Spacecraft Swarm Research Articles

Phase-space density control based on configuration invariant of spacecraft swarm

This paper investigates a phase-space density control based on configuration invariant for large-scale spacecraft swarms. By introducing Jordan-reduced dynamics and the configuration invariant to characterize relative orbits, the macroscopic swarm dynamics is presented with respect to the temporal evolution of phase space density. The density migration of the spacecraft swarm in phase space is modeled as a specific convection–diffusion process, where the diffusion term promotes swarm spreading and the convection term guides the swarm towards a designated region for uniform distribution. Through local density estimation and defining the convection and diffusion terms, the feedback control’s specific form is proposed and its exponential stability is proved. Particularly, the formulation of the convection term outside the target region and the combined kernel function for local density estimation help in avoiding sporadic isolated spacecraft. Numerical results of spacecraft swarm deployment validate the effectiveness and superiority of phase-space density control.

Trajectory Planning of Spacecraft Swarm Reconfiguration Using Reachable Set-Based Collision Constraints

Trajectory Planning of Spacecraft Swarm Reconfiguration Using Reachable Set-Based Collision Constraints

Generation of Top‐Boundary Conditions for 3D Ionospheric Models Constrained by Auroral Imagery and Plasma Flow Data

AbstractData products relating to auroral arc systems are often sparse and distributed while ionospheric simulations generally require spatially continuous maps as boundary conditions at the topside ionosphere. Fortunately, all‐sky auroral imagery can provide information to fill in the gaps. This paper describes three methods for creating electrostatic plasma convection maps from multi‐spectral imagery combined with plasma flow data tracks from heterogeneous sources. These methods are tailored to discrete arc structures with coherent morphologies. The first method, “reconstruction,” builds the electric potential map (from which the flow field is derived) out of numerous arc‐like ridges that are then optimized against the plasma flow data. This method is designed for data from localized swarms of spacecraft distributed in both latitude and longitude. The second method, “replication,” uses a 1D across‐arc flow data track and replicates these data along a determined primary and secondary arc boundary while simultaneously scaling and rotating to keep the flow direction parallel to the arc and the flow shear localized at the arc boundaries. The third, “weighted replication,” performs a replication on two data tracks and calculates a weighted average between them, where the weighting is based on data track proximity. This paper shows the use of these boundary conditions in driving and assessing 3D auroral ionospheric, multi‐fluid simulations.

Swarm-to-swarm orbital pursuit method under delta-v maneuver for space pursuit-evasion

This paper investigates the orbital pursuit strategy for spacecraft swarms, where both pursuers and evaders possess limited delta-v maneuvering capabilities. Given that swarms can consist of numerous members, ranging from dozens to thousands, the swarm-to-swarm problem has significant coupling effects that cannot be solved by merely superimposing one-to-one or few-to-few problems. Otherwise, one would cause a dimension explosion in decision-making space. To avoid this issue, the swarm orbital pursuit problem is divided into two coupled problems: swarm target allocation and orbital maneuver. First, considering the relative orbit state between pursuers and evaders and estimated orbital maneuver costs of pursuit, the swarm target allocation problem is formulated into three coupled sub-problems, i.e., target allocation order, target allocation for sub-swarms, and target allocation for individuals. These sub-problems are solved by the presented double-layer contract net protocol algorithm to maximize task completion efficiency. Then, the orbital maneuver problem is decomposed into two coupled problems to maximize pursuit benefits, i.e., long-range rendezvous, and close-distance game maneuvers. For the long-range rendezvous, the optimal Lambert algorithm is developed to efficiently obtain the discrete optimal pursuit time and corresponding orbital transfer maneuver. To address close-distance games more proficiently, a hybrid orbital maneuver algorithm, combining the proximal policy optimization and the Lambert algorithm is proposed. Finally, comparison simulations verified the effectiveness and superiority of the proposed method.

