Discretization Performance and Accuracy Analysis for the Rocket Powered Descent Guidance Problem

D. Malyuta, T. Reynolds, M. Szmuk, M. Mesbahi, B. Acikmese, J. M. Carson

AIAA Scitech 2019 Forum

In this paper we analyze the performance and accuracy properties of several differential equation discretization methods in the context of powered descent guidance for pinpoint planetary landing. The guidance problem is formulated as a continuous-time 6-DoF optimal control problem with nonlinear dynamics and a multitude of state and control constraints. This problem is to be solved via a direct method whereby it is temporally discretized and solved iteratively as a sequence of parameter optimization problems. Proper discretization thus becomes crucial if the resulting thrust commands are to be reproducible by the real vehicle. Moreover, proper discretization can decrease the overall time required to obtain a solution, and ultimately to satisfy a real-time computational requirement. We thus carry out a Monte Carlo performance comparison of the piecewise constant, piecewise linear, Runga-Kutta and three pseudospectral discretization methods. We study the method’s performance and accuracy, and discuss how each method may impact the ability to achieve a real-time solution. 

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