Cluster Flight Research Articles

Effects of Geometry Configurations on Ambiguity Function for Cluster Flight Netted Radar

提出了集分离航天器与网络雷达为一体的簇飞行网络雷达概念.通过引入双基地雷达模糊函数，给出簇飞行网络雷达模糊函数定义和计算步骤，研究了雷达几何构型和簇飞行雷达之间相对有界基线对模糊函数的影响.数值计算结果表明：与单基地雷达模糊函数相比，网络雷达模糊函数主瓣宽度明显变窄，簇飞行模式下可变基线对雷达模糊函数的影响不大；雷达模糊函数应主要考虑目标飞行速度和接收距离变化的影响.最后，给出了簇飞行网络雷达模糊函数的一种上界.

Problem A of the 9th China trajectory optimization competition: Results found at Tsinghua University

This paper presents the crucial method for obtaining results of Tsinghua University in the 9th China Trajectory Optimization Competition (CTOC-9). To monitor the usage of the important frequency resources of GEO satellites, CTOC-9 focuses on the orbit design and trajectory optimization of satellite cluster flight for geostationary orbit (GEO) satellite beams monitoring missions. The three cluster satellite orbits and complex constraints cause much difficulties in the design and optimization. The search for the globally optimal mission trajectory with multi-impulse orbit maneuver is performed in two steps. The first step involves a roughly global search in the search space that has been bounded based on the fuel constraints, the monitoring conditions and the formation flying model of three monitoring cluster satellites. To bound the global search space, several legs are patched together to represent the whole trajectory of monitoring mission, and the impulses occurring in the patch points are estimated by the Hohmann transfer. And the particle swarm optimization (PSO) algorithm is modified and then employed to the multi-leg optimization. The second step involves the local optimization of the multi-impulse patched-conic legs which stand out from the roughly global search. The main task of the local optimization is to solve a series of J2 perturbed Lambert problems by the homotopic approach. Based on the impulsive results, some specific subtasks are selected and re-optimized to reduce the number of subtasks. Of the many trajectories found, the optimal trajectory submitted for the competition is reported. A post-competition result is reported, which is with the primary objective of 19.61 days, prior to the winner of 20.43 days.

Problem B of 9th China Trajectory Optimization Competition: Problem description and summary of the results

From September 1st 2017 to October 15th 2017, the 9th China Trajectory Optimization Competition was jointly hold by the Chinese Society of Theoretical and Applied Mechanics, Beijing Institute of Technology, Beijing Institute of Electronic System Engineering, Tsinghua Space Center. The competition contains two problems, where problem A focuses on the cluster flight orbit design and optimization for GEO satellite beams monitoring, and problem B focuses on the design and deployment of a satellite navigation regional augmentation system. In this short communication, a brief description of problem B is reviewed, then the competition results and a brief discussion are given.

Problem A of 9th China trajectory optimization competition: Problem description and summary of the results

From September 1st 2017 to October 15th 2017, the 9th China Trajectory Optimization Competition (CTOC) was jointly held by the Chinese Society of Theoretical and Applied Mechanics, Beijing Institute of Technology, Beijing Institute of Electronic System Engineering, and Tsinghua Space Center. The competition contains two problems, where problem A focuses on the cluster flight orbit design and optimization for GEO satellite beams monitoring, and problem B focuses on the design and deployment of a satellite navigation regional augmentation system. In this short communication, a brief history of China trajectory optimization competition is reviewed firstly. Then, description of problem A is presented. Finally, the competition results and brief discussion are given.