An introductory review of swarm technology for spacecraft on‐orbit servicing

AbstractThis review paper presents a comprehensive evaluation and forward‐looking perspective on the underexplored topic of servicing target objects using spacecraft swarms. Such targets can be known or unknown, cooperative or uncooperative, and pose significant challenges in modern space operations due to their inherent complexity and unpredictability. Successfully servicing space objects is vital for active debris removal and broader on‐orbit servicing tasks such as satellite maintenance, repair, refueling, orbital assembly, and construction. Significant effort has been invested in the literature to explore the servicing of targets using a single spacecraft. Given its advantages and benefits, this paper expands the discussion to encompass a swarm approach to the problem. This review covers various single‐spacecraft approaches and presents a critical examination of the existing, although limited, body of work dedicated to servicing orbital objects using multiple spacecraft. The focus is also broadened to include some influential studies concerning the characterization, capture, and manipulation of physical objects by general multiagent systems, a subject with significant parallels to the core interest of this manuscript. Furthermore, this article also delves into the realm of simultaneous localization and mapping, highlighting its application within close‐proximity operations in space, especially when dealing with unknown uncooperative targets. Special attention is paid to the benefits that this field can receive from distributed multiagent architectures. Finally, an exploration of the promising field of swarm robotics is presented, with an emphasis on its potential to revolutionize the servicing of orbital target objects. Concurrently, a survey of general research directly engaging swarms in the orbital context is conducted. This review aims to bridge the knowledge gap and stimulate further research in the underexplored domain of servicing space targets with spacecraft swarms.

Rapid generation of time-optimal rendezvous trajectory based on convex optimisation and DNN

Abstract The minimum flight time of spacecraft rendezvous is one of the fundamental indexes for mission design. This paper proposes a rapid trajectory planning method based on convex optimisation and deep neural network (DNN). The time-optimal trajectory planning problem is reconstructed into a double-layer optimisation framework, with the inner being a convex optimisation problem and the outer being a root-finding problem. The thrust properties corresponding to time-optimal control are analysed theoretically. A DNN-based rapid planning method (DNN-RPM) is put forward to improve computational efficiency, in which the trained DNN provides a high-quality initial guess for Newton’s method. The DNN-RPM is extended to search for the optimal entering angle of natural-motion circumnavigation orbit injection problem and the minimum reconfiguration time of spacecraft swarm. Numerical simulations show that the proposed method can improve the computational efficiency while ensuring the calculation accuracy.

Distributed Event-Triggered Model Predictive Control for Spacecraft Swarm

Distributed Event-Triggered Model Predictive Control for Spacecraft Swarm

BLISS: Interplanetary exploration with swarms of low-cost spacecraft

Leveraging advancements in micro-scale technology, we propose a fleet of autonomous, low-cost, small solar sails for interplanetary exploration. The Berkeley Low-cost Interplanetary Solar Sail (BLISS) project aims to utilize small-scale technologies to create a fleet of tiny interplanetary spacecraft for rapid, low-cost exploration of the inner solar system. This paper describes the hardware required to build a ∼10 g spacecraft using a 1 m2 solar sail steered by micro-electromechanical systems (MEMS) inchworm actuators. The trajectory control to a NEO, here 101955 Bennu, is detailed along with the low-level actuation control of the solar sail and the specifications of proposed onboard communication and computation. Two other applications are also shortly considered: sample return from dozens of Jupiter-family comets and cometary nuclei imaging. The paper concludes by discussing the fundamental scaling limits and future directions for steerable autonomous miniature solar sails with onboard custom computers and sensors.

Resilient Formation Tracking of Spacecraft Swarm Against Actuation Attacks: A Distributed Lyapunov-Based Model Predictive Approach

Resilient Formation Tracking of Spacecraft Swarm Against Actuation Attacks: A Distributed Lyapunov-Based Model Predictive Approach

Development of a Hardware Demonstration Platform for Multispacecraft Reconnaissance of Small Bodies

