Formation Flying Research Articles

Finite-time distributed hierarchical control for satellite cluster with collision avoidance

In this paper, a novel distributed hierarchical control method for small satellites with multiple disturbances and input constraints is investigated by combining formation flying and satellite cluster. First, a finite-time convergent extended state observer (FTCESO) is developed to estimate the external disturbance with high precision, and a non-singular fast terminal sliding mode controller (NFTSMC) is proposed to maintain the specific configuration of leader-satellites and the finite time convergence is theoretically proved. Then, an improved artificial potential field method with collision avoidance and damping characteristics is proposed for the follower-satellite, so that the follower-satellite can keep a collision-avoidance relative distance from corresponding leader-satellite with the desired communication range. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed method.

Retrieving and Validating Leaf and Canopy Chlorophyll Content at Moderate Resolution: A Multiscale Analysis with the Sentinel-3 OLCI Sensor.

ESA’s Eighth Earth Explorer mission “FLuorescence EXplorer” (FLEX) will be dedicated to the global monitoring of the chlorophyll fluorescence emitted by vegetation. In order to properly interpret the measured fluorescence signal, essential vegetation variables need to be retrieved concomitantly. FLEX will fly in tandem formation with Sentinel-3 (S3), which conveys the Ocean and Land Color Instrument (OLCI) that is designed to characterize the atmosphere and the terrestrial vegetation at a spatial resolution of 300 m. In support of FLEX’s preparatory activities, this paper presents a first validation exercise of OLCI vegetation products against in situ data coming from the 2018 FLEXSense campaign. During this campaign, leaf chlorophyll content (LCC) and leaf area index (LAI) measurements were collected over croplands, while HyPlant DUAL images of the area were acquired at a 3 m spatial resolution. A multiscale validation strategy was pursued. First, estimates of these two variables, together with the combined canopy chlorophyll content (CCC = LCC × LAI), were obtained at the HyPlant spatial resolution and were compared against the in situ measurements. Second, the fine-scale retrieval maps from HyPlant were coarsened to the S3 spatial scale as a reference to assess the quality of the OLCI vegetation products. As an intermediary step, vegetation products extracted from Sentinel-2 data were used to compare retrievals at the in-between spatial resolution of 20 m. For all spatial scales, CCC delivered the most accurate estimates with the smallest prediction error obtained at the 300 m resolution (R2 of 0.74 and RMSE = 26.8 μg cm-2). Results of a scaling analysis suggest that CCC performs well at the different tested spatial resolutions since it presents a linear behavior across scales. LCC, on the other hand, was poorly retrieved at the 300 m scale, showing overestimated values over heterogeneous pixels. The introduction of a new LCC model integrating mixed reflectance spectra in its training enabled to improve by 16% the retrieval accuracy for this variable (RMSE = 10 μg cm–2 for the new model versus RMSE = 11.9 μg cm-2 for the former model).

Adaptive Robust Trajectory Tracking Control of Multiple Quad-Rotor UAVs with Parametric Uncertainties and Disturbances.

Recently, formation flying of multiple unmanned aerial vehicles (UAVs) found numerous applications in various areas such as surveillance, industrial automation and disaster management. The accuracy and reliability for performing group tasks by multiple UAVs is highly dependent on the applied control strategy. The formation and trajectories of multiple UAVs are governed by two separate controllers, namely formation and trajectory tracking controllers respectively. In presence of environmental effects, disturbances due to wind and parametric uncertainties, the controller design process is a challenging task. This article proposes a robust adaptive formation and trajectory tacking control of multiple quad-rotor UAVs using super twisting sliding mode control method. In the proposed design, Lyapunov function-based adaptive disturbance estimators are used to compensate for the effects of external disturbances and parametric uncertainties. The stability of the proposed controllers is guaranteed using Lyapunov theorems. Two variants of the control schemes, namely fixed gain super twisting SMC (STSMC) and adaptive super twisting SMC (ASTSMC) are tested using numerical simulations performed in MATLAB/Simulink. From the results presented, it is verified that in presence of disturbances, the proposed ASTSMC controller exhibits enhanced robustness as compared to the fixed gain STSMC.