Path Planning of UAVs Based on Collision Probability and Kalman Filter

For clusters of UAVs, the scale and density of the cluster determine its ability to solve the task. With the increasing density of aerial vehicles, effectively planning a reasonable flight path and avoiding conflicts among flight paths have become key problems for UAV clusters. The traditional control method is to detect potential conflicts through radar monitoring or location reporting in the air and to then change the flight path, including the height, heading, and speed, through manual instruction. To solve the problem of path conflicts for UAV clusters, a method for calculating the collision probabilities of UAVs is established under the constraints of mission space and the number of UAVs. In cluster flight mode, automatic tracking and prediction of UAV cluster tracks are implemented to avoid path conflicts in clusters. In addition, to address the inconsistency problem because of noise caused by the state information of multi UAV communication under a dynamic environment, a state estimation method is proposed based on the Kalman algorithm. To achieve aircraft track planning, cluster state prediction and collision probability are eventually calculated to avoid the clusters of formation UAVs conflicting on paths during flight. Finally, the simulation results verify the validity and effectiveness of the proposed method in multi UAV formation flight planning.

Design of Bounded Relative Trajectories in the Earth Zonal Problem

Numerical methods have proven to be reliable tools in generating long-term bounded relative trajectories in nontrivial dynamical environments. Yet, none of the existing procedures have a systematic approach to come up with all of the bounded relative trajectories associated with a variety of satellites in Earth orbit. In this paper, such a systematic procedure is developed based on the assumption that any trajectory, except at critical inclinations, is either periodic or quasi periodic in the four-dimensional Routh reduced system describing the motion of a mass particle about an axisymmetric body. This allows key design parameters to be identified, such as the nodal period and the node drift per nodal period, which are later used to constrain a differential corrector scheme looking for families of quasi-periodic invariant tori that yield bounded relative motion in the Earth-centered inertial frame. Numerical simulations show that the computed solutions are good candidates for cluster flight missions at a large range of altitude and inclination values.

Consensus of satellite cluster flight using an energy-matching optimal control method

This paper presents an optimal control method for consensus of satellite cluster flight under a kind of energy matching condition. Firstly, the relation between energy matching and satellite periodically bounded relative motion is analyzed, and the satellite energy matching principle is applied to configure the initial conditions. Then, period-delayed errors are adopted as state variables to establish the period-delayed errors dynamics models of a single satellite and the cluster. Next a novel satellite cluster feedback control protocol with coupling gain is designed, so that the satellite cluster periodically bounded relative motion consensus problem (period-delayed errors state consensus problem) is transformed to the stability of a set of matrices with the same low dimension. Based on the consensus region theory in the research of multi-agent system consensus issues, the coupling gain can be obtained to satisfy the requirement of consensus region and decouple the satellite cluster information topology and the feedback control gain matrix, which can be determined by Linear quadratic regulator (LQR) optimal method. This method can realize the consensus of satellite cluster period-delayed errors, leading to the consistency of semi-major axes (SMA) and the energy-matching of satellite cluster. Then satellites can emerge the global coordinative cluster behavior. Finally the feasibility and effectiveness of the present energy-matching optimal consensus for satellite cluster flight is verified through numerical simulations.

Orbit design and control method for satellite clusters and its applications to NetSat project

In this paper, an optimal orbit design and control method for satellite clusters is presented and the method is applied to the four pico/nano-satellite system NetSat. Firstly, the relative motion based on relative eccentricity/inclination vectors is reviewed. Then, an optimal orbit design method for the cluster flight is developed, and the initial states of satellites in the cluster are derived using a graphical representation of the relative eccentricity/inclination vectors combined with a constrained nonlinear programming method. Next, a novel satellite cluster feedback control method is designed, and an optimal three-maneuver strategy is proposed, which could maintain the satellites in a bounded relative motion, satisfying the tight fuel consumption constraints and fuel balance for a long operational lifetime. Finally, the feasibility and effectiveness of the optimal orbit design and control for satellites cluster and its application to NetSat project are verified through numerical simulations.

