An optimal deployment strategy for multi-plane satellite constellation using a generalized non-planar maneuver

Abstract

Satellite constellation deployment is a cohesive mission where the trajectories of satellites must be planned concurrently. This paper presents an Integrated Program for Optimal Deployment of a Satellite Constellation (PODSC) consisting of \(m\) non-identical satellites in any desired arrangement in \(n\) orbital planes. The PODSC can optimize the scheduling of mission timelines, ensuring effective coordination with the trajectory of each satellite. This involves meticulous planning that considers temporal constraints and regards collision avoidance constraint. Additionally, the PODSC can select the most favorable deployment strategy, considering the trade-offs between time and fuel consumption across all possible deployment methods. The PODSC also utilizes an innovative Perturbed Multi-impulsive Inclined transfer trajectory Amalgamated with a modified Lambert targeting problem (PMIAL). The main idea of designing the mentioned maneuver is to eliminate the defects of the Lambert Targeting Problem (LTP). The LTP cannot account for space perturbations. Moreover, the LTP faces challenges when attempting to align the transfer trajectory tangentially with the final orbit in situations where there exists a substantial disparity in inclination and right ascension between the initial and final orbits. The PMIAL establishes three consecutive steps to fix the mentioned defects. Balancing the trade-off between time and achieving optimal fuel consumption will be possible by applying a hybrid IWO/PSO (The hybrid Invasive Weed Optimization/Particle Swarm Optimization) optimization algorithm in both PMIAL and PODSC. The case study will involve simulating two constellation deployment missions, with a particular focus on considering the Earth’s oblateness as a notable perturbation; however, the proposed algorithms can consider any space perturbations.