The next frontier in space exploration involves visiting some of the 2 million small bodies scattered throughout the solar system. However, these missions are expected to be challenging due to the surface irregularities of these bodies and the very low gravity, which makes steps like getting into orbit very complex. For these reasons, reconnaissance is crucial for small body exploration before taking on ambitious orbital, surface, and sample-return missions. Our previous work developed IDEAS, an automated design software for small body reconnaissance mission development using spacecraft swarms. A critical challenge to furthering such designs is the lack of hardware demonstration platforms for interplanetary spacecraft operations. In this paper, we present MAPS (Multi-Agent Photogrammetry of Small bodies), a hardware platform to demonstrate critical reconnaissance operations of multi-spacecraft missions identified by the IDEAS framework. MAPS uses UAVs as the autonomous agents that perform reconnaissance operations. The UAVs use their visual feed to generate a 3D surface map of a small body mockup, which is encountered along their flight path. In this paper, we examine the various design elements of a small body surface reconstruction mission inside the MAPS testbed. These elements are used for designing reference trajectories of the participating UAVs, which is enforced using a tracking feedback control law. We then formulate the small-body mapping problem as an MINLP problem, which is handled by the Automated Swarm Designer module of the IDEAS framework. The solutions are implemented inside the MAPS, and shape models generated from the UAV feeds are compared.

Starling Formation-Flying Optical Experiment (StarFOX): System Design and Preflight Verification

The Starling Formation-Flying Optical Experiment (StarFOX) is intended as the first on-orbit demonstration of autonomous distributed angles-only navigation for spacecraft swarms. StarFOX applies the angles-only Absolute and Relative Trajectory System (ARTMS), a navigation architecture consisting of three innovative algorithms: image processing, which identifies and tracks multiple targets in images from a single camera without a priori relative orbit knowledge; batch orbit determination, which autonomously initializes orbit estimates for visible swarm members; and sequential orbit determination, which continuously refines the swarm state by fusing measurements from multiple observers exchanged over an intersatellite link. Nonlinear dynamics and measurement models provide sufficient observability to estimate absolute orbits, relative orbits, and auxiliary states using only bearing angles without maneuvers. StarFOX will be conducted using a four-CubeSat swarm as part of the NASA Starling mission, and simulations of experiment scenarios demonstrate that ARTMS meets mission performance requirements. Results indicate that mean bearing angle errors are below 35′′ (), initial target range errors are below 20% of true separation, and steady-state range errors are below 2% (). Absolute orbit estimation accuracy is on the order of 100 m. Hardware-in-the-loop tests display robust navigation under a variety of conditions, enabling autonomous, ubiquitous navigation with minimal ground interaction for future distributed missions.

Event-trigger-based cluster coordinated control of spacecraft swarm under switching topology

This paper investigates the cluster coordination problem of spacecraft swarms with non-negative defined directed communication topology in the context of multi-mission parallel operations. In this design, an intrinsic plasticity based echo state network is established to approximate the nonlinear term of relative attitude dynamics, and an improved event-triggered transmission mechanism is proposed to decrease the redundant communication among spacecraft. A novel cluster coordination control law under fixed non-negative topology is developed based on the echo state neural network and the event-triggered transmission mechanism. Furthermore, an extended cluster coordinated control law is proposed for the switching topology case. By using Lyapunov stability theory and graph theory, it is demonstrated that intra-cluster attitude coordination can be achieved under the proposed control laws and Zeno behavior can be excluded. Finally, numerical examples are given to illustrate the validity and superiority of our results.

Characteristic Scales of Complexity and Coherence within Interplanetary Coronal Mass Ejections: Insights from Spacecraft Swarms in Global Heliospheric Simulations

