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Mathematical Sciences

Research project: Trajectory Optimisation

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We are interested in trajectory optimisation problems especially those with combinatorial aspects, merging classical approaches from optimal control theory and nonlinear optimisation with techniques from mixed-integer programming and discrete optimisation. Our work is supported by the European Space Agency (ESA), the Clean Sky Initiative of the Horizon 2020 European Union Funding Programme, and the Brazilian "Science without Borders" scheme. Our partners include Thales Aerospace, the University of Federal Armed Forces Munich, the University of Bremen and the Technical University Munich.    

Trajectory Optimisation
Multiple fly-by trajectories

Multiple fly-by trajectories

Multiple fly-by trajectories i.e. gravity-assist trajectories for interplanetary missions. When travelling among the planets, one needs to minimize the propellant mass needed by the spacecraft and its launch vehicle. The amount of propellant needed depends largely on the chosen route. Gravity assisted flyby maneuvers can be used to transfer angular momentum from a planet to a spacecraft approaching the planet from behind in it's progress about the sun. Finding the right order and exact nature of such flyby maneuvers introduces a combinatorial component into the overall fuel minimization problem, making it exceedingly difficult to solve.    

Unmanned Aerial Vehicles

Unmanned Aerial Vehicles (UAVs) in disaster assessment, response and management

These vehicles can be employed to help rescue teams in ecological, geological, meteorological, hydrological and human-induced disasters, improving deployment of energy, human and material resources where they are most needed. While the utilisation of powered UAVs has been broadly investigated already, the employment of unpowered UAVs, such as gliders, has not being well explored. This kind of vehicle presents a much lower cost when compared with powered UAVS, which allows disaster management teams to treat them as expendable vehicles, allowing to focus efforts on completing rescuing tasks instead of manoeuvring expensive vehicles into safe landing areas. Routing UAVs to various different areas to assess damage and rescuing needs again introduces a difficult combinatorial component into the problem.    

Flight path optimisation to minimise CO2 and NOx

Flight path optimisation to minimise CO2 and NOx emissions

Air traffic has been growing continuously over the last decades and this trend is expected to continue into the future. Major airports are facing more than thousand aircraft movements a day, leading to considerable impact of the surrounding communities in terms of noise and air pollution. To ensure air traffic growth that is environmentally sustainable and well accepted by the European population, the European Commission has formulated a 75% reduction in CO2 emissions per passenger kilometre, a 90% reduction in NOx emissions, and a perceived noise emission of flying aircraft by 65%. One possibility to reduce emission and noise is through aircraft trajectory optimization, which can contribute to benefits for all stakeholders. The AWACS project (Adaption of WORHP to Avionics Constraints) improves and extends the functionality of existing computational tools to ensure that aircrafts can follow an emission-minimal flight path.    

Related research groups

Operational Research
Computational Optimisation


Image credit: (c) ESA



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