Distributed Robust Formation Flying and Attitude Synchronization of Spacecraft

AbstractThis paper considers the spacecraft formation flying (SFF) with a desired attitude. Two control problems are studied. One is the formation control of multiple spacecraft and the other is th...

GNSS-based hardware-in-the-loop simulations of spacecraft formation flying with the global ionospheric model TIEGCM

Low-earth-orbit (LEO) spacecraft formation flying (SFF) simulated on the Virginia Tech Formation Flying Testbed (VTFFTB) demonstrated the feasibility of detecting simplified ionospheric electron density (Ne) structures (i.e., one-dimensional equatorial plasma bubbles/EPBs) utilizing a differential total electron content (TEC) method. The Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIEGCM) is used to greatly enhance the ionospheric Ne simulation capability and fidelity (e.g., dimension, resolution, more realistic space weather processes) of GNSS-based hardware-in-the-loop (HIL) simulations in the current work. An algorithm is developed to incorporate TIEGCM 4D ionospheric Ne profiles into the VTFFTB HIL infrastructure by simulating the TEC impacts on multi-band GNSS signals. First, a series of first-principle analyses on ionospheric Ne retrieval accuracy are presented using software-based LEO SFF simulations in the TIEGCM ionosphere. Subsequently, two HIL ionospheric space weather observation simulation test cases, EPB and Tongues-of-Ionization (TOI), are simulated on the VTFFTB to demonstrate the enhanced 4D ionospheric simulation capability and evaluate the Ne retrieval characteristics. The Ne retrieval techniques are validated and characterized in the TIEGCM ionosphere via both software and HIL simulations. In principle, the technique developed is expected to be applicable to other similar simulation platforms, as well as other global or regional ionospheric models. This is advantageous for future GNSS testing, HIL simulations, and technology developments.

Ultra-Dense LEO Satellite Based Formation Flying

In this article, we consider a downlink ultra-dense LEO-based multi-terminal satellite system where multiple satellites fly in formation to serve a number of ground terminal stations for data transmission. Benefited from the dense satellite constellation, high channel capacity can be achieved via the massive virtual antenna array formed by multiple satellites. We aim at exploring how the satellite distribution and formation size influence the channel capacity in this case. We first derive the upper bound of the channel capacity in the general multi-antenna satellite networks. The single-antenna satellite case is considered where we present the specific forms of the derived capacity bounds to prove that the capacity first increases linearly then increases more and more slowly with the satellite formation size, and there exists an optimal LEO satellite distribution to achieve the maximum capacity of the system. Simulation results verify our theoretical analysis and show that such statements also hold for the general multi-antenna satellite case.

Overview of surfing aircraft vortices for energy

Surfing Aircraft Vortices for Energy (SAVE) refers to the behavior that an aircraft “rides” on the vortex of the front aircraft just like the formation flying of migratory birds and it can also provide guidance for the aircraft that is difficult to avoid entering the front vortex, reduce the incidence of flight accidents caused by the vortex, and improve the safe operation ability of civil aviation. The technology has the advantages of saving energy and increasing range, which is a hot issue in the field of aviation research. Firstly, this paper analyzes the main research contents, technological developments and applications in the field of SAVE at home and abroad. Then discusses the key technologies of SAVE such as aerodynamic principles, control of SAVE, safety guarantee, path planning, and related experimental verification technologies. Finally, the development and application trend of SAVE technology in military and civil aviation fields and its corresponding benefits brought by it will be pointed out.

Improved successive approximation control for formation flying at libration points of solar-earth system.

