Trajectory optimization for solar sail in cislunar navigation constellation with minimal lightness number

Abstract In view of the limitations of the existing libration-point satellite navigation systems in cislunar space, this paper replaces satellites with solar sails to construct a cislunar navigation constellation and is devoted to the trajectory optimization of solar sails to minimize the lightness number control. The Artificial Lagrangian Points (ALPs) yielded by solar sail in the Sun–Earth+Moon system benefit from the advantages of numberless equilibria and out-of-plane displacement, when compared with the classical Lagrangian points. Limited to the manufacturing of sail film in practice, the candidate constellation architecture in the shape of a cube is constructed based on the optimization of the average lightness number required at ALPs. Considering the lunar gravity, the Hamiltonian-structure-preserving (HSP) controller achieved by changing the sail's attitude and lightness number is developed to stabilize the sails' trajectories near the ALPs. Moreover, an optimal quasi-periodic trajectory with minimum lightness number control is searched for through differential evolution algorithm evolving the controller gains and initial states of orbits. There are three important contributions of the trajectory optimization for a sail in the cislunar navigation constellation: firstly, the large amounts of ALPs break the restrictions on the number and plane of the five classical Lagrangian equilibrium solutions to enlarge the selection of constellations; secondly, the station keeping tool HSP controller powerfully ensures the boundedness of the ALP's trajectory; thirdly, using the optimization algorithm to generate ALP orbits effectively avoids the time consumption of differential correction, which is more convenient and general for the natural trajectory design of ALPs.

[1]  Y. K. Cheung,et al.  An Elliptic Lindstedt--Poincaré Method for Certain Strongly Non-Linear Oscillators , 1997 .

[2]  Shijie Xu,et al.  Transfer to a Multi-revolution Elliptic Halo orbit in Earth–Moon Elliptic Restricted Three-Body Problem using stable manifold , 2015 .

[3]  Henry J. Pernicka,et al.  Numerical determination of Lissajous trajectories in the restricted three-body problem , 1987 .

[4]  Camilla Colombo,et al.  Solar Radiation Pressure Hamiltonian Feedback Control for Unstable Libration-Point Orbits , 2017 .

[5]  Zhihua Qu,et al.  Distributed finite-time consensus of nonlinear systems under switching topologies , 2014, Autom..

[6]  Harald Schuh,et al.  Precise positioning with current multi-constellation Global Navigation Satellite Systems: GPS, GLONASS, Galileo and BeiDou , 2015, Scientific Reports.

[7]  Daniel J. Scheeres,et al.  Stabilizing Motion Relative to an Unstable Orbit: Applications to Spacecraft Formation Flight , 2003 .

[8]  Zhihua Qu,et al.  Distributed estimation of algebraic connectivity of directed networks , 2013, Syst. Control. Lett..

[9]  Ming Xu,et al.  Structure-Preserving Stabilization for Hamiltonian System and its Applications in Solar Sail , 2009 .

[10]  Kathleen C. Howell,et al.  Families of orbits in the vicinity of the collinear libration points , 1998 .

[11]  Chaoyong Li,et al.  Adaptive backstepping-based flight control system using integral filters , 2009 .

[12]  Shijie Xu,et al.  Low-energy transfers to a Lunar multi-revolution elliptic halo orbit , 2015 .

[13]  Lei Zhang,et al.  A Universe Light House — Candidate Architectures of the Libration Point Satellite Navigation System , 2014, Journal of Navigation.

[14]  Robert W. Farquhar,et al.  Lunar communications with libration-point satellites. , 1967 .

[15]  Jinjun Shan,et al.  A novel algorithm for generating libration point orbits about the collinear points , 2014 .

[16]  Colin R. McInnes,et al.  Periodic Orbits Above the Ecliptic in the Solar-Sail Restricted Three-Body Problem , 2007 .

[17]  J. Masdemont,et al.  QUASIHALO ORBITS ASSOCIATED WITH LIBRATION POINTS , 1998 .

[18]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[19]  J. Marsden,et al.  Dynamical Systems, the Three-Body Problem and Space Mission Design , 2009 .

[20]  D. Richardson,et al.  Analytic construction of periodic orbits about the collinear points , 1980 .

[21]  Colin R. McInnes,et al.  Impact of Optical Degradation on Solar Sail Mission Performance , 2007 .

[22]  Sanguk Lee,et al.  COMMUNICATIONS SATELLITE SYSTEM BY USING MOON ORBIT SATELLITE CONSTELLATION , 2003 .

[23]  Colin R. McInnes,et al.  Solar Sailing: Technology, Dynamics and Mission Applications , 1999 .

[24]  Abdelhamid Tayebi,et al.  Unit Quaternion-Based Output Feedback for the Attitude Tracking Problem , 2008, IEEE Transactions on Automatic Control.

[25]  Jianping Yuan,et al.  Modeling and analysis of periodic orbits around a contact binary asteroid , 2015 .

[26]  Olvi L. Mangasarian,et al.  Exact penalty functions in nonlinear programming , 1979, Math. Program..

[27]  Russell C. Eberhart,et al.  Solving Constrained Nonlinear Optimization Problems with Particle Swarm Optimization , 2002 .

[28]  Ming Xu,et al.  A New Constellation Configuration Scheme for Communicating Architecture in Cislunar Space , 2013 .