Multi-impulse Shape-based Trajectory Optimization for Target Chasing in On-orbit Servicing Missions

On-orbit servicing is a range of orbital services that comprises visual inspection, refueling, repairing, upgrading, assembly, and debris removal. It intends to increase the satellites' lifetime and enhance their performance. This paper proposes a methodology for designing smooth trajectories for long-range rendezvous of servicing satellites with moving targets, in on-orbit servicing missions. The methodology employs a multi-impulse shape-based trajectory planning algorithm for in-plane orbit transfer, based on the two-body problem. A multiobjective constrained optimization architecture is developed using a genetic algorithm to determine the optimal trajectories in the sense of Pareto optimality. Transfer time and control effort are considered as Pareto cost functions. Arriving at an orbiting target upon completion of the transfer and limitations in orbital elements are included as constraints. The latter constraint will help reduce the risk of collision in populated orbits by not entering those orbits, but maybe crossing them. The design variables are the orbital elements of the intermediate orbits, and the number and location of impulses. The location of the first impulse in the parking orbit indicates the waiting time before the commencement of orbit transfer that can impact the optimal solution when chasing a dynamic target. Compared to trajectory design methods using continuous thrust, the proposed technique has fewer design variables. The set of Pareto frontier solutions provides an on-orbit servicing mission with decision-making capabilities to choose a solution compatible with the priority requirements of the mission. The proposed methodology is specifically valid for the low Earth orbital regime (100-2000 Km altitude), where the gravitational field of the Earth dominates disturbances such as solar pressure, and the gravity of other celestial objects. To remain in this regime, constraints on intermediate orbits are imposed to ensure the altitude at apoapsides do not exceed 2000 km and at periapsides remains above 100 km. The performance of the resulting methodology is then compared with that of an optimal Lambert approach, in different case studies.