JS
J. Slimmens
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1
With the development of space research into novel areas, new complex problems arise. The interest in solving space routing problems considering large numbers of targets has recently grown. This paper proposes a novel method to solve the optimal trajectory in such combinatorial space routing problems. This paper focuses on a global optimisation algorithm implemented to solve the problem posed in the 4th Global Trajectory Optimisation Com- petition (GTOC4). The solution is a trajectory of multiple legs, where each leg links two targets and has a specific flight time. To enable the use of the powerful mixed-integer linear problem solver software, Solving Constraint Integer Programs (SCIP), the routing problem concerned with visiting as many target bodies with a predetermined fuel and time budget is split into linear sub-problems. The Fixed Budget sub-problem selects a subset of the given set of targets. The Full Tour sub-problem orders the targets in the subset, and the Fixed Tour sub-problem optimises the flight time for every leg of the given trajectory to find the solution with the lowest total fuel consumption. Each of these sub-problems is formulated in a linear form and is solved using SCIP. The global optimisation algorithm evolves a population where every individual exists of a set of initial guesses for the time of flight values. Analysis shows that initialising this population with a mix of randomly generated individuals and individuals containing a constant value for all entries leads to the fastest convergence towards the optimal solution. In a population of 20, seeding ten individuals is found to be optimal. It is also found that the algorithm performance can be further increased by evolving individuals with infeasible solutions instead of iterating them until a feasible solution is found and eliminating the Full Tour sub-problem. These simplifications allow for an increase in the cost budget multiplier, which leads to finding better objective values without further increasing computational time. The best-performing setup, which uses a cost budget multiplier of 10, can find the optimal solution to the test problem in 100% of the runs, on average in 9 iterations, with a computation time of 5.82 seconds per evaluation. The results show that the global optimisation algorithm produces results that closely match known results for GTOC4 consistently and accurately.
...
With the development of space research into novel areas, new complex problems arise. The interest in solving space routing problems considering large numbers of targets has recently grown. This paper proposes a novel method to solve the optimal trajectory in such combinatorial space routing problems. This paper focuses on a global optimisation algorithm implemented to solve the problem posed in the 4th Global Trajectory Optimisation Com- petition (GTOC4). The solution is a trajectory of multiple legs, where each leg links two targets and has a specific flight time. To enable the use of the powerful mixed-integer linear problem solver software, Solving Constraint Integer Programs (SCIP), the routing problem concerned with visiting as many target bodies with a predetermined fuel and time budget is split into linear sub-problems. The Fixed Budget sub-problem selects a subset of the given set of targets. The Full Tour sub-problem orders the targets in the subset, and the Fixed Tour sub-problem optimises the flight time for every leg of the given trajectory to find the solution with the lowest total fuel consumption. Each of these sub-problems is formulated in a linear form and is solved using SCIP. The global optimisation algorithm evolves a population where every individual exists of a set of initial guesses for the time of flight values. Analysis shows that initialising this population with a mix of randomly generated individuals and individuals containing a constant value for all entries leads to the fastest convergence towards the optimal solution. In a population of 20, seeding ten individuals is found to be optimal. It is also found that the algorithm performance can be further increased by evolving individuals with infeasible solutions instead of iterating them until a feasible solution is found and eliminating the Full Tour sub-problem. These simplifications allow for an increase in the cost budget multiplier, which leads to finding better objective values without further increasing computational time. The best-performing setup, which uses a cost budget multiplier of 10, can find the optimal solution to the test problem in 100% of the runs, on average in 9 iterations, with a computation time of 5.82 seconds per evaluation. The results show that the global optimisation algorithm produces results that closely match known results for GTOC4 consistently and accurately.
