Multiple-burn trajectory optimization and guidance design for In-Orbit-Service missions

In-Orbit-Service (IOS) has moved from visionary proposal to operational necessity for keeping orbits safe, sustainable and affordable. In fact, repairing, refuelling, upgrading or de-orbiting aging satellites lowers replacement costs and reduces collision risk. The lowering of launch prices has sharpened commercial interest; indeed, market studies foresee a multi-billion-dollar commercial sector expanding at a high growth rate over the coming decade. For these reasons, this thesis work aims to plan and validate impulsive rendezvous manoeuvres through a modular MATLAB tool for IOS that combines an optimization process based on an evolutionary algorithm (EA) with a 3-DOF orbital simulator. The aim of the optimization process is to minimize propellant consumption in terms of the ΔV provided by a classic Lambert’s problem. For this purpose, three evolutionary algorithms with a dedicated cost function have been tested: Particle Swarm Optimization (PSO), Differential Evolution (DE) and Covariance Matrix Adaptation (CMA-ES). When compared to reference transfer optimizations from the literature, the three algorithm implementations show negligible differences with those in the literature, demonstrating their high reliability. For multi-target optimization, the algorithms were combined with a Traveling Salesman Problem (TSP) formulation, since propellant consumption and time of flight (TOF) depend strongly on the order in which target satellites are visited. This TSP-EA formulation is particularly valuable for IOS and Active Debris Removal (ADR) missions, where a single chaser may need to service or de-orbit several spacecraft distributed across different orbits. All the optimal parameters provided by the EA (i.e., the time of flight, the target satellite departure true anomaly and the two ΔV values) are passed to the orbital simulator. This simulator propagates the spacecraft states via a classic fourth-order Runge–Kutta (RK4) integrator, in which at each integration sub-step the dynamic model computes the translational state derivatives of the spacecraft and the GNC algorithm updates the throttle command and thrust direction of the chaser. The guidance logic is open-loop during the first burn, in which thrust is aligned with the optimized Lambert ΔV₁_target direction and lasts until this impulse is fully delivered by the propulsion system. After this first impulse, the algorithm switches to two closed-loop phases: the coasting and the second burn. The coasting phase lasts until a predefined target Argument of Latitude (θ_target) is reached without any propulsion. The second burn starts immediately after the coasting phase and during that the algorithm continuously adjusts thrust direction to match the target satellite’s velocity. This second burn lasts until the Lambert ΔV₂_target is reached. Representative campaigns covering scenarios such as Sun-Synchronous Orbit (SSO) transfers, Low Earth Orbit (LEO) two-impulse paths and multi-target servicing missions show close agreement between desired and simulated results in terms of ΔV, time of flight, relative velocity and orbital parameters. The resulting framework delivers fast and reliable insight into propellant needs and guidance performance, helping mission designers to achieve quicker evaluation of In-Orbit-Servicing scenarios.