Debris Avoidance Maneuvers for Spacecraft in a Cluster

Spacecraft formation flying and satellite cluster flight have seen growing interest in the last decade. However, the problem of finding the optimal debris collision avoidance maneuver for a satellite in a cluster has received little attention. This paper develops a method for choosing the timing for conducting minimum-fuel avoidance maneuvers without violating the cluster intersatellite maximal distance limits. The mean semimajor axis difference between the maneuvering satellite and the other satellites is monitored for the assessment of a maneuver possibility. In addition, three techniques for finding optimal maneuvers under the constraints of cluster keeping are developed. The first is an execution of an additional cluster-keeping maneuver at the debris time of closest approach, the second is a global all-cluster maneuver, and the third is a fuel-optimal maneuver, which incorporates the cluster-keeping constraints into the calculation of the evasive maneuver. The methods are demonstrated and compared. The first methodology proves to be the most fuel-efficient. The global maneuver guarantees boundedness of the intersatellite distances as well as fuel and mass balance. However, it is rather fuel-expensive. The last method proves to be useful at certain timings and is a compromise between fuel consumption and the number of maneuvers.

Cluster flight control for fractionated spacecraft on an elliptic orbit

This paper deals with the stabilization of cluster flight on an elliptic reference orbit by the Hamiltonian structure-preserving control using the relative position measurement only. The linearized Melton’s relative equation is utilized to derive the controller and then the full nonlinear relative dynamics are employed to numerically evaluate the controller’s performance. In this paper, the hyperbolic and elliptic eigenvalues and their manifolds are treated without distinction notations. This new treatment not only contributes to solving the difficulty in feedback of the unfixed-dimensional manifolds, but also allows more opportunities to set the controlled frequencies of foundational motions or to optimize control gains. Any initial condition can be stabilized on a Kolmogorov–Arnold–Moser torus near a controlled elliptic equilibrium. The motions are stabilized around the natural relative trajectories rather than track a reference relative configuration. In addition, the bounded quasi-periodic trajectories generated by the controller have advantages in rapid reconfiguration and unpredictable evolution.

Relative Reachable Domain for Spacecraft with Initial State Uncertainties

The reachable domain is a geometric description of the maneuverability of a spacecraft under control and/or measurement uncertainties. In this paper, the reachable domain concept is introduced into the field of satellite relative motion and termed the relative reachable domain. The relative reachable domain geometrically represents the effects of the initial control and/or measurement uncertainties on relative motion. A general method is developed to find the envelope of the coplanar relative reachable domain for arbitrary reference orbits, by evaluating the extremal values of the potentially accessible radius with respect to a given reference position. The relative reachable domain formulations are analytically expressed for circular reference orbits. It is shown that the relative reachable domain is a convenient tool for analyzing a variety of cluster flight mission problems. Several practical applications are suggested, including determining the upper bound on the separation distances among satellites. It is also shown that the relative reachable domain can be used for assessing the collision risk and that, in some situations, the relative reachable domain is more reliable than existing collision assessment methods. Numerical examples demonstrate the usefulness of the proposed method for finding the relative reachable domain and show that the analytical calculation of the relative reachable domain is accurate even in the case of noncoplanar perturbed motion.

Covariance analysis of differential drag-based satellite cluster flight

One possibility for satellite cluster flight is to control relative distances using differential drag. The idea is to increase or decrease the drag acceleration on each satellite by changing its attitude, and use the resulting small differential acceleration as a controller. The most significant advantage of the differential drag concept is that it enables cluster flight without consuming fuel. However, any drag-based control algorithm must cope with significant aerodynamical and mechanical uncertainties. The goal of the current paper is to develop a method for examination of the differential drag-based cluster flight performance in the presence of noise and uncertainties. In particular, the differential drag control law is examined under measurement noise, drag uncertainties, and initial condition-related uncertainties. The method used for uncertainty quantification is the Linear Covariance Analysis, which enables us to propagate the augmented state and filter covariance without propagating the state itself. Validation using a Monte-Carlo simulation is provided. The results show that all uncertainties have relatively small effect on the inter-satellite distance, even in the long term, which validates the robustness of the used differential drag controller.