In deep space exploration, the libration points (especially L2 point) of solar-earth system is a re-search hotspot in recent years. Space station and telescope can be arranged at this point, and it does not need too much kinetic energy. Therefore, it is of great significance to arrange flight formation on the libration point of solar-earth for scientific research. However, the flight keeping control technology of flight formation on the solar-earth libration points (also called Lagrange points) is one of the key problems to be solved urgently. Based on the nonlinear dynamic model of formation flying, the improved successive approximation algorithm is used to achieve formation keeping con-trol. Compared with the control algorithm based on orbital elements, this control algorithm has the advantages of high control accuracy and short control time in formation keeping control of solar-earth libration points. The disadvantage is that the calculation is complicated. But, with the devel-opment of computer technology, the computational load is gradually increasing, and there will be more extensive application value in the future. Finally, the error and control simulations of the formation flying of the spacecraft with the libration points of the solar-earth system are carried out for two days. The simulation results show that the method can quickly achieve the requirements of high-precision control.

Modelling of flight performance benefits for similar and hybrid jet airline formations

Avian formation flight has always inspired technology protagonists to mimic and harness associated benefits for the aviation industry. This paper discusses the performance benefits of similar and hybrid jet airliners flying in formation. The aerodynamic forces are modelled through potential flow theory. The lateral and vertical spacing is varied to estimate advantages in range. For simplicity, only cruise performance is analysed. By employing formation flying in wide-body aircrafts, an increase in range up to 65% is observed relative to standard flight. In addition to that, an optimal switching point during cruise flight is evaluated to give equal benefits to both aircrafts flying in formation. The study proposes a new concept of shared airspace where different aircrafts cooperate on long routes for fuel savings. However, the findings reported in this paper are of theoretical nature and high-fidelity models and experimentation is considered necessary to further evaluate the benefits of formation flying. Moreover, existing distancing restrictions between two aircrafts, imposed by regulatory authorities, are also a potential limitation in successful realisation of commercial formation flight.

Modelling of flight performance benefits for similar and hybrid jet airline formations

Avian formation flight has always inspired technology protagonists to mimic and harness associated benefits for the aviation industry. This paper discusses the performance benefits of similar and hybrid jet airliners flying in formation. The aerodynamic forces are modelled through potential flow theory. The lateral and vertical spacing is varied to estimate advantages in range. For simplicity, only cruise performance is analysed. By employing formation flying in wide-body aircrafts, an increase in range up to 65% is observed relative to standard flight. In addition to that, an optimal switching point during cruise flight is evaluated to give equal benefits to both aircrafts flying in formation. The study proposes a new concept of shared airspace where different aircrafts cooperate on long routes for fuel savings. However, the findings reported in this paper are of theoretical nature and high-fidelity models and experimentation is considered necessary to further evaluate the benefits of formation flying. Moreover, existing distancing restrictions between two aircrafts, imposed by regulatory authorities, are also a potential limitation in successful realisation of commercial formation flight.

Unique role of small satellites in empowering spacecraft formation flying missions

Spacecraft formation flying avails unprecedented means of conducting space missions compared to a single conventional large monolithic platform. Chiefly, formation flying enables sparse and synthes...

Research on obstacle avoidance technology of fixed wing formation based on improved artificial potential field method with stereo vision

To solve the problem that distributed fixed wing formation cannot know all the other aircraft states through the ground station and may collide, the improved artificial potential field method based on binocular stereo vision was proposed. This method makes the fixed wing aircraft not need to obtain the position information of other fixed wing aircraft from the ground station, but only need the binocular stereo vision module to obtain the relative position and relative speed information of other fixed wing aircraft. These two parameters are used to improve the traditional artificial potential field method to meet the requirements of distributed fixed wing formation flight. The experimental results show that the improved artificial potential field method improves the safety and reliability of distributed fixed wing formation flying.

