Global Optimization of Interplanetary Transfers with Deep Space Maneuvers Using Differential Algebra
In this chapter, differential algebra is used to globally optimize multi-gravity assist interplanetary trajectories with deep space maneuvers. A search space pruning procedure is adopted, and the trajectory design is decomposed into a sequence of sub-prob
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Global Optimization of Interplanetary Transfers with Deep Space Maneuvers Using Differential Algebra Pierluigi Di Lizia, Roberto Armellin, Francesco Topputo, Franco Bernelli-Zazzera, and Martin Berz
Abstract In this chapter, differential algebra is used to globally optimize multigravity assist interplanetary trajectories with deep space maneuvers. A search space pruning procedure is adopted, and the trajectory design is decomposed into a sequence of sub-problems. As far as differential algebra is used, the objective function and the constraints are represented by Taylor series of the design variables over boxes in which the search space is divided. Thanks to the polynomial representation of the function and the constraints, a coarse grid can be used, and an efficient design space pruning is performed. The manipulation of the polynomials eases the subsequent local optimization process, so avoiding the use of stochastic optimizers. These aspects, along with the efficient management of the list of boxes, make differential algebra a powerful tool to design multi-gravity assist transfers including deep-space maneuvers. Keywords Global optimization • Multi-gravity assist transfer • Deep-space maneuver • Search space pruning • Differential algebra
P. Di Lizia (*) • R. Armellin • F. Topputo • F. Bernelli-Zazzera Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy e-mail: [email protected]; [email protected]; [email protected]; [email protected] M. Berz Department of Physics and Astronomy, Michigan State University, East Lansing MI 48824, USA e-mail: [email protected] G. Fasano and J.D. Pinte´r (eds.), Modeling and Optimization in Space Engineering, Springer Optimization and Its Applications 73, DOI 10.1007/978-1-4614-4469-5_8, # Springer Science+Business Media New York 2013
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List of Acronyms DA DSM FP GASP MGA
8.1
Differential algebra Deep space maneuver Floating point Gravity assist space pruning Multi-gravity assist
Introduction
The preliminary design of impulsive interplanetary transfers is usually carried out in the frame of the patched-conics approximation. Within this context, different conic arcs are linked together to define the whole transfer trajectory. The patchedconics method allows the designer to define multiple gravity assist (MGA) transfers. MGA trajectories are usually made up of a sequence of planet-to-planet transfers in which the spacecraft exploits each planet encounter to achieve a velocity change. This method is well established in astrodynamics, and several past missions have used MGA trajectories to reach both inner and outer planets. In the last two decades, mission designers have exploited the benefits of approaching complex MGA problems from a global optimization standpoint. Nowadays, the aim of the trajectory design is not only to find a solution, but also to find the best solution in terms of propellant consumption, while still achieving the mission goals. In the formalism of global optimizati
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