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.