This paper presents a decentralized, model predictive control algorithm for the optimal guidance and reconfiguration of swarms of spacecraft composed of hundreds to thousands of agents with limited capabilities. In previous work, J 2-invariant orbits have been found to provide collision-free motion for hundreds of orbits in a low Earth orbit. This paper develops real-time optimal control algorithms for the swarm reconfiguration that involve transferring from one J 2-invariant orbit to another while avoiding collisions and minimizing fuel. The proposed model predictive control-sequential convex programming algorithm uses sequential convex programming to solve a series of approximate path planning problems until the solution converges. 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. Multiple time steps, time-varying collision constraints, and communication requirements are developed to guarantee stability, feasibility, and robustness of the model predictive control-sequential convex programming algorithm.
This paper presents a distributed, guidance and control algorithm for reconfiguring swarms composed of hundreds to thousands of agents with limited communication and computation capabilities. This algorithm solves both the optimal assignment and collision-free trajectory generation for robotic swarms, in an integrated manner, when given the desired shape of the swarm (without pre-assigned terminal positions). The optimal assignment problem is solved using a distributed auction assignment that can vary the number of target positions in the assignment, and the collision-free trajectories are generated using sequential convex programming. Finally, model predictive control is used to solve the assignment and trajectory generation in real time using a receding horizon. The model predictive control formulation uses current state measurements to resolve for the optimal assignment and trajectory. The implementation of the distributed auction algorithm and sequential convex programming using model predictive control produces the Swarm Assignment and Trajectory Optimization (SATO) algorithm that transfers a swarm of robots or vehicles to a desired shape in a distributed fashion. Once the desired shape is uploaded to the swarm, the algorithm determines where each robot goes and how it should get there in a fuel-efficient, collision-free manner. Results of flight experiments using multiple quadcopters show the effectiveness of the proposed SATO algorithm.
This paper presents several new open-loop guidance methods for spacecraft swarms composed of hundreds to thousands of agents with each spacecraft having modest capabilities. These methods have three main goals: preventing relative drift of the swarm, preventing collisions within the swarm, and minimizing the propellant used throughout the mission. The development of these methods progresses by eliminating drift using the Hill-Clohessy-Wiltshire equations, removing drift due to nonlinearity, and minimizing the J2 drift. In order to verify these guidance methods, a new dynamic model for the relative motion of spacecraft is developed. These dynamics include the two main disturbances for spacecraft in Low Earth Orbit (LEO), J2 and atmospheric drag. Using this dynamic model, numerical simulations are provided at each step to show the effectiveness of each method and to see where improvements can be made. The main result is a set of initial conditions for each spacecraft in the swarm which provides the trajectories for hundreds of collision-free orbits in the presence of J2. Finally, a multi-burn strategy is developed in order to provide hundreds of collision-free orbits under the influence of atmospheric drag. This last method works by enforcing the initial conditions multiple times throughout the mission thereby providing collision-free trajectories for the duration of the mission.
This paper presents partially decentralized path planning algorithms for swarms of spacecraft composed of hundreds to thousands of agents with each spacecraft having limited computational capabilities. In our prior work, J2-invariant orbits have been found to provide collision free motion for hundreds of orbits. This paper develops algorithms for the swarm reconfiguration which involves transferring from one J2-invariant orbit to another avoiding collisions and minimizing fuel. To perform collision avoidance, it is assumed that the spacecraft can communicate their trajectories with each other. The algorithm uses sequential convex programming to solve a series of approximate path planning problems until the solution converges. Two decentralized methods are developed: a serial method where the spacecraft take turn updating their trajectories and a parallel method where all of the spacecraft update their trajectories simultaneously. Nomenclature Iset of spacecraft that are to be avoided J 2 second harmonic coefficient of earth K set of spacecraft that have not converged L size of trust region for convex optimization M final iteration of sequential convex programming N number of spacecraft R minimum distance between spacecraft to avoid a collision R e radius of the earth R safe secondary collision radius, 1.5R
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