Optimal Multi-Impulse Orbit Transfer Using Nonlinear Relative Motion Dynamics

Abstract

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.

Simultaneous dynamic optimization: A trajectory planning method for nonholonomic car-like robots

“…Trajectory planning has become a critical aspect of automation science; the applications of this process range from satellite orbit transfer [2], missile guidance [3], unmanned aerial vehicle navigation [4][5][6], anti-submarine search [7,8], hazardous environment exploration [9] and autonomous parking assistance [10,11]. In this work, we focus on the trajectory planning of car-like robots.…”

How Many Impulses Redux

“…For the most part, preliminary mission design methods rely on lowfidelity dynamical models, which in turn, frequently leads to analytical propagation of the state dynamics through Keplerian orbit models [20] or by utilizing the solution of Lambert's problem [21][22][23][24][25]. Impulsive maneuvers are also used extensively for formation flight optimal control problems [26][27][28][29][30][31][32][33][34][35][36] and orbit reachability analyses problems [37][38][39][40][41][42][43].…”