arXiv subjects

Thomas Caleb

Publications and source records attributed to Thomas Caleb.

5 recordsLinked to original sources

arXiv2025

Non-linear stochastic trajectory optimisation

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.

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arXiv2025

Optimization of Transfers linking Ballistic Captures to Earth-Moon Periodic Orbit Families

The design of transfers to periodic orbits in the Earth-Moon system has regained prominence with NASA's Artemis and CNSA's Chang'e programs. This work addresses the problem of linking ballistic capture trajectories - exploiting multi-body dynamics for temporary lunar orbit insertion - with bounded periodic motion described in the circular restricted three-body problem (CR3BP). A unified framework is developed for optimizing bi-impulsive transfers to families of periodic orbits via a high-order polynomial expansion of the CR3BP dynamics. That same expansion underlies a continuous parameterization of periodic orbit families, enabling rapid targeting and analytic sensitivity. Transfers to planar periodic orbit families - such as Lyapunov L1/L2 and distant retrograde orbits (DROs) - are addressed first, followed by extension to spatial families - such as butterfly and halo L1/L2 orbits - with an emphasis towards near-rectilinear halo orbits (NRHOs). Numerical results demonstrate low-{\Delta}v solutions and validate the method's adaptability for designing lunar missions. The optimized trajectories can inform an established low-energy transfer database, enriching it with detailed cost profiles that reflect both transfer feasibility and underlying dynamical relationships to specific periodic orbit families. Finally, the proposed transfers provide reliable estimates for rapid refinement, making them readily adaptable for further optimization across mission-specific needs.

astro-ph.EP↗

arXiv2025

Chance constraints transcription and failure risk estimation for stochastic trajectory optimisation

Stochastic trajectory optimisation under uncertainty requires robust constraint satisfaction through chance constraints. However, existing transcription methods remain limited to scalar constraints or highly specific structures while introducing substantial conservatism. This work presents two general-purpose transcription methods for multi-dimensional Gaussian chance constraints for trajectory optimisation problems under uncertainty. The spectral radius method extends existing methods to arbitrary multi-dimensional constraints with reduced conservatism. The refined first-order method achieves superior tightness with linear complexity. In addition, a d-th order risk estimation methodology provides conservative failure probability estimates with limited conservatism in high dimensions in quadratic complexity. Applied to an optimal control with uncertainties setting, the first-order transcription achieves near-optimal fuel consumption while maintaining the failure risk below the target. The spectral radius method incurs approximately 0.7 kg additional fuel consumption due to excessive conservatism and a 51% increase in computational time due to its cubic complexity. High-dimensional tests show that the proposed risk estimation method provides accurate risk estimates, while previously developed methods exhibit exponential growth in conservatism with respect to constraint dimension.

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arXiv2025

Taylor polynomial-based constrained solver for fuel-optimal low-thrust trajectory optimisation

This paper presents differential algebra-based differential dynamic programming (DADDy), a publicly available C++ framework for constrained, fuel-optimal low-thrust trajectory optimisation. The method uses differential algebra (DA) for two purposes: automatic differentiation and high-order Taylor expansions of the dynamics. These expansions replace many expensive numerical propagations with polynomial evaluations, reducing computational effort while preserving solution quality. The framework combines two complementary modules. First, a differential dynamic programming (DDP)/iterative linear-quadratic regulator (iLQR) stage computes an almost-feasible trajectory from imperfect initial guesses. Second, a polynomial-accelerated Newton stage enforces full feasibility with fast local convergence. Equality and inequality constraints are handled through an augmented Lagrangian formulation, and a pseudo-Huber homotopy is used to improve robustness for fuel-optimal objectives. The solver is evaluated on benchmark transfers in Sun-centred, Earth-Moon, and Earth-centred dynamical environments. Across these cases, the most robust configuration (iLQRDyn) converged systematically and reduced run time by 70% (Sun-centred), 51-88% (Earth-Moon), and 41-55% (Earth-centred) relative to the corresponding baseline. When convergent, the DDP-based variants are faster still. Overall, the results show that DA-based acceleration can substantially improve practical efficiency while retaining robust convergence behaviour on the tested benchmark set.

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arXiv2023

Stable sets mapping with Taylor differential algebra with application to ballistic capture orbits around Mars

Ballistic capture orbits offer safer Mars injection at longer transfer time. However, the search for such an extremely rare event is a computationally intensive process. Indeed, it requires the propagation of a grid sampling the whole search space. This work proposes a novel ballistic capture search algorithm based on Taylor differential algebra propagation. This algorithm provides a continuous description of the search space compared to classical grid sampling research and focuses on areas where the nonlinearities are the largest. Macroscopic analyses have been carried out to obtain cartography of large sets of solutions. Two criteria, named consistency and quality, are defined to assess this new algorithm and to compare its performances with classical grid sampling of the search space around Mars. Results show that differential algebra mapping works on large search spaces, and automatic domain splitting captures the dynamical variations on the whole domain successfully. The consistency criterion shows that more than 87% of the search space is guaranteed as accurate, with the quality criterion kept over 80%.

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