Space swarms,enabled by the miniaturization of spacecraft,have the potential capability to lower costs,increase efficiencies,and broaden the horizons of space missions.The formation control problem of large-scale spac...Space swarms,enabled by the miniaturization of spacecraft,have the potential capability to lower costs,increase efficiencies,and broaden the horizons of space missions.The formation control problem of large-scale spacecraft swarms flying around an elliptic orbit is considered.The objective is to drive the entire formation to produce a specified spatial pattern.The relative motion between agents becomes complicated as the number of agents increases.Hence,a density-based method is adopted,which concerns the density evolution of the entire swarm instead of the trajectories of individuals.The density-based method manipulates the density evolution with Partial Differential Equations(PDEs).This density-based control in this work has two aspects,global pattern control of the whole swarm and local collision-avoidance between nearby agents.The global behavior of the swarm is driven via designing velocity fields.For each spacecraft,the Q-guidance steering law is adopted to track the desired velocity with accelerations in a distributed manner.However,the final stable velocity field is required to be zero in the classical density-based approach,which appears as an obstacle from the viewpoint of astrodynamics since the periodic relative motion is always time-varying.To solve this issue,a novel transformation is constructed based on the periodic solutions of Tschauner-Hempel(TH)equations.The relative motion in Cartesian coordinates is then transformed into a new coordinate system,which permits zero-velocity in a stable configuration.The local behavior of the swarm,such as achieving collision avoidance,is achieved via a carefully-designed local density estimation algorithm.Numerical simulations are provided to demonstrate the performance of this approach.展开更多
Partial differential equation-based(PDE-based) surface design generates surfaces from PDEs with given boundary conditions. In this paper, design of triangular Bézier surfaces satisfying triharmonic equations is p...Partial differential equation-based(PDE-based) surface design generates surfaces from PDEs with given boundary conditions. In this paper, design of triangular Bézier surfaces satisfying triharmonic equations is presented. We propose three sets of boundary control points for triharmonic triangular Bézier surfaces design by solving the systems of the linear equations with unique solutions. Moreover, we compare these three methods by some representative examples.展开更多
基金co-supported by the Strategic Priority Program on Space Science of the Chinese Academy of Sciences (No.XDA15014902)the Key Research Program of the Chinese Academy of Sciences (No. ZDRW-KT-2019-1-0102)
文摘Space swarms,enabled by the miniaturization of spacecraft,have the potential capability to lower costs,increase efficiencies,and broaden the horizons of space missions.The formation control problem of large-scale spacecraft swarms flying around an elliptic orbit is considered.The objective is to drive the entire formation to produce a specified spatial pattern.The relative motion between agents becomes complicated as the number of agents increases.Hence,a density-based method is adopted,which concerns the density evolution of the entire swarm instead of the trajectories of individuals.The density-based method manipulates the density evolution with Partial Differential Equations(PDEs).This density-based control in this work has two aspects,global pattern control of the whole swarm and local collision-avoidance between nearby agents.The global behavior of the swarm is driven via designing velocity fields.For each spacecraft,the Q-guidance steering law is adopted to track the desired velocity with accelerations in a distributed manner.However,the final stable velocity field is required to be zero in the classical density-based approach,which appears as an obstacle from the viewpoint of astrodynamics since the periodic relative motion is always time-varying.To solve this issue,a novel transformation is constructed based on the periodic solutions of Tschauner-Hempel(TH)equations.The relative motion in Cartesian coordinates is then transformed into a new coordinate system,which permits zero-velocity in a stable configuration.The local behavior of the swarm,such as achieving collision avoidance,is achieved via a carefully-designed local density estimation algorithm.Numerical simulations are provided to demonstrate the performance of this approach.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12071057,11671068).
文摘Partial differential equation-based(PDE-based) surface design generates surfaces from PDEs with given boundary conditions. In this paper, design of triangular Bézier surfaces satisfying triharmonic equations is presented. We propose three sets of boundary control points for triharmonic triangular Bézier surfaces design by solving the systems of the linear equations with unique solutions. Moreover, we compare these three methods by some representative examples.
