Fuel-Optimal Control for Multiple Spacecraft Formation Flying With Relative Motion Constraints

In this paper, the fuel-optimal control problem of multiple spacecraft formation flying with relative motion constaints is addressed via the indirect optimization method. As opposed to the most existing works where the formation deployment/reconfiguration problem is formulated on the chief-deputy topology or the total fuel consumption is optimized in the
$\ell _{2}$
-norm sense, the presented methodology manages to identify the
$\ell _{1}$
-optimal control law for a distributed formation structure, in which each spacecraft satisfies the periodicity (or energy-matching) condition and relative geometry requirement. In particular, the homotopic approach in conjunction with a linearization method is adopted so as to reduce the inherent sensitivity of the two-point boundary-value problem, and the fuel-optimal solution can be successfully targeted. The results are validated in Laser Interferometer Space Antenna, a project initiated for gravitational wave detection.