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Shape control of spacecraft formation using a virtual spring-damper mesh
Institution:1. School of Aeronautics and Astronautics, Central South University, Changsha 410083, China;2. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
Abstract:This paper derives a distance-based formation control method to maintain the desired formation shape for spacecraft in a gravitational potential field. The method is an analogy of a vir-tual spring-damper mesh. Spacecraft are connected virtually by spring-damper pairs. Convergence analysis is performed using the energy method. Approximate expressions for the distance errors and control accelerations at steady state are derived by using algebraic graph representations and results of graph rigidity. Analytical results indicate that if the underlying graph of the mesh is rigid, the convergence to a static shape is assured, and higher formation control precision can be achieved by increasing the elastic coefficient without increasing the control accelerations. A numerical exam-ple of spacecraft formation in low Earth orbit confirms the theoretical analysis and shows that the desired formation shape can be well achieved using the presented method, whereas the orientation of the formation can be kept pointing to the center of the Earth by the gravity gradient. The method is decentralized, and uses only relative measurement information. Constructing a distributed virtual structure in space can be the general application area. The proposed method can serve as an active shape control law for the spacecraft formations using propellantless internal forces.
Keywords:Formation shape control  Graph rigidity  Internal forces  PD control  Spacecraft formation flying  Spacecraft guidance and control  Spring-damper mesh
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