Non-linear stochastic trajectory optimisation

TL;DR

This paper introduces SODA, a novel stochastic trajectory optimization method combining differential algebra and Gaussian mixture models to handle non-Gaussian uncertainties in nonlinear space environments.

Contribution

It presents a new solver for chance-constrained trajectory optimization that efficiently propagates non-Gaussian uncertainties and enforces adaptive safety margins.

Findings

SODA outperforms linear variants in nonlinear regimes.

SODA provides tighter safety constraints and improved robustness.

Validated on diverse space trajectory problems.

Abstract

Designing robust space trajectories in nonlinear dynamical environments, such as the Earth-Moon circular restricted three-body problem (CR3BP), poses significant challenges due to sensitivity to initial conditions and non-Gaussian uncertainty propagation. This work introduces a novel solver for discrete-time chance-constrained trajectory optimization under uncertainty, referred to as stochastic optimization with differential algebra (SODA). SODA combines differential algebra (DA) with adaptive Gaussian mixture decomposition to efficiently propagate non-Gaussian uncertainties, and enforces Gaussian multidimensional chance constraints. This work further introduces a risk allocation strategy across mixture components that enables tight and adaptive distribution of safety margins. The framework is validated on four trajectory design problems of increasing dynamical complexity, from heliocentric transfers to challenging Earth-Moon CR3BP scenarios. A linear variant, the linear stochastic optimization with differential algebra (L-SODA) solver, recovers deterministic performance with minimal overhead under small uncertainties, while the nonlinear SODA solver yields improved robustness and tighter constraint satisfaction in strongly nonlinear regimes. Results highlight SODA's ability to generate accurate, robust, and computationally tractable solutions, supporting its potential for future use in uncertainty-aware space mission design.