Distributed Control for Satellite Cluster Flight Under Different Communication Topologies

Cluster flight algorithms enable the operation of multiple satellites within given distance bounds for long periods of time. Synchronizing the states of the satellites in the cluster is important for both cluster establishment and cluster keeping. This paper offers two distributed orbit control laws with fixed-magnitude thrust for satellite cluster flight based on mean-orbital elements. These controllers are capable of synchronizing the convergence of orbital elements among all satellites. Intersatellite communication is represented by weighted digraphs, and the related stability properties of the closed-loop control system are examined. Global asymptotic stability is proven for the first controller using nonsmooth analysis, whereas the second controller is shown to be only locally asymptotically stable. Furthermore, it is proven that chattering in the thrust direction is unavoidable when using fixed-magnitude thrusters and continuous weights. The occurrence of chattering is analyzed with respect to constant weights and time-varying weights. Two approaches are suggested to mitigate chattering: fast-varying weights and thrust modulation. Numerical simulations are performed to validate the analysis.

Optimal Target States for Satellite Cluster Flight Control on Near-Circular Orbits

One of the methods for maintaining a cluster of satellites in long-term bounded relative distances is keeping the satellites on near-circular orbits having the same mean semimajor axes and mean inclinations. This approach allows some freedom in determining the reference mean semimajor axis and reference mean inclination for the cluster. In this paper, this freedom is used to find the optimal target values of the mean semimajor axis and mean inclination, with the optimization criteria being either the total propellant consumption of the cluster or the fuel consumption differences among satellites. The optimization problems are solved analytically, assuming that a fixed-magnitude thruster is used for closed-loop orbit control, and new results are presented, providing simple closed-form expressions for the optimal target states. Simulations are used for validating the results, showing that much propellant can be saved by properly setting the cluster reference orbit.

Improved initialization conditions and single impulsive maneuvers for $$\hbox {J}_{2}$$ J 2 -invariant relative orbits

The determination of the initial conditions for long-term bounded relative motion under natural perturbations is an important theme in satellite cluster flight. Considering the most significant perturbation of the geopotential, namely, the \(\hbox {J}_{2}\) term, many researchers have proposed \(\hbox {J}_{2}\)-mitigating initial conditions for satellite-bounded relative motion. To improve the existing \(\hbox {J}_{2}\)-invariant conditions, two new methods for finding the correction factor are presented in this paper. In these two methods, Method 1 is obtained by minimizing the possible maximum drift in the along-track relative motion. However, Method 2 is designed by nullifying the rates of change of the bounds of the relative motion. Then the geometric character, such as the self-intersection of the \(\hbox {J}_{2}\)-invariant relative orbits, is discussed. The conditions of 0, 1 and 2 (the possible maximum number) self-intersection points are also derived. Then, using Gauss’s equations of planetary motion, an analytical optimal single-impulsive maneuver is deduced to guarantee the secular bounded relative motion under \(\hbox {J}_{2}\), too. Some numerical simulations are performed to validate the corresponding theoretical predictions. The results demonstrate that the proposed methods enhance performance for achieving the bounded relative motion under \(\hbox {J}_{2}\) effects and can be used for future satellite cluster flight missions.

Satellite cluster flight using on-off cyclic control

Nano-satellite clusters and disaggregated satellites are new concepts in the realm of distributed satellite systems, which require complex cluster management – mainly regulating the maximal and minimal inter-satellite distances on time scales of years – while utilizing simple on-off propulsion systems. The simple actuators and long time scales require judicious astrodynamical modeling coupled with specialized orbit control. This paper offers a satellite cluster orbit control law which works for long time scales in a perturbed environment while utilizing fixed-magnitude thrusters. The main idea is to design a distributed controller which balances the fuel consumption among the satellites, thus mitigating the effect of differential drag perturbations. The underlying methodology utilizes a cyclic control algorithm based on a mean orbital elements feedback. Stability properties of the closed-loop cyclic control system do not adhere to the classical Lyapunov stability theory, so an effort is made to define and implement a suitable stability theory of noncompact equilibria sets. A state selection scheme is proposed for efficiently establishing a low Earth orbit cluster. Several simulations, including a real mission study, and several comparative investigations, are performed to show the strengths of the proposed control law.

