Multi-impulse smooth trajectory design for long-range rendezvous with an orbiting target using multi-objective non-dominated sorting genetic algorithm

Abstract

This paper develops a methodology to generate Pareto optimal trajectories for long-range rendezvous of a servicing satellite with a moving target, in an on-orbit servicing mission. The methodology employs a multi-impulse shape-based trajectory planning algorithm for in-plane orbit transfer, based on the two-body problem. We first derive the necessary and sufficient conditions that determine the set of smooth impulsive trajectories connecting the servicing satellite to the orbiting target. The Pareto optimal trajectories from this set are then obtained using a constrained multi-objective optimization algorithm developed based on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). In a mission, an optimal solution from the Pareto frontier set may be selected based on the mission requirements. Transfer time and control effort are the two Pareto cost functions that are considered in the multi-objective optimization. To reduce the risk of collision in populated orbits and to remain in an orbital regime, we include restrictions on orbital elements as part of the constraints. Further, a maximum available impulse is considered as an upper-bound for velocity changes in an impulsive trajectory. The number of impulses along with the location of the first impulse in the parking orbit and the orbital parameters of the intermediate orbits form the set of design variables. The key advantage of the proposed trajectory optimization methodology compared to its counterparts using continuous thrust is the significant reduction of the number of design variables. Finally, we demonstrate the superiority of the developed trajectory planner by comparing its results with those obtained from another multi-objective evolutionary algorithm called the Multi-Objective Genetic Algorithm and an optimal Lambert approach based on single-objective optimization.