Many aspects of the 3D structure and evolution of interplanetary coronal mass ejections (ICMEs) remain unexplained. Here, we investigate two main topics: (1) the coherence scale of magnetic fields inside ICMEs, and (2) the dynamic nature of ICME magnetic complexity. We simulate ICMEs interacting with different solar winds using the linear force-free spheromak model incorporated into the EUHFORIA model. We place a swarm of ∼20,000 spacecraft in the 3D simulation domain and characterize ICME magnetic complexity and coherence at each spacecraft based on the simulated time series. Our simulations suggest that ICMEs retain a lower complexity and higher coherence along their magnetic axis, but that a characterization of their global complexity requires crossings along both the axial and perpendicular directions. For an ICME of initial half angular width of 45° that does not interact with other large-scale solar wind structures, global complexity can be characterized by as little as 7–12 spacecraft separated by 25°, but the minimum number of spacecraft rises to 50–65 (separated by 10°) if interactions occur. Without interactions, ICME coherence extends for 45°, 20°–30°, 15°–30°, and 0°–10° for B, B ϕ , B θ , and B r , respectively. Coherence is also lower in the ICME west flank compared to the east flank due to Parker spiral effects. Moreover, coherence is reduced by a factor of 3–6 by interactions with solar wind structures. Our findings help constrain some of the critical scales that control the evolution of ICMEs and aid in the planning of future dedicated multispacecraft missions.

The Threat of Satellite Constellations: Growing swarms of spacecraft in orbit are outshining the stars, and scientists fear no one will do anything to stop it.

The Threat of Satellite Constellations: Growing swarms of spacecraft in orbit are outshining the stars, and scientists fear no one will do anything to stop it.

Distributed cooperative control with collision avoidance for spacecraft swarm reconfiguration via reinforcement learning

This article investigates an adaptive, distributed, and cooperative control strategy for the problem of spacecraft swarm reconfiguration, which involves assembling the spacecraft at a close distance to one another while avoiding collisions and keeping spacecraft far from an obstacle. The key idea is to transform their opposite indices into equivalent ones by using soft and hard constraints. The proposed control strategy is inspired by the actor–critic framework of reinforcement learning (RL) algorithms: The soft constraint is designed by using a critic neural network (NN) for assembling and avoiding obstacles, while collisions among the spacecraft are prevented based on the hard constraint established in an artificial potential field (APF). By drawing support from this idea of equivalent transformation, the adaptive, distributed, and cooperative controller is devised by using an actor NN of the RL algorithm, an APF, and Backstepping control technology. The action NNs are used to estimate the input signals of the desired control and the undesired effects due to disturbance from the APF, and the expected control performance is then obtained by minimizing the output of the critic NN. The computational burden incurred by the NNs is significantly reduced by reducing the number of parameters that need to be learned by NNs. Lyapunov stability theory is used to guarantee that all signals in this closed-loop system are ultimately uniformly bounded to ensure its stability. The results of simulations of a swarm of spacecraft demonstrated the effectiveness of the proposed control strategy.

Communication-Aware Orbit Design for Small Spacecraft Swarms Around Small Bodies

Exploration of small Solar System bodies has traditionally been performed by monolithic spacecraft carrying several science instruments. However, instruments often cannot be operated simultaneously due to requirements including viewing angle, illumination, power, and data constraints. This has motivated interest in architectures in which a swarm of small spacecraft, each carrying one instrument, studies a small body after being deployed by a carrier spacecraft; such architectures hold promise to yield significant improvements in mission efficiency, increased data quality, and reduced mission duration. A key difficulty is the selection of orbits for the spacecraft, which must satisfy not only instrument requirements but also communication and data storage constraints. To address this, we propose a novel gradient-based optimization algorithm that simultaneously optimizes spacecraft orbits, observations, and communications; the approach captures instrument requirements, communication bandwidth, and memory usage, and it accommodates irregular gravity field models and surface geometries. Numerical simulations of a six-spacecraft swarm studying the 433 Eros asteroid show that the approach results in a 67.9% increase in data returned as compared to a communication-agnostic approach. Collectively, these results enable system designers to quickly assess the end-to-end performance of multispacecraft constellations, and represent a first step toward communication-aware design of multispacecraft missions for small Solar System body exploration.

Discrete-Time Attitude Tracking Synchronization for Swarms of Spacecraft Exploiting Interference

The attitude tracking synchronization control of an orbit-predetermined leader–follower spacecraft swarm for the space moving target is discussed in this paper. The information exchange between all spacecraft is assumed to be discrete in time and on the undirected connected graph. Moreover, due to the demand for saving communication resources, wireless interference has been utilized, which allows all the neighbors of a spacecraft to access the same channel frequency spectrum simultaneously. Then the backstepping control algorithm is designed to let the spacecraft (β,A)-practically stably synchronize their states and track a time-varying trajectory in the presence of unknown fading channels. Finally, simulation is provided to verify that using the proposed control scheme, the attitude tracking synchronization can be achieved with high precision.

