Constellation Phasing of Spacecraft in Near-Circular, In-Plane Orbits using Low-Thrust Trajectory Optimization

We present a trajectory optimization problem to be used in the planning of orbital maneuvers for spacecraft operating in a constellation. The 3-DOF orbital motion of each spacecraft, governed by central body gravity and low-thrust propulsion, is expressed in a planet-centered inertial frame with Cartesian state vectors. Path constraints on each spacecraft include bounds on altitude, thrust magnitude, and propellant consumption. Terminal constraints enforce all spacecraft to achieve near-circular motion in the same orbital plane with desired altitude and in-plane angular spacing between spacecraft. The numerical example in this paper considers a cluster of spacecraft deployed into the same parking orbit by a launch vehicle. We apply our problem formulation to perform simultaneous orbit phasing and station-keeping of the spacecraft in minimum-time. The problem is approached using sequential convex programming (SCP) with a First-Order Hold interpolation, multiple-shooting based discretization scheme. The solution is applied in a nonlinear simulation to verify satisfaction of constraints.