# Pontryagin-Bellman Differential Dynamic Programming for Low-Thrust Trajectory Optimization with Path Constraints

arXiv: https://arxiv.org/abs/2502.20291 · HTML: https://mlsanity.com/paper/2502.20291/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2025.

## Built on by (most cited first, 1 of 1)

- [MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning](https://mlsanity.com/paper/2605.13305/) (2026)

## Abstract (arXiv)

We present a Differential Dynamic Programming framework that parameterizes the control via Pontryagin's Minimum Principle, for constrained low-thrust trajectory optimization. This approach, dubbed Pontryagin-Bellman Differential Dynamic Programming (PDDP), optimizes the costates using a null-space trust-region method, solving a series of quadratic subproblems derived from first- and second-order sensitivities. Terminal equality constraints are handled via a general augmented Lagrangian method, while continuous-time state-path constraints are enforced using a quadratic penalty approach. The resulting solution method represents a significant improvement over classical indirect methods, which are known to face challenges for state-constrained problems. The flexibility of PDDP in handling various state-path constraints is demonstrated through minimum-radius and eclipse-avoidance trajectories in cislunar space. Finally, a trade study against indirect multiple shooting shows that PDDP achieves higher convergence rates overall, indicating improved robustness to poor initial guesses.