Minimum-Fuel Finite-Thrust Relative Orbit Maneuvers via Indirect Heuristic Method

Fuel-optimal space trajectories in the Euler–Hill frame represent a subject of great relevance in astrodynamics, in consideration of the related applications to formation flying and proximity maneuvers involving two or more spacecraft. This research is based upon employing a Hamiltonian approach to determining minimum-fuel trajectories of specified duration. The necessary conditions for optimality (that is, the Pontryagin minimum principle and the Euler–Lagrange equations) are derived for the problem at hand. A switching function is also defined, and it determines the optimal sequence and durations of thrust and coast arcs. The analytical nature of the adjoint variables conjugate to the dynamics equations leads to establishing useful properties of these trajectories, such as the maximum number of thrust arcs in a single orbital period and a remarkable symmetry property, which holds in the presence of certain boundary conditions. Furthermore, the necessary conditions allow translating the optimal control p...

[1]  Angelo Miele.  General Variational Theory of the Flight Paths of Rocket-Powered Aircraft, Missiles and Satellite Carriers , 1959 .

[2]  Peter J. Angeline,et al.  Evolutionary Optimization Versus Particle Swarm Optimization: Philosophy and Performance Differences , 1998, Evolutionary Programming.

[3]  John E. Prussing,et al.  OPTIMAL IMPULSIVE INTERCEPT WITH LOW-THRUST RENDEZVOUS RETURN , 1993 .

[4]  Theodore N. Edelbaum,et al.  OPTIMAL SPACE TRAJECTORIES , 1969 .

[5]  E. Mooij,et al.  Performance Evaluation of Global Trajectory Optimization Methods for a Solar Polar Sail Mission , 2009 .

[6]  Derek F Lawden,et al.  Optimal trajectories for space navigation , 1964 .

[7]  B. H. Billik,et al.  Some optimal low-acceleration rendezvous maneuvers , 1964 .

[8]  Mayer Humi,et al.  Fuel-optimal rendezvous in a general central force field , 1993 .

[9]  Thomas Carter,et al.  Fuel-optimal maneuvers of a spacecraft relative to a point in circular orbit , 1984 .

[10]  George Leitmann.  Variational Problems with Bounded Control Variables , 1962 .

[11]  Slawomir J. Nasuto,et al.  Search space pruning and global optimisation of multiple gravity assist spacecraft trajectories , 2007, J. Glob. Optim..

[12]  Bruce A. Conway,et al.  Particle Swarm Optimization Applied to Space Trajectories , 2010 .

[13]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[14]  Thomas Carter,et al.  Optimal Power-Limited Rendezvous with Upper and Lower Bounds on Thrust , 1996 .

[15]  T. Carter,et al.  Fuel-Optimal Rendezvous Near a Point in General Keplerian Orbit , 1987 .

[16]  John E. Prussing,et al.  Optimal two- and three-impulse fixed-time rendezvous in the vicinityof a circular orbit , 1970 .

[17]  M. W. Weeks,et al.  Optimal Trajectories for Spacecraft Rendezvous , 2007 .

[18]  Jean Pierre Marec,et al.  Optimal Space Trajectories , 1979 .

[19]  Nguyen X. Vinh.  General theory of optimal trajectory for rocket flight in a resisting medium , 1973 .

[20]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[21]  Pradipto Ghosh,et al.  Particle Swarm Optimization of Multiple-Burn Rendezvous Trajectories , 2012 .

[22]  O. Weck,et al.  A COMPARISON OF PARTICLE SWARM OPTIMIZATION AND THE GENETIC ALGORITHM , 2005 .

[23]  Russell C. Eberhart,et al.  Comparison between Genetic Algorithms and Particle Swarm Optimization , 1998, Evolutionary Programming.

[24]  Bruce A. Conway,et al.  Spacecraft Trajectory Optimization: Swarming Theory Applied to Space Trajectory Optimization , 2010 .

[25]  David B. Spencer,et al.  Identifying Optimal Interplanetary Trajectories through a Genetic Approach , 2006 .

[26]  John E. Prussing,et al.  Optimal Two- and Three-Impulse Fixed-Time Rendezvous in the Vicinity of a Circular Orbit , 2003 .

[27]  John E. Prussing,et al.  Optimal four-impulse fixed-time rendezvous in the vicinity of a circular orbit. , 1969 .

[28]  P. Gill,et al.  User's Guide for SOL/NPSOL: A Fortran Package for Nonlinear Programming. , 1983 .

[29]  Massimiliano Vasile,et al.  On testing global optimization algorithms for space trajectory design , 2008 .

[30]  Bruce A. Conway,et al.  Optimal finite-thrust rendezvous trajectories found via particle swarm algorithm , 2012 .

[31]  Lee,et al.  [American Institute of Aeronautics and Astronautics 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference - Austin, Texas ()] 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference - Aeroelastic Studies on a Folding Wing Configuration , 2005 .

[32]  B. Conway,et al.  Particle swarm optimization applied to impulsive orbital transfers , 2012 .

[33]  Russell C. Eberhart,et al.  Recent advances in particle swarm , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).