Distributed Spacecraft Path Planning and Collision Avoidance via Reciprocal Velocity Obstacle Approach

This paper presents the development of a combined linear quadratic regulation and reciprocal velocity obstacle (LQR/RVO) control algorithm for multiple satellites during close proximity operations. The linear quadratic regulator (LQR) control effort drives the spacecraft towards their target position while the reciprocal velocity obstacle (RVO) provides collision avoidance capabilities. Each spacecraft maneuvers independently, without explicit communication or knowledge in term of collision avoidance decision making of the other spacecraft in the formation. To assess the performance of this novel controller different test cases are implemented. Numerical results show that this method guarantees safe and collision-free maneuvers for all the satellites in the formation and the control performance is presented in term of Δv and fuel consumption

Optimal Reconfiguration of Formation Flying Spacecraft--a Decentralized Approach

This paper introduces a hierarchical, decentralized, and parallelizable method for dealing with optimization problems with many agents. It is theoretically based on a hierarchical optimization theorem that establishes the equivalence of two forms of the problem, and this idea is implemented using DMOC (Discrete Mechanics and Optimal Control). The result is a method that is scalable to certain optimization problems for large numbers of agents, whereas the usual “monolithic” approach can only deal with systems with a rather small number of degrees of freedom. The method is illustrated with the example of deployment of spacecraft, motivated by the Darwin (ESA) and Terrestrial Planet Finder (NASA) missions

Decentralized Formation Flying Control in a Multiple-Team Hierarchy

This paper presents the prototype of a system that addresses these objectives-a decentralized guidance and control system that is distributed across spacecraft using a multiple-team framework. The objective is to divide large clusters into teams of manageable size, so that the communication and computational demands driven by N decentralized units are related to the number of satellites in a team rather than the entire cluster. The system is designed to provide a high-level of autonomy, to support clusters with large numbers of satellites, to enable the number of spacecraft in the cluster to change post-launch, and to provide for on-orbit software modification. The distributed guidance and control system will be implemented in an object-oriented style using MANTA (Messaging Architecture for Networking and Threaded Applications). In this architecture, tasks may be remotely added, removed or replaced post-launch to increase mission flexibility and robustness. This built-in adaptability will allow software modifications to be made on-orbit in a robust manner. The prototype system, which is implemented in MATLAB, emulates the object-oriented and message-passing features of the MANTA software. In this paper, the multiple-team organization of the cluster is described, and the modular software architecture is presented. The relative dynamics in eccentric reference orbits is reviewed, and families of periodic, relative trajectories are identified, expressed as sets of static geometric parameters. The guidance law design is presented, and an example reconfiguration scenario is used to illustrate the distributed process of assigning geometric goals to the cluster. Next, a decentralized maneuver planning approach is presented that utilizes linear-programming methods to enact reconfiguration and coarse formation keeping maneuvers. Finally, a method for performing online collision avoidance is discussed, and an example is provided to gauge its performance

Manoeuvre Planning Architecture for the Optimisation of Spacecraft Formation Flying Reconfiguration Manoeuvres

Formation flying of multiple spacecraft collaborating toward the same goal is fast becoming a reality for space mission designers. Often the missions require the spacecraft to perform translational manoeuvres relative to each other to achieve some mission objective. These manoeuvres need to be planned to ensure the safety of the spacecraft in the formation and to optimise fuel management throughout the fleet. In addition to these requirements is it desirable for this manoeuvre planning to occur autonomously within the fleet to reduce operations cost and provide greater planning flexibility for the mission. One such mission that would benefit from this type of manoeuvre planning is the European Space Agency’s DARWIN mission, designed to search for extra-solar Earth-like planets using separated spacecraft interferometry. This thesis presents a Manoeuvre Planning Architecture for the DARWIN mission. The design of the Architecture involves identifying and conceptualising all factors affecting the execution of formation flying manoeuvres at the Sun/Earth libration point L2. A systematic trade-off analysis of these factors is performed and results in a modularised Manoeuvre Planning Architecture for the optimisation of formation flying reconfiguration manoeuvres. The Architecture provides a means for DARWIN to autonomously plan manoeuvres during the reconfiguration mode of the mission. The Architecture consists of a Science Operations Module, a Position Assignment Module, a Trajectory Design Module and a Station-keeping Module that represents a multiple multi-variable optimisation approach to the formation flying manoeuvre planning problem. The manoeuvres are planned to incorporate target selection for maximum science returns, collision avoidance, thruster plume avoidance, manoeuvre duration minimisation and manoeuvre fuel management (including fuel consumption minimisation and formation fuel balancing). With many customisable variables the Architecture can be tuned to give the best performance throughout the mission duration. The implementation of the Architecture highlights the importance of planning formation flying reconfiguration manoeuvres. When compared with a benchmark manoeuvre planning strategy the Architecture demonstrates a performance increase of 27% for manoeuvre scheduling and fuel savings of 40% over a fifty target observation tour. The Architecture designed in this thesis contributes to the field of spacecraft formation flying analysis on various levels. First, the manoeuvre planning is designed at the mission level with considerations for mission operations and station-keeping included in the design. Secondly, the requirements analysis and implementation of Science Operation Module represent a unique insight into the complexity of observation scheduling for exo-planet analysis missions and presents a robust method for autonomously optimising that scheduling. Thirdly, in-depth analyses are performed on DARWIN-based modifications of existing manoeuvre optimisation strategies identifying their strengths and weaknesses and ways to improve them. Finally, though not implemented in this thesis, the design of a Station-keeping Module is provided to add station-keeping optimisation functionality to the Architecture

