Abstract
This paper investigates the use of evolutionary algorithms for the optimization of time-constrained impulsive multirendezvous missions. The aim is to find the minimum- Δ V trajectory that allows a chaser spacecraft to perform, in a prescribed mission time, a complete tour of a set of targets, such as space debris or artificial satellites, which move on the same orbital plane at slightly different altitudes. For this purpose, a two-level design approach is pursued. First, an outer-level combinatorial problem is defined, dealing with the simultaneous optimization of the sequence of targets and the rendezvous epochs. The suggested approach is first tested by assuming that all transfer legs last exactly the same amount of time; then, the time domain is discretized over a finer grid, allowing a more appropriate sizing of the time window allocated for each leg. The outer-level problem is solved by an in-house genetic algorithm, which features an effective permutation-preserving solution encoding. A simple, but fairly accurate, heuristic, based on a suboptimal four-impulse analytic solution of the single-target rendezvous problem, is used when solving the combinatorial problem for a fast guess at the transfer cost, given the departure and arrival epochs. The outer-level problem solution is used to define an inner-level NLP problem, concerning the optimization of each body-to-body transfer leg. In this phase, the encounter times are further refined. The inner-level problem is tackled through an in-house multipopulation self-adaptive differential evolution algorithm. Numerical results for case studies including up to 20 targets with different time grids are presented.
Highlights
A multirendezvous (MRR) trajectory concerns the motion of an active spacecraft, the chaser, which executes a sequence of maneuvers to rendezvous with multiple passive targets, such as space debris or artificial satellites in Earth’s orbit
This paper investigates the use of evolutionary algorithms for the optimization of time-constrained impulsive multirendezvous missions
In addition to the population size nP and the maximum number of generations nG that are common to all population-based metaheuristics, typical Genetic Algorithms (GA) hyperparameters are the crossover probability pc, which represents the probability that the parents are replaced by the generated offspring at the end of the crossover phase; the mutation probability pm, which is the probability that a individual undergoes a random mutation during the mutation phase; and other operator-specific parameters, such as the depth of the reverse mutation operator
Summary
A multirendezvous (MRR) trajectory concerns the motion of an active spacecraft, the chaser, which executes a sequence of maneuvers to rendezvous with multiple passive targets, such as space debris or artificial satellites in Earth’s orbit. While similar, the problem here investigated is more complex than a standard TSP, as the cost associated with traveling between any two targets changes with time due to the orbital dynamics With this analogy in mind, several attempts have been made to find the optimal solution of the MRR problem by using algorithms developed in the context of operational research. Other metaheuristic methods consist of the iterative refinement of a set of (possibly random) initial solutions and guarantee the tour completeness at any point in the optimization process For this reason, they are suited to plan MRR missions aimed at visiting all the targets of the chosen set. Different ADR missions are considered, including up to 20 targets in close coplanar and circular orbits
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