Statistical Analysis of the Role of Invariant Manifolds on Robust Trajectories
Published in Journal of Guidance, Control, and Dynamics, 2025
Optimal Solutions and Invariant Manifolds
Incorporating robustness against operational uncertainties during preliminary mission design is particularly critical in multibody dynamical environments, where the inherent dynamical chaos can significantly influence solution behavior. While the dynamical structures are known to shape the solution space in multibody dynamical systems by providing a global template for the solution space, their relationship to missed thrust design remains relatively unknown. Through comprehensive statistical analysis, we establish that optimal low-thrust solutions, both robust and non-robust, exhibit strong correlation with the underlying dynamical structures, while the broader feasible solution space demonstrates significant deviation from these natural pathways. Notably, robust optimal solutions maintain comparable, and in certain cases superior, manifold proximity to the dynamical structures relative to their non-robust counterparts. This finding suggests that natural dynamical structures can be systematically exploited to achieve both optimality and robustness against operational uncertainties in missed thrust design.
Recommended citation: Amlan Sinha and Ryne Beeson, "Statistical Analysis of the Role of Invariant Manifolds on Robust Trajectories", Journal of Guidance, Control, and Dynamics, Vol. 48, No. 8 (2025), pp. 1818-1839, doi: doi/abs/10.2514/1.G008818.