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Low-thrust Optimal Trajectories using Differential Dynamic - Programming enhancing the effects of Orbital Perturbations
Full text linkLow-thrust Trajectory Optimisation through Differential Dynamic Programming Method based on Keplerian Orbital Elements
Full text linkIntroduction to a Keplerian-Orbital-Element-Based Optimisation Approach Via Differential Dynamic Programming
Full text linkMulti-Revolution Low-Thrust Trajectory Optimisation Using Differential Dynamic Programming in Orbital Element Formulation
Full text linkSpace planetary missions' analysis with low-thrust propulsion includes orbit raising and de-orbiting manoeuvres which can involve multiple revolutions resulting in a spiralling motion of the satellite. The launch of large constellation satellites is increasing the number of satellites launched per month and the design of their trajectory to be positioned in their operational orbit. This problem is particularly relevant when low-thrust satellites are considered that are characterised by a continuous thrust and are getting more involved in the design of new missions since they grant a greater final operational mass thanks to their high specific impulse. The optimisation of low-thrust trajectories involving a larger number of orbit revolutions is a challenging problem. Differential dynamic programming is one of the techniques that can be used to solve nonlinear optimal control problems. This method based on the application of Bellman principle of optimality defines a feedback control law solving necessary optimality conditions during the backward sweep discretising the overall problem in several decision steps and checks for the functional cost reduction during the forward integration to accept or reject the computed control law. In the last years, differential dynamic programming technique evolved thanks to the formulation of the hybrid differential dynamic programming proposed by Lantoine and Russell which maps the required derivatives recursively using state transition matrices and the stochastic differential dynamic programming which introduces random perturbations that can affect the dynamics. However, all past works deal with orbital dynamics expressed in terms of Cartesian coordinates and in only one paper orbital elements are used as state representation, but the rendezvous problem is not solved. This paper presents a systematic procedure for the optimisation of multi-revolution low-thrust trajectories using the differential dynamic programming technique based on orbital elements as state rep-representation of the dynamics. Lagrange and Gauss planetary equations are used to model the spacecraft dynamics to include both conservative and non-conservative accelerations. Some planetary missions like orbit raising for large constellations considering the engine specifics of actual satellites are used to test the proposed approach including also J2 orbital perturbation
A New Analytical Method for Eclipse Entry/Exit Positions Determination Considering a Conical Shadow and an Oblate Earth Surface
Full text linkA New Methodology for the Solution of the Stiffness Problem Applied to Low-Thrust Trajectory Optimisation in Terms of Orbital Elements Using Differential Dynamic Programming
Full text linkA System-Level Engineering Approach to Define the Social Value Rating of Earth Remote Sensing Missions Through Sustainable Development Goals
Full text linkIn 2015, the UN state members agreed on the “Transforming our world: the 2030 Agenda for Sustainable Development” document to drive the evolution of humanity in the close future. A great effort has been placed to understand how space missions and their data can support the goals fulfilment, both by private entities and public organisations like the European Space Agency (ESA) or United Nations Office for Outer Space Affairs (UNOOSA). This paper proposes a method to evaluate the level of support that a space missions used for Earth observation in Low Earth Orbit (LEO) can provide to each goal, using a set of indices based on missions' and payloads' performance related to Earth Observation (EO) services. Eight Earth observation services have been selected for this study: mapping, disaster monitoring, forestry, agriculture, geology, oceanography, hydrology, meteorology. Each of these services has its own performance requirements and can support many different goals. Using the relationship between mission performance and services together with the original correlation between the services and the Sustainable Development Goals 2030 (SDG2030), the final assessment of an Earth Observation mission towards each goal is achieved
Analytical determination of eclipse entry and exit points considering a conical shadow and oblate Earth
Full text linkThis paper presents a new analytical procedure to model the umbra generated during an eclipse considering an oblate ellipsoid of rotation as occulting body and a conical shadow. The method is based on purely geometrical considerations and results in the analytical definition of the entry and exit points from the conical shadow starting from the knowledge of the Sun position vector, the occulting body position vector and the orbital elements of the spacecraft orbiting the occulting body. The conical shadow also permits analytical definition of the entry and exit points of the penumbra region, which cannot be defined by using the classic cylindrical approach. Some numerical applications are proposed to test the effectiveness of the analytical formulations and to check the error in the prediction of the time spent in the shadow by the satellite. Finally, a discussion between the new conical shadow model and the classic cylindrical eclipse is carried out to see the improvements introduced by the refined geometry and the effects on space missions focusing on the cumulative error when multiple revolutions are considered
A system-level engineering approach for preliminary performance analysis and design of global navigation satellite system constellations
Full text linkThis paper presents a system-level engineering approach for the preliminary coverage performance analysis and the design of a generic Global Navigation Satellite System (GNSS) constellation. This analysis accounts for both the coverage requirements and the robustness to transient or catastrophic failures of the constellation. The European GNSS, Galileo, is used as reference case to prove the effectiveness of the proposed tool. This software suite, named GNSS Coverage Analysis Tool (G-CAT), requires as input the state vector of each satellite of the constellation and provides the performance of the GNSS constellation in terms of coverage. The tool offers an orbit propagator, an attitude propagator, an algorithm to identify the visibility region on the Earth’s surface from each satellite, and a counter function to compute how many satellites are in view from given locations on the Earth’s surface. Thanks to its low computational burden, the tool can be adopted to compute the optimal number of satellites per each orbital plane by verifying if the coverage and accuracy requirements are fulfilled under the assumption of uniform in-plane angular spacing between coplanar satellites
Low Thrust Multiple Revolution Transfer Design Using Artificial Potential Guidance in the Phase Space
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