Optimal Finite Thrust Guidance Methods for Constrained Satellite Proximity Operations Inspection Maneuvers

Algorithms are developed to find optimal guidance for an inspector satellite operating nearby a resident space object (RSO). For a non-maneuvering RSO, methods are first developed for a satellite subject to maximum slew rates to conduct an initial inspection of an RSO, where the control variables include the throttle level and direction of the thrust. Second, methods are developed to optimally maneuver a satellite with on/off thrusters into a natural motion circumnavigation or teardrop trajectory, subject to lighting and collision constraints. It is shown that for on/off thrusters, a control sequence can be parameterized to a relatively small amount of control variables and the relative states can be analytically propagated as a function of those control variables. For a maneuvering RSO, differential games are formulated and solved for an inspector satellite to achieve multiple inspection goals, such as aligning with the Sun vector or matching the RSO\u27s energy. The developed algorithms lead to fuel and time savings which can increase the mission life and capabilities of inspector satellites and thus improve space situational awareness for the U.S. Air Force

Two-Stage Path Planning Approach for Designing Multiple Spacecraft Reconfiguration Maneuvers

The paper presents a two-stage approach for designing optimal reconfiguration maneuvers for multiple spacecraft. These maneuvers involve well-coordinated and highly-coupled motions of the entire fleet of spacecraft while satisfying an arbitrary number of constraints. This problem is particularly difficult because of the nonlinearity of the attitude dynamics, the non-convexity of some of the constraints, and the coupling between the positions and attitudes of all spacecraft. As a result, the trajectory design must be solved as a single 6N DOF problem instead of N separate 6 DOF problems. The first stage of the solution approach quickly provides a feasible initial solution by solving a simplified version without differential constraints using a bi-directional Rapidly-exploring Random Tree (RRT) planner. A transition algorithm then augments this guess with feasible dynamics that are propagated from the beginning to the end of the trajectory. The resulting output is a feasible initial guess to the complete optimal control problem that is discretized in the second stage using a Gauss pseudospectral method (GPM) and solved using an off-the-shelf nonlinear solver. This paper also places emphasis on the importance of the initialization step in pseudospectral methods in order to decrease their computation times and enable the solution of a more complex class of problems. Several examples are presented and discussed

Autonomous distributed LQR/APF control algorithms for CubeSat swarms manoeuvring in eccentric orbits

Spacecraft formation flying has shown to be promising approach to enhance mission capabilities. Nevertheless, formation flying presents several control challenges which escalate as the numbers of elements in the formation is increased. The objective of this paper is to develop decentralised control algorithms to regulate the station-keeping, reconfiguration and collision avoidance of spacecraft in formation around eccentric reference orbits using the combination of a Linear Quadratic Regulator (LQR) and an Artificial Potential Function (APF). Within this control scheme, the LQR will provide station-keeping and reconfiguration capabilities toward desired positions, while optimizing fuel consumption and the APF will ensure collision free manoeuvres between the elements of the formation during manoeuvres. The controller is designed under the assumption of continuous thrust as a standard LQR problem using the Pontryagin minimum principle, an APF based in normalized Gaussian functions and the Tschauner and Hempel (TH) equations as the relative dynamics model

Decentralized Model Predictive Control of Swarms of Spacecraft Using Sequential Convex Programming

This paper presents a decentralized, model predictive control algorithm for the reconfiguration of swarms of spacecraft composed of hundreds to thousands of agents with limited capabilities. In our prior work, sequential convex programming has been used to determine collision-free, fuel-efficient trajectories for the reconfiguration of spacecraft swarms. This paper uses a model predictive control approach to implement the sequential convex programming algorithm in real-time. By updating the optimal trajectories during the reconfiguration, the model predictive control algorithm results in decentralized computations and communication between neighboring spacecraft only. Additionally, model predictive control reduces the horizon of the convex optimizations, which reduces the run time of the algorithm