Designing robust spacecraft trajectories in highly non?linear dynamical environments, most notably the circular restricted three?body problem (CR3BP), remains difficult because small variations in the initial state can amplify dramatically and because the associated uncertainties quickly become non?Gaussian. To address these issues we introduce SODA (Stochastic Optimisation with Differential Algebra), a new publicly available solver for discrete?time, chance?constrained trajectory optimisation under uncertainty.

SODA exploits Differential Algebra (DA) to build high?order Taylor models of the dynamics, cost and constraint functions. This provides automatic differentiation and an accurate local polynomial description of the system behaviour. When the non?linearity index of a propagation step exceeds a prescribed threshold, the state distribution is automatically divided into smaller Gaussian components using an adaptive Gaussian?Mixture Model (GMM) decomposition. The adaptive splitting captures the evolution of non?Gaussian uncertainties while keeping the number of mixture components modest.

The resulting Gaussian mixture is then processed by a multidimensional Gaussian chance?constraint transcription, which yields a sufficient deterministic condition for the original probabilistic constraints. A complementary failure?risk estimation routine supplies an upper bound on the true violation probability for each mixture component without requiring Monte-Carlo estimations. By allocating the global risk budget across components—tightening safety margins where the estimated risk is low and relaxing them where it is high—SODA achieves an adaptive, tight distribution of safety margins without sacrificing feasibility.

The framework is exercised on several benchmark trajectory?design problems of increasing dynamical difficulty, ranging from the two?body problem to demanding CR3BP scenarios. In every case the solver produces trajectories that satisfy the prescribed chance constraints, with failure probabilities matching the admissible levels.

These results demonstrate that SODA provides an accurate, robust and computationally efficient methodology for uncertainty?aware space?mission design, paving the way for its adoption in future interplanetary and cislunar trajectory optimisation workflows.