Abstract To reduce the optimal but large Δ v of the fixed-short-time two impulse Lambert rendezvous between two spacecrafts along two coplanar circular orbits, the three-impulse Lambert rendezvous optimized via the optimization algorithm-interval analysis (IA) is proposed in this paper. The purpose of optimization is to minimize the velocity increment of the fixed-short-time three-impulse Lambert rendezvous. The optimization algorithm IA is given for solving the rendezvous optimization problem with multiple uncertain variables, and strong nonlinearity and nonconvexity. Numerical examples of the time-open, coplanar-circular-orbit, multiple-revolution Lambert rendezvous with a parking time optimized via the optimization algorithm IA are firstly undertaken to validate the feasibility of the optimization algorithm IA by comparing the optimization results with those of the globally optimal Hohmann transfer. The results indicate that the globally optimal parameters of the time-open coplanar-circular-orbit multiple-revolution Lambert rendezvous can be obtained by the optimization algorithm IA, and the initial separation angle of two spacecrafts with different orbit radius can be adjusted to obtain the globally optimal and small Δ v by distributing an optimal parking time. After that, for the fixed-short-time two-impulse Lambert rendezvous problem without sufficient time to adjust the separation angle by distributing a parking time like the open-time Lambert rendezvous problem, three-impulse Lambert rendezvous involving multiple optimization variables is given and the variables are optimized by the optimization algorithm IA to obtain an optimal and small Δ v . Numerical simulation indicates that the optimal and small Δ v of the fixed short time, three-impulse Lambert rendezvous can be obtained using the optimization algorithm IA.
[1]
J. Palmore.
An Elementary Proof Of the Optimality of Hohmann Transfers
,
1984
.
[2]
Thomas J. Fill,et al.
Extension of Gauss' method for the solution of Kepler's equation
,
1979
.
[3]
Daniele Mortari,et al.
Constrained Multiple-Revolution Lambert's Problem
,
2010
.
[4]
Richard H. Battin,et al.
An elegant Lambert algorithm
,
1983
.
[5]
Giulio Avanzini,et al.
A Simple Lambert Algorithm
,
2008
.
[6]
Yasuo Fujii,et al.
An interval arithmetic method for global optimization
,
1979,
Computing.
[7]
Steven P. Burns,et al.
Lambert Guidance Routine Designed to Match Position and Velocity of Ballistic Target
,
2004
.
[8]
E. van Kampen,et al.
Optimization of Time-Open Constrained Lambert Rendezvous Using Interval Analysis
,
2013
.
[9]
Guo-Jin Tang,et al.
Optimization of multiple-impulse, multiple-revolution, rendezvous-phasing maneuvers
,
2007
.
[10]
L. Rider.
Characteristic Velocity Requirements for Impulsive Thrust Transfers Between Non Co-Planar Circular Orbits
,
1961
.
[11]
Eldon Hansen,et al.
Global optimization using interval analysis
,
1992,
Pure and applied mathematics.
[12]
Jian Li,et al.
Multiple-Revolution Solutions of the Transverse-Eccentricity-Based Lambert Problem
,
2010
.
[13]
R. Baker Kearfott,et al.
Introduction to Interval Analysis
,
2009
.
[14]
John E. Prussing,et al.
Optimal multiple-impulse time-fixed rendezvous between circular orbits
,
1984
.
[15]
Panagiotis Tsiotras,et al.
Optimal Two-Impulse Rendezvous Using Multiple-Revolution Lambert Solutions
,
2003
.
[16]
G. Hargreaves.
Interval Analysis in Matlab
,
2002
.
[17]
R. C. Blanchard,et al.
A note on Lambert's theorem.
,
1966
.