On Novel Adaptive Coordinated Control for Spacecraft Formation: An Adjustable Performance Approach

This paper investigates an adaptive coordinated control problem of spacecraft formation flying (SFF) system subject to uncertain mass and external perturbations. First, a general unified structure is proposed to represent the adjustable performance functions like the exponentially and appointed-time convergent ones. Then, an adaptive coordinated controller is developed based on a two-layer performance envelope to characterize the transient and steady-state formation maneuvering behaviors quantitatively of SFF system. Compared with the existing coordinated control approaches, the prominent advantage of the proposed one is that the preassigned position tracking and consensus tracking performance is guaranteed simultaneously while maintaining the scheduled formation configuration. Meanwhile, the users can configure and adjust the convergence rate (like the exponential or finite-time convergence) of the formation tracking errors by choosing different parameters arbitrarily in the unified structure for the performance functions. Finally, a group of numerical examples are organized to validated the effectiveness of the proposed coordinated control approach.

Adaptive Fixed-Time 6-DOF Coordinated Control of Multiple Spacecraft Formation Flying with Input Quantization

This paper investigates the fixed-time coordinated control problem of six-degree-of-freedom (6-DOF) dynamic model for multiple spacecraft formation flying (SFF) with input quantization, where the communication topology is assumed directed. Firstly, a new multispacecraft nonsingular fixed-time terminal sliding mode vector is derived by using neighborhood state information. Secondly, a hysteretic quantizer is utilized to quantify control force and torque. Utilizing such a quantizer not only can reduce the required communication rate but also can eliminate the control chattering phenomenon induced by the logarithmic quantizer. Thirdly, a 6-DOF fixed-time coordinated control strategy with adaptive tuning laws is proposed, such that the practical fixed-time stability of the controlled system is ensured in the presence of both upper bounds of unknown external disturbances. It theoretically proves that the relative tracking errors of attitude and position can converge into the regions in a fixed time. Finally, a numerical example is exploited to show the usefulness of the theoretical results.

Fixed-time attitude coordination control for spacecraft with external disturbance

This paper studies the fixed-time stability of attitude coordination control for spacecraft formation flying (SFF) in the presence of some external disturbance. Firstly, to ensure that the states converge to the origin within a fixed time, a novel nonsingular terminal sliding mode surface (NTSMS) is designed. The convergence time is bounded by some predefined constants. Secondly, an attitude synchronization controller is proposed based on the designed NTSMS, which guarantees the fixed-time stability of SFF under an undirected communication topology. Finally, a fixed-time adaptive control law is designed for cases in which the boundary of the external disturbance is unknown. The fixed-time stability is guaranteed by a revised form of the proposed NTSMS. Simulation results show that the proposed controllers provide fixed-time stability and outperform existing finite-time controllers.

Assessing the Climate Impact of Formation Flights

An operational measure that is inspired by migrant birds aiming toward the mitigation of aviation climate impact is to fly in aerodynamic formation. When this operational measure is adapted to commercial aircraft it saves fuel and is, therefore, expected to reduce the climate impact of aviation. Besides the total emission amount, this mitigation option also changes the location of emissions, impacting the non-CO2 climate effects arising from NOx and H2O emissions and contrails. Here, we assess these non-CO2 climate impacts with a climate response model to assure a benefit for climate not only due to CO2 emission reductions, but also due to reduced non-CO2 effects. Therefore, the climate response model AirClim is used, which includes CO2 effects and also the impact of water vapor and contrail induced cloudiness as well as the impact of nitrogen dioxide emissions on the ozone and methane concentration. For this purpose, AirClim has been adopted to account for saturation effects occurring for formation flight. The results of the case studies show that the implementation of formation flights in the 50 most popular airports for the year 2017 display an average decrease of fuel consumption by 5%. The climate impact, in terms of average near surface temperature change, is estimated to be reduced in average by 24%, with values of individual formations between 13% and 33%.

