge (magnetic and electric fields) that can be used to keep the desired relative distances and orientations considering J2 perturbation. The proposed controller contains a feedback control using a real-time fuel-optimal control approach is considered for satellite formation control in eccentric orbits based on the developed linear J2 dynamic model. Comprehensive simulation numerical results confirmed the capability of Lorentz force to correct the drift in the relative position of formation flying due to the effect of J2, these corrections depend on the value of charge to mass ratio and magnitude of the relative position.

Ionospheric Drag for Satellite Formation Control

Constellations of miniaturized satellites that provide novel and cost-effective capabilities are a growing trend for space systems. Economically viable miniature satellite constellations commonly necessitate the exclusion of propulsion systems. A difference in neutral aerodynamic forces between spacecraft, resulting from interactions with the thermosphere, is the prevailing propulsion-free method for maintaining low-Earth-orbit constellations. This work investigates charged aerodynamic forces, which are caused by an electrically charged platform’s interaction with the ionosphere (ionospheric drag), as an actuation mechanism for satellite formation control. Numerical propagations of the relative motion between identically shaped neutral and charged spheres, with artificial surface voltages ranging between and V, indicate that the ensuing magnitude of differential drag, due to ionospheric drag, can nullify an initial 1 m relative semimajor axis within 4 min in the most optimal conditions simulated. Thus, with no technology optimization, this work concludes that ionospheric drag caused by spacecraft charging is sufficient for actuating changes in the orbital semimajor axis; however, it is inferior when compared to techniques for generating differences in neutral drag. Future work will investigate the optimization of ionospheric aerodynamic technologies and techniques to increase the effectiveness of charged aerodynamic formation control.

Output Regulation Control for Satellite Formation Flying Using Differential Drag

This paper proposes a new approach of using differentials in aerodynamic drag in combination with thrusters to control satellite formation flying in low Earth orbits. Parameterized output regulation theory for formation-flying missions with combined control action is developed based on the Schweighart–Sedwick relative dynamics equations. The theory is implemented to precisely track the different trajectories of reference relative motion and eliminates the effects of the perturbations. The parametric Lyapunov algebraic equation is proposed to ensure the stability of the linear relative model subject to saturated inputs. The main goal of this study is to approve the viability of using the differentials in aerodynamic drag to precisely control different formation-flying missions. Numerical simulations using a high-fidelity relative dynamics model and a high-precision orbit propagator are implemented to validate and analyze the performance of the proposed control algorithm in comparison with the linear quadratic regulator algorithm based on actual satellite models.

On the exploitation of differential aerodynamic lift and drag as a means to control satellite formation flight

For a satellite formation to maintain its intended design despite present perturbations (formation keeping), to change the formation design (reconfiguration) or to perform a rendezvous maneuver, control forces need to be generated. To do so, chemical and/or electric thrusters are currently the methods of choice. However, their utilization has detrimental effects on small satellites’ limited mass, volume and power budgets. Since the mid-80s, the potential of using differential drag as a means of propellant-less source of control for satellite formation flight is actively researched. This method consists of varying the aerodynamic drag experienced by different spacecraft, thus generating differential accelerations between them. Its main disadvantage, that its controllability is mainly limited to the in-plain relative motion, can be overcome using differential lift as a means to control the out-of-plane motion. Due to its promising benefits, a variety of studies from researchers around the world have enhanced the state-of-the-art over the past decades which results in a multitude of available literature. In this paper, an extensive literature review of the efforts which led to the current state-of-the-art of different lift and drag-based satellite formation control is presented. Based on the insights gained during the review process, key knowledge gaps that need to be addressed in the field of differential lift to enhance the current state-of-the-art are revealed and discussed. In closer detail, the interdependence between the feasibility domain/the maneuver time and increased differential lift forces achieved using advanced satellite surface materials promoting quasi-specular or specular reflection, as currently being developed in the course of the DISCOVERER project, is discussed.