Saturation-Aware Robust Trajectory Optimization for Reusable Launch Vehicles via Differentiable Physics
The high-angle-of-attack flip maneuver of reusable launch vehicles presents significant challenges for robust trajectory optimization due to the combined effects of highly nonlinear dynamics, aerodynamic uncertainties, and actuator saturation. This paper presents a differentiable physics framework for saturation-aware robust trajectory optimization. At its core, a Differentiable Particle Tube Control (DPTC) scheme is developed to optimize uncertainty evolution through an ensemble-based distribution shaping strategy. State uncertainty is represented by a Lagrangian particle ensemble, while hard actuator projection operators are embedded directly into the computational graph, enabling the joint optimization of the nominal feedforward trajectory and a time-varying feedback policy via end-to-end backpropagation. The proposed framework is evaluated against an automatic differentiation-based Successive Convexification (AD-SCvx) baseline combined with a conventional covariance steering feedback strategy. Six-degree-of-freedom Monte Carlo simulations demonstrate that, although the baseline achieves nominal fuel-optimal solutions, its unconstrained feedback formulation becomes susceptible to actuator saturation under aerodynamic disturbances, leading to degraded closed-loop robustness. In contrast, the proposed DPTC framework proactively performs a constraint-aware performance trade-off by relaxing spatial tracking to preserve critical control authority. These results demonstrate that integrating differentiable physics with ensemble-based optimization provides an effective and practical framework for robust guidance in highly constrained aerospace flight systems.