Disturbance observer based finite-time coordinated attitude tracking control for spacecraft on SO(3)

To solve the problem of attitude synchronization control for spacecraft formation flying (SFF) suffering from external disturbances under a directed communication topology, a sliding mode disturbance observer (SMDO) based on the finite-time control strategy is developed to observe the time-varying external disturbance via estimating the upper bound of its first derivative. Meanwhile, the rotation matrix is employed to describe the attitude of SFF for the purpose of the avoidance of singularity and unwinding phenomenon. As for the attitude synchronization and the tracking control architecture, a sliding mode surface (SMS) is given such that the control objective can be achieved. The effectiveness and the validity of the proposed method are elaborated via theoretical analysis and numerical simulations.

NCAnt: A Network Coding-Based Multipath Data Transmission Scheme for Multi-UAV Formation Flying Networks

Network coding based multipath transmission method has been shown to improve the reliability and throughput of end-to-end data delivery for ad hoc networks. However, when it is adapted to flying ad hoc networks (FANETs), multipath establishment and maintenance scheme should be elaborately designed due to frequently local topology changes during UAVs' formation flying. This letter proposes a network-coding-aware multipath routing protocol NCAnt. It achieves reliable end-to-end transmission by maximizing recoding opportunities based on the ant colony optimization (ACO). Moreover, the positive feedback mechanism of ant colony pheromone is utilized to reduce the routing reconstruction cost under frequent local topology changes. Simulation results show NCAnt can provide up to 50% additional coding opportunities and achieves lower path recovery delay than baseline schemes.

A Submillimeter Level Relative Navigation Technology for Spacecraft Formation Flying in Highly Elliptical Orbit.

Spacecraft formation flying (SFF) in highly elliptical orbit (HEO) has attracted a great deal of attention in many space exploration applications, while precise guidance, navigation, and control (GNC) technology—especially precise ranging—are the basis of success for such SFF missions. In this paper, we introduce a novel K-band microwave ranging (MWR) equipment for the on-orbit verification of submillimeter-level precise ranging technology in future HEO SFF missions. The ranging technique is a synchronous dual one-way ranging (DOWR) microwave phase accumulation system, which achieved a ranging accuracy of tens of microns in the laboratory environment. The detailed design and development process of the MWR equipment are provided, ranging error sources are analyzed, and relative orbit dynamic models for HEO formation scenes are given with real perturbations considered. Moreover, an adaptive Kalman filter algorithm is introduced for SFF relative navigation design, incorporating process noise uncertainty. The performance of SFF relative navigation while using MWR is tested in a hardware-in-the-loop (HIL) simulation system within a high-precision six degrees of freedom (6-DOF) moving platform. The final range estimation errors from MWR using the adaptive filter were less than 35 m and 8.5 m/s for range rate, demonstrating the promising accuracy for future HEO formation mission applications.

Optimal strategies for selecting coordinators

We study optimal election sequences for repeatedly selecting a (very) small group of leaders among a set of participants (players) with publicly known unique ids. In every time slot, every player has to select exactly one player that it considers to be the current leader, oblivious to the selection of the other players, but with the overarching goal of maximizing a given parameterized global (“social”) payoff function in the limit. We consider a quite generic model, where the local payoff achieved by a given player depends, weighted by some arbitrary but fixed real parameter, on the number of different leaders chosen in a round, the number of players that choose the given player as the leader, and whether the chosen leader has changed w.r.t. the previous round or not. The social payoff can be the maximum, average or minimum local payoff of the players. Possible applications include quite diverse examples such as rotating coordinator-based distributed algorithms and long-haul formation flying of social birds. Depending on the weights and the particular social payoff, optimal sequences can be very different, from simple round-robin where all players chose the same leader alternatingly every time slot to very exotic patterns, where a small group of leaders (at most 2) is elected in every time slot. Moreover, we study the question if and when a single player would not benefit w.r.t. its local payoff when deviating from the given optimal sequence, i.e., when our optimal sequences are Nash equilibria in the restricted strategy space of oblivious strategies. As this is the case for many parameterizations of our model, our results reveal that no punishment is needed to make it rational for the players to optimize the social payoff.