Saturation-Aware Robust Trajectory Optimization for Reusable Launch Vehicles via Differentiable Physics

This paper presents a distribution-agnostic robust trajectory-optimization framework based on chance-constrained reinforcement learning. The uncertainty is represented here through initial conditions and process noise, with the only requirement being that it can be sampled. A deterministic nominal trajectory is first computed offline, and reinforcement learning is then used only to robustify that baseline through a structured affine closed-loop correction law comprising a feedforward control adjustment and time-varying feedback gains. Probabilistic feasibility is enforced empirically through rollout-based upper-tail quantiles, while terminal dispersion is regulated through covariance-feasibility penalties. The framework is assessed on two materially different trajectory design problems. The flagship case study is a three-dimensional multi-impulse Earth-Mars transfer, where the learned policy is benchmarked against a recent robust trajectory-optimization reference under Gaussian uncertainty and then evaluated under bounded uniform uncertainty and under process disturbances not seen during training. The second case study is a stochastic atmospheric pinpoint rocket landing problem, used to assess portability to a short-horizon continuous-thrust setting with drag, mass depletion, and glide-slope constraints. The results show that the proposed framework can remain competitive in upper-tail fuel cost while preserving probabilistic feasibility, and that the same robustification scaffold can be carried across heterogeneous spacecraft trajectory planning problems without redesign of its core stochastic-control structure.

Uncertainties and disturbances in robotic systems, such as aerodynamic forces, are fundamentally outcomes of physical interactions with the environment, manifesting as learnable spatiotemporal sequences rather than random noise. However, achieving high-precision control for robotic systems operating in unstructured environments is often hindered by complex unmodeled dynamics and external disturbances. While learning-based methods offer powerful approximation capabilities, they typically suffer from heavy reliance on offline training and lack theoretical guarantees. Conversely, traditional robust control strategies are predominantly reactive, limited to instantaneous estimation without the foresight to anticipate future disturbance trends. To bridge this gap, this paper proposes a differentiable data-enabled Koopman control framework termed DEKC. Unlike black-box approaches, DEKC adopts a hybrid modeling strategy that retains the nominal physics model while employing a deep neural network to parameterize the lifting function of Koopman operator for unknown residual dynamics. Crucially, the framework formulates disturbances as a dynamical system, learning their temporal evolution in a global linear space. This enables the prediction of future disturbance trajectories, which are explicitly integrated into controller for preemptive compensation. Furthermore, an online backward gradient update mechanism is introduced to ensure real-time adaptation to time-varying uncertainties. Numerical simulations on a tethered space robot demonstrate the efficacy of the proposed DEKC in mitigating highly coupled uncertainties. Complementing these results, real-world experiments on a quadrotor substantiate its superiority in tracking agile trajectories under uncertainties induced by aerodynamics and suspended payload.

Traversing crests, ledges, and ditches at high speed often launches vehicles into the air, and a mishandled landing presents a substantial crash hazard. We show that the airborne phase is barely controllable: on a 1383 kg platform the wheel angular-momentum budget caps the recoverable pitch-rate change at roughly $9$-$13^\circ$/s in the tighter nose-up direction under drive at typical takeoff wheel speeds, and at about twice that in the reverse-inclusive braking direction; driving the wheels to their drivetrain hard limit raises the measured nose-up ceiling to only $16$-$18^\circ$/s. Takeoff pitch-rate disturbances beyond this directional budget are physically unrecoverable in flight, so the decisive leverage lies before takeoff. DART (Dual-Axis Airborne Reachability-Gated Torque-Reaction) back-propagates the landing constraint into a closed-form certified feasible-takeoff set, which supplies a conservative go/no-go condition and a pre-takeoff speed-shaping law. In flight, DART regulates pitch and roll via steer-resolved wheel-reaction torque, governed by a per-flight roll latch derived from the yaw-coupling analysis. In deterministic full-scale simulation in BeamNG.tech, a calibrated pre-takeoff speed regulator reduces touchdown speed by 36% and raises on-target landings from 0/30 to 30/30. Under the same steep-lip approach the airborne law completes 29/30 safe landings under crash-avoidance bounds versus 0/30 for reaction-wheel-style PD (RW-PD) and time-optimal bang-bang (TOBB). On banked run-ups DART holds the median pitch error at or below $2^\circ$ at every cross-slope, with the largest baseline separation at $γ=12^\circ$. Across disturbance regimes, the latch preserves pitch-only allocation on low-disturbance entries and enables dual-axis control when roll becomes binding. All results are from simulation; hardware validation remains open.