ESA GNC Conference Papers Repository

Uncertainty Propagation in Approach Guidance, Navigation & Control Systems Using Differential Algebra
Kostas Konstantinidis, Dario Izzo
Presented at:
Virtual Conference 2021
Full paper:

Future landing and close-approach missions will require increasingly complex Guidance, Navigation & Control (GN&C) systems. It is important that the design and analysis of these non-linear and complex GN&C systems can be performed accurately and efficiently. A crucial aspect of such analysis is uncertainty propagation in models of GN&C systems, traditionally performed either by linearizing them at the cost of accuracy or by performing accurate but computationally expensive Monte Carlo simulations. A compromise between the two is offered by Differential Algebra (DA), a numerical technique to automatically compute high order Taylor expansions of a given function. In the DA framework, the Taylor expansion of a system model function is calculated once at relatively high computational expense. This expansion however can then be used to evaluate any input value around the nominal at negligible computational cost. DA thus offers the possibility to reduce the computational effort significantly while maintaining accuracy. In this paper, we describe the application of the DA framework for non-linear uncertainty propagation in a GN&C model for asteroid landing operations. We then investigate the computational efficiency and accuracy of this novel approach compared to standard approaches.