Quadratic-Based Computation of Four-Impulse Optimal Rendezvous near Circular Orbit

Thewell-knownproblemofminimizingthetotalcharacteristicvelocityofaspacecraftinanimpulsiverendezvous with a satellite in circular orbit is considered by using the Clohessy ‐Wiltshire equations. It is well known that, for boundary conditions in the plane of the orbit, four impulses at most are required. The mathematical framework is presented for four-impulse optimal rendezvous near a circular orbit resulting in relatively simple formulas that determine if four impulses are required and, if so, how the four optimal velocity increments can be calculated.

[1]  T. N. Edelbaum.  A general solution for minimum impulse transfers in the near vicinity of a circular orbit , 1967 .

[2]  J. Potter,et al.  Optimization of Midcourse Velocity Corrections , 1965 .

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

[4]  D. Jezewski,et al.  Primer vector theory applied to the linear relative-motion equations. [for N-impulse space trajectory optimization , 1980 .

[5]  John M. Eggleston,et al.  Optimum Time to Rendezvous , 1960 .

[6]  Jean Albert Kechichian,et al.  Techniques of accurate analytic terminal rendezvous in near-circular orbit , 1992 .

[7]  A primer on the primer , 1968 .

[8]  T. Carter.  State Transition Matrices for Terminal Rendezvous Studies: Brief Survey and New Example , 1998 .

[9]  J. M. Neff,et al.  Minimum-fuel rescue trajectories for the Extravehicular Excursion Unit , 1991 .

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

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

[12]  C. McInnes,et al.  Autonomous rendezvous using artificial potential function guidance , 1995 .

[13]  L. Neustadt.  Optimization, a Moment Problem, and Nonlinear Programming , 1964 .

[14]  F. T. Geyling,et al.  Satellite perturbations from extra-terrestrial gravitation and radiation pressure , 1960 .

[15]  Thomas Carter,et al.  Linearized impulsive rendezvous problem , 1995 .

[16]  M. Handelsman,et al.  Primer Vector on Fixed-Time Impulsive Trajectories , 1967 .

[17]  J. B. Jones.  Optimal rendezvous in the neighborhood of a circular orbit , 1976 .

[18]  Thomas Carter,et al.  Optimal impulsive space trajectories based on linear equations , 1991 .

[19]  John E. Prussing,et al.  Optimal Multiple-Impulse Satellite Evasive Maneuvers , 1994 .

[20]  D. Jezewski,et al.  An analytic approach to optimal rendezvous using Clohessy-Wiltshire equations , 1979 .