Standard chance-constrained spacecraft guidance typically relies on the assumption that uncertainties in vehicle states obey Gaussian statistics. In frontier applications such as the cislunar environment or deep space flybys, the dynamics can be particularly nonlinear, and time between measurements can be long, leading to the need to make decisions whose outcomes produce non-Gaussian distributions. This paper demonstrates a non-Gaussian confidence boundary technique for stochastic guidance in such applications. Our approach is to consider the true confidence contour as a perturbation of the one predicted from covariance, then to derive perturbed boundary geometry from computed higher-order statistical moments. Applying this technique to so-called "banana-shaped distributions", found in orbital mechanics problems, enables a simple parameterization of the confidence contour using the skew and kurtosis tensors. This parameterization is then applied to a stochastic and nonlinear impulsive spacecraft maneuver targeting problem, with special treatment of a relevant non-convex constraint.
This work investigates nonlinear uncertainty propagation in perturbed astrodynamics, focusing on the rapid characterization of non-Gaussian distributions and the construction of three-dimensional "banana-shaped" confidence boundaries. To bridge the gap between computationally int…
Covariance steering provides an efficient framework for designing linear stochastic feedback policies, but its extension to nonlinear systems relies on a Gaussian surrogate obtained through local linearization. Because this surrogate may differ substantially from the true nonline…
Motivated by stochastic model predictive control applications, we present a semi-algebraic approach to constraint tightening for chance-constrained systems with unbounded additive disturbances and saturated inputs. The saturated error dynamics are handled via their exact piecewis…
We propose a stochastic behavioral modeling framework, termed Gaussian behaviors, which augments a deterministic linear time-invariant (LTI) behavior with a Gaussian noise component. We show that this notion is a tractable subclass of stochastic behaviors and encompasses classica…
We characterize a notion of system comparison, termed as $(T_e,γ,δ)$-similarity, for non-deterministic nonlinear systems. Building on a similar notion recently proposed for stable linear systems, the proposed notion characterizes the dissimilarity between the outputs, measured us…
The modulating function method is an algebraic framework that, thus far, has been used for state and parameter estimation, as well as fault detection, of linear, fractional-order, distributed, and some nonlinear systems. At the core of the method lies the modulating function, whi…