Orbit Injection Considerations for Cluster Flight of Nanosatellites

Cluster flight is defined as the operation of multiple cooperative satellites under minimum and maximum distance constraints. Unlike traditional orbit injection of multiple noncooperative satellites, judicious constraints should be imposed on the orbit injection of a cluster. Moreover, the orbital injection should enable a fuel-efficient cluster establishment maneuver. This study develops constraints for the orbit injection of a satellite cluster. Evaluation of feasible orbit injection scenarios is performed. Particular launch vehicles and a concomitant set of orbital injection scenarios are found, which are the most suitable for long-term operation of a cluster. In addition, an efficient cluster establishment control method is developed, which prevents the cluster from drifting apart too rapidly. Several orbit injection scenarios are simulated and their feasibility for a planned cluster flight mission is evaluated. It is shown that both the Polar Satellite Launch Vehicle and the Dnepr launcher can be used. In addition, a new customized release procedure is developed, which guarantees cross-track separation among the satellites, a desirable feature in a number of practical missions.

Nanosatellite Cluster Keeping Under Thrust Uncertainties

One of the emerging topics in the realm of distributed space systems is cluster flight of nanosatellites. As opposed to formation flight, cluster flight does not dictate strict limits on the geometry of the cluster, and is hence more suitable for implementation in nanosatellites, which usually do not carry highly accurate sensors and actuators. The actuators are usually simple fixed-magnitude thrusters, which are prone to many sources of errors, such as attitude determination and control errors. In this context, the purpose of this paper is to develop a cluster-keeping control law that is capable of long-term operation under thrust uncertainties, assuming fixed-magnitude thrust provided by a simple cold-gas thruster. To that end, mean orbital elements are used for designing an inverse-dynamics controller. It is shown that, in the differential mean elements space, this controller is time-optimal. An adaptive enhancement is developed to mitigate the thrust pointing errors and restore the original optimal performance, thus saving much fuel. Several simulations and comparative studies are performed to validate the analytical results.

Distributed asynchronous planning and task allocation algorithm for autonomous cluster flight of fractionated spacecraft

For autonomous cluster flight of fractionated spacecraft, planning and task allocation are important as they bridge the gap between the top-level layer (interpreting inputs from the environment) and the bottom-level layer (local controllers) of the distributed space system. This paper presents an asynchronous distributed algorithm that is able to implement planning and task allocation concurrently, instead of one-by-one. First of all, the planning and task allocation problem is formulated in a generalised way. Then the core algorithm is presented, which consists of iterations between two parts. One is the construction of the list of tasks to be allocated and the assignment on-board each module. The other is the consensus process among different constructions of modules by exchanging local information between neighbours, where deconfliction rules are tailored for asynchronous situations. The former part is based on an auction algorithm, while the latter one takes advantage of a consensus algorithm. The entire process iterates asynchronously between those two parts until the planning and task allocation are agreed by all modules. In this paper simulation results are presented, which demonstrate the performance of the asynchronous algorithm not only when fractionated spacecraft operate under nominal conditions, but also when it experiences network disconnects or new tasks.

Closed-loop distance-keeping for long-term satellite cluster flight

Cluster flight is a term used for describing multiple satellites that are being held within pre-defined minimum and maximum distances for long time intervals, possibly the entire mission. This technology is required for a myriad of space architectures and missions, including disaggregated space architectures. Whereas the literature is abundant with works on control laws for satellite formation flying, there are only a handful of works on control of cluster flight. The purpose of the current work is to develop a cluster flight control algorithm, which is able to keep the satellites of the cluster within pre-specified minimum and maximum distances, while utilizing small amounts of propellant. The newly developed algorithm relies on the natural inter-satellite distance dynamics. The algorithm incorporates realistic mission constraints, such as constant-magnitude thrust, and is implemented in feedback form, steering the mean elements to judiciously selected reference values. Simulations indicate that a few tens of grams of propellent are sufficient for operating a cluster flight mission in excess of 1 year, using low specific-impulse thrusters.