Optimal Multi-Impulse Orbit Transfer Using Nonlinear Relative Motion Dynamics

Trajectory planning for satellite formation flying missions requires the ability to find the optimal control law to transfer a satellite from one periodic relative orbit to another. This article modifies Jezewski’s linear impulsive trajectory optimization method for solving nonlinear problems described in the relative coordinate frame, and proposes the concept of standard problems for the initialization of the optimizer. With this modified optimizer and the standard problem concept, the article studies the impulse number, the cost, and the nonlinearity of fixed-time coplanar transfer problems.

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

[2]  Bruce A. Conway,et al.  Spacecraft Trajectory Optimization: Contents , 2010 .

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

[4]  Jonathan P. How,et al.  Spacecraft Formation Flying: Dynamics, Control and Navigation , 2009 .

[5]  Sang-Young Park,et al.  Hybrid optimization for multiple-impulse reconfiguration trajectories of satellite formation flying , 2009 .

[6]  B. Conway.  Spacecraft Trajectory Optimization , 2014 .

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

[8]  K. C. Howell,et al.  Transfers between libration-point orbits in the elliptic restricted problem , 1994 .

[9]  S. Vadali,et al.  Formation Establishment and Reconfiguration Using Impulsive Control , 2005 .

[10]  Sergio A. Alvarez,et al.  Quadratic-Based Computation of Four-Impulse Optimal Rendezvous near Circular Orbit , 2000 .

[11]  L.M. Mailhe,et al.  Initialization and resizing of formation flying using global and local optimization methods , 2004, 2004 IEEE Aerospace Conference Proceedings (IEEE Cat. No.04TH8720).

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

[13]  William E. Wiesel.  Optimal impulsive control of relative satellite motion , 2003 .

[14]  H. Schaub,et al.  Impulsive Feedback Control to Establish Specific Mean Orbit Elements of Spacecraft Formations , 2001 .

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

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