In this paper, leader-follower formation and reconfiguration problems based on the periodic orbits of the nonlinear relative dynamics along a circular orbit are considered. First, initial conditions of coplanar and noncoplanar relative orbits are characterized by the initial true anomaly, mean motion, semimajor axis, eccentricity, and inclination angle of the follower's inertial orbit. Based on the property of null controllability with vanishing energy of the Hill-Clohessy-Wiltshire equations, L1 suboptimal feedback controllers are designed via the linear quadratic regulator theory. Simulation results for three examples are given. A comparison with the reconfiguration problem based on the periodic orbits of the Hill-Clohessy-Wiltshire equations shows that replacement by nonlinear periodic orbits does not increase the L 1-norm of the feedback control.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Electrical and Electronic Engineering
- Applied Mathematics