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Hybrid Differential Dynamic Programming Algorithm for Low-Thrust Trajectory Design Using Exact High-Order Transition Maps

Maestrini, Michele, Di Lizia, Pierluigi, Armellin, Roberto and Russell, Ryan P (2018) Hybrid Differential Dynamic Programming Algorithm for Low-Thrust Trajectory Design Using Exact High-Order Transition Maps In: 69th International Astronautical Congress 2018, 1 - 5 October, 2018, Bremen, Germany.

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Optimal orbital trajectories are obtained through the solution of highly nonlinear large-scale problems. In the case of low-thrust propulsion applications, the spacecraft benefits from high specific impulses and, hence, greater payload mass. However, these missions require a high count of orbital revolutions and, therefore, display augmented sensitivity to many disturbances. Solutions to such problems can be tackled via a discrete approach, using optimal feedback control laws. Historically, differential dynamic programming (DDP) has shown outstanding results in tackling these problems. A state of the art software that implements a variation of DDP has been developed by Whiffen (2006) and it is used by NASA’s DAWN mission. One of the latest techniques implemented to deal with these discrete constrained optimizations is the Hybrid Differential Dynamic Programming (HDDP) algorithm, introduced by Lantoine and Russell (2012). This method complements the reliability and efficiency of classic nonlinear programming techniques with the robustness to poor initial guesses and the reduced computational effort of DDP. The key feature of the algorithm is the exploitation of a second order state transition matrix procedure to propagate the needed partials, decoupling the dynamics from the optimization. In doing so, it renders the integration of dynamical equations suitable for parallelization. Together with the possibility to treat constrained problems, this represents the greatest improvement of classic DDP. Nevertheless, the major limitation of this approach is the high computational cost to evaluate the required state transition matrices. Analytical derivatives, when available, have shown a significant reduction in the computational cost and time for HDDP application. This work applies differential algebra (DA) to HDDP to cope with this limitation. DA is introduced to obtain state transition matrices as polynomial maps. These maps come directly from the integration of the dynamics of the system, removing the dedicated algorithmic step and reducing its computational cost. Moreover, by operating on polynomial maps, all the solutions of local optimization problems are treated through differential algebraic techniques. This approach allows users to deal with higher order expansions of the cost, without modifying the algorithm. From the examples provided, it emerges that increasing the order of the expansions does not yield a better convergence rate. Additionally, it causes numerical instability of the algorithm to arise, as well as a noticeable increase on computational time due to the number of polynomial coefficients that ought to be computed.

Item Type: Conference or Workshop Item (Conference Paper)
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
Maestrini, Michele
Di Lizia, Pierluigi
Russell, Ryan P
Date : 2018
Copyright Disclaimer : Copyright ©2018 by the International Astronautical Federation (IAF). All rights reserved.
Depositing User : Melanie Hughes
Date Deposited : 02 Oct 2018 16:56
Last Modified : 22 May 2019 14:00

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