VuAB Recovery
A cost effective way of reusing the Vulcain Aft Bay
Bachelor thesis
(2018)
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A.H.H. Toeter, C.A. Dek, J. Slimmens, J. Overkamp, J.A.J. van Zijl, P. Areso Rossi, Ricardo Machado, J.J.C. Hereijgers, T. Hoppenbrouwer, V. Kiliç, M.C. Naeije, M. Coppola, D. Zarouchas
The first launch of the Ariane 6 launch vehicle is planned for 2020, however in its current design no significant part of the launcher will be reusable. A current trend in the global space market is decreasing the costs of spacecraft launches through recovery, retrieval and refurbishment of parts of launchers. As a first step towards this market demand, it is to be investigated whether it is cost-effective to recover, refurbish and reuse the key components of the first stage of the Ariane 6, which are contained in the Vulcain Aft Bay (VuAB). This is where the engine, fuel lines, thrust frame and electronics are attached. The team has the task to develop a cost effective way of reusing the Vulcain Aft Bay. In the preceding report, multiple concepts were analysed and one concept was selected to complete the conceptual design. This concept consists of an Inflatable Heat Shield for re-entry, a Parafoil to control the flight at lower altitudes and a Mid-Air retrieval using a helicopter to perform a soft landing. A functional analysis was performed to define concept specific functions. This was done by means of a Functional Flow Diagram and Functional Breakdown Structure. In order to fulfil these functions, simulations were created of the most critical moments of the mission. One set of simulations analyse the trajectory of the system throughout the mission, predicting the location of landing. The other set of simulations is used to predict the critical load cases of the system. The aforementioned simulations were used to design the individual components of the system. By integrating these simulations and managing the iteration process, the overall system characteristics and configuration were established. The system was then analysed for sustainability, reliability, risk, maintainability and safety. The requirement compliance of the system was then updated, detailing which requirements have achieved full compliance, marginal compliance, no compliance and which have not been sufficiently investigated. Proposals to make all requirements fully compliant are included in a feasibility analysis. These include different design approaches for the team and design changes to the VuAB to accommodate the recovery system. From there strategies on future verification and validation activities was set forth together with operational, refurbishment and production plans. These plans and the design of the system were used to create an updated business model with return on investment figures, which predict a significant cost reduction on a per launch basis within five years. Finally a set of future recommendations and plan is proposed for the continuation of the project.
...
The first launch of the Ariane 6 launch vehicle is planned for 2020, however in its current design no significant part of the launcher will be reusable. A current trend in the global space market is decreasing the costs of spacecraft launches through recovery, retrieval and refurbishment of parts of launchers. As a first step towards this market demand, it is to be investigated whether it is cost-effective to recover, refurbish and reuse the key components of the first stage of the Ariane 6, which are contained in the Vulcain Aft Bay (VuAB). This is where the engine, fuel lines, thrust frame and electronics are attached. The team has the task to develop a cost effective way of reusing the Vulcain Aft Bay. In the preceding report, multiple concepts were analysed and one concept was selected to complete the conceptual design. This concept consists of an Inflatable Heat Shield for re-entry, a Parafoil to control the flight at lower altitudes and a Mid-Air retrieval using a helicopter to perform a soft landing. A functional analysis was performed to define concept specific functions. This was done by means of a Functional Flow Diagram and Functional Breakdown Structure. In order to fulfil these functions, simulations were created of the most critical moments of the mission. One set of simulations analyse the trajectory of the system throughout the mission, predicting the location of landing. The other set of simulations is used to predict the critical load cases of the system. The aforementioned simulations were used to design the individual components of the system. By integrating these simulations and managing the iteration process, the overall system characteristics and configuration were established. The system was then analysed for sustainability, reliability, risk, maintainability and safety. The requirement compliance of the system was then updated, detailing which requirements have achieved full compliance, marginal compliance, no compliance and which have not been sufficiently investigated. Proposals to make all requirements fully compliant are included in a feasibility analysis. These include different design approaches for the team and design changes to the VuAB to accommodate the recovery system. From there strategies on future verification and validation activities was set forth together with operational, refurbishment and production plans. These plans and the design of the system were used to create an updated business model with return on investment figures, which predict a significant cost reduction on a per launch basis within five years. Finally a set of future recommendations and plan is proposed for the continuation of the project.