Stochastic Trajectory Optimization of a Swarm of Spacecraft Exploring the Rings of Saturn

This article presents outcomes of a stochastic optimization technique for trajectories of spacecraft exploring the rings of Saturn. Despite data obtained by Cassini and Voyager on their missions to Saturn, many questions regarding the formation and dynamics of Saturn's rings and planetary rings in general remain unanswered. Sending traditional large spacecraft prove to be problematic as collisions and the probability of mission failure increase dramatically in the dynamically dense region of space within planetary rings. Because of this, a swarm of small unmanned probes with decentralized communication structures and research instruments distributed amongst the swarm can provide a possible solution. In this paper, the practicality of such a swarm mission is investigated through a stochastic model of the mission trajectory dynamics with the goal of minimizing fuel consumption across the entire swarm while avoiding collisions between swarm agents and dynamic rigid body ring particles. Known probability distributions of ring particle dynamical variables (velocity, rotation rate, size) are used to define random variable parameters in a system of differential equations defined by artificial potential fields describing the swarm dynamics. Using a Monte Carlo method, the stochastic optimization problem is solved yielding probabilities of various possible swarm trajectories with the lowest fuel consumption and probability of mission completion without collisions. These optimal parameters can then be onboarded to a swarm of spacecraft allowing them to explore the rings of Saturn following optimal trajectories.

A Novel Decentralized Consensus-Based Tracking Control for Exploration of Saturn's Rings

A better comprehension of the formation of Saturn's rings is crucial to understand our solar system. Many questions remain unanswered despite the successes of the Cassini and Voyager missions to Saturn. Traditional large spacecraft prove to be problematic within planetary rings because collisions and consequent mission failure increase dramatically in the rings’ dynamically dense environment. Using a swarm of small unmanned probes with decentralized control and communication structures that are equipped with research instruments distributed amongst the swarm is a possible solution. This paper presents a novel, decentralized consensus-based tracking control algorithm for guiding such a swarm. This control algorithm is characterized by a trajectory generator based on worst-case assumptions about both communication structures and the ring particle environment. Optimal model parameters, numerically calculated through the Monte Carlo method with the goal of minimizing fuel consumption and avoiding collisions, are used to generate an optimal reference trajectory for the swarm of spacecraft. A feedback tracking control with the optimal reference trajectory is designed under the assumption of unreliable and non-instantaneous communication among individual swarm agents. The effectiveness of the proposed control algorithm is validated numerically in MATLAB/Simulink.

Safe, Delta--Efficient Spacecraft Swarm Reconfiguration Using Lyapunov Stability and Artificial Potentials

Spacecraft swarms can achieve mission objectives otherwise impossible by monolithic satellites. To this end, swarms need to autonomously reconfigure their relative motion while complying with spacecraft constraints. Convex optimization provides safety and efficiency for arbitrary reconfigurations at high computational cost. Comparatively, closed-form solutions are computationally efficient but do not guarantee optimality and compliance to constraints in general cases. This work proposes a novel control architecture with Lyapunov functions and artificial potentials based on relative orbit elements that promise the numerical efficiency of closed-form solutions and the general applicability of convex optimization solvers. The novel Lyapunov functions are designed using analytical lower bounds calculated using the current control tracking errors. When the functions are used with a feedback control scheme modeled after the optimal, closed-form solutions for binary system reconfiguration, the resulting controller is both computationally and efficient. To address safety and state constraints in general, reference governors based on artificial potential functions enable computationally efficient collision avoidance using only neighbor state information. The controllers are validated in example mission simulations representative of Starling-1 and the Van Allen Swarm. In these missions, the controllers demonstrate safe, -efficient, and computationally tractable swarm reconfiguration, enabling future swarming missions.