Differential-Flatness-Based Trajectory Planning for Direct Helicopter Shipboard Landing with Geometry-Aware Final-Landing Constraints

Autonomous helicopter shipboard landing requires the generation of dynamically feasible trajectories that can accurately match the time-varying motion of a moving deck while maintaining desirable near-deck geometric and kinematic characteristics. This paper proposes a differential-flatness-based trajectory planning method for single-phase direct shipboard landing from a cruising state in the vicinity of the ship. The landing trajectory is planned in the flat-output space of a simplified differentially flat helicopter model and parameterized using the minimum-control-effort trajectory representation, MINCO, together with an unconstrained optimization formulation. To improve the final landing process, a set of geometry-aware final-landing constraints is developed by explicitly accounting for the relative pose, relative motion, and near-deck geometry between the helicopter and the moving deck. These constraints enforce terminal motion-state matching and regulate the landing-gear/deck geometry, relative tangential velocity, and relative tilt angle in the near-deck region. Comprehensive simulation studies, including ablation and parameter-sensitivity analyses, computational comparisons, Monte Carlo evaluations, and closed-loop validation with a full nonlinear UH-60 model, demonstrate that the proposed method can efficiently generate trackable shipboard landing trajectories with improved terminal consistency and pre-touchdown geometric and kinematic regulation. Additional closed-loop sensitivity tests show that the tested trajectories remained executable under moderate high-level gain variations, while accurate terminal horizontal alignment remains dependent on deck-motion prediction accuracy.