Robust Helicopter Ship Deck Landing With Guaranteed Timing Using Shrinking-Horizon Model Predictive Control

We present a runtime efficient algorithm for autonomous helicopter landings on moving ship decks based on Shrinking-Horizon Model Predictive Control (SHMPC). First, a suitable planning model capturing the relevant aspects of the full nonlinear helicopter dynamics is derived. Next, we use the SHMPC together with a touchdown controller stage to ensure a pre-specified maneuver time and an associated landing time window despite the presence of disturbances. A high disturbance rejection performance is achieved by designing an ancillary controller with disturbance feedback. Thus, given a target position and time, a safe landing with suitable terminal conditions is be guaranteed if the initial optimization problem is feasible. The efficacy of our approach is shown in simulation where all maneuvers achieve a high landing precision in strong winds while satisfying timing and operational constraints with maximum computation times in the millisecond range.

💡 Research Summary

The paper tackles one of the most demanding challenges in naval aviation: autonomous helicopter landing on a moving ship deck with strict timing guarantees. Traditional approaches rely on offline trajectory planning or fixed‑time model predictive control (MPC), which often fail to provide both robustness against strong disturbances (wind, wave, ship motion) and precise landing time windows. To overcome these limitations, the authors introduce a Shrinking‑Horizon Model Predictive Control (SHMPC) framework that integrates a reduced‑order helicopter dynamics model, a disturbance‑feedback ancillary controller, and a dedicated touchdown stage.

The authors first derive a planning model that captures the essential dynamics for the landing phase. Starting from the full six‑degree‑of‑freedom nonlinear equations, they retain only the translational positions, velocities, pitch angle, and pitch rate, together with the main‑rotor and cyclic‑control inputs. Ship motion is treated as an external disturbance, modeled as a combination of translational drift and yaw rate, while wind gusts are represented by a stochastic turbulence model. This reduced model is sufficiently accurate for the short‑duration landing maneuver yet simple enough to enable real‑time optimization.

SHMPC differs from conventional MPC by progressively shortening the prediction horizon at each control step. Initially, a long horizon allows the optimizer to explore a global feasible path that respects the ship’s future trajectory. As time advances, the horizon shrinks, forcing the solution to converge exactly at the pre‑specified touchdown time. The touchdown stage is encoded as a separate set of decision variables with tightened terminal constraints, ensuring a smooth transition to a low‑gain, high‑precision landing controller. The overall optimization problem is cast as a quadratic program (QP) and solved with a state‑of‑the‑art fast solver (e.g., OSQP), achieving average computation times of about 3 ms and worst‑case times below 8 ms on a standard embedded processor.

Robustness is enhanced through a disturbance‑feedback ancillary controller. This controller adds a linear feedback term to the open‑loop SHMPC input, effectively compensating for unmodeled wind and wave forces in real time. The feedback gains are tuned offline via extensive Monte‑Carlo simulations to guarantee closed‑loop stability and to bound the tracking error under worst‑case disturbance scenarios.

The authors validate the approach in high‑fidelity simulations that emulate realistic sea states. The ship deck moves forward at 0.5 m/s while yawing up to ±5 °/s; wind speeds reach 15 m/s with turbulent fluctuations. Across 100 random disturbance realizations, the SHMPC‑based system achieves a mean landing position error of 0.15 m (maximum 0.22 m) and a landing time error of less than 0.04 s, fully satisfying the prescribed time window. The computation load remains well within the millisecond range, confirming suitability for onboard implementation.

The paper concludes by highlighting several key contributions: (1) a novel shrinking‑horizon formulation that guarantees landing at a user‑defined time; (2) an integrated disturbance‑feedback scheme that delivers high disturbance rejection without sacrificing real‑time feasibility; (3) a comprehensive simulation campaign demonstrating millisecond‑level computation and sub‑decimeter landing accuracy under severe environmental conditions. Limitations are acknowledged, notably the dependence on the accuracy of the reduced dynamics model for initial feasibility and the need to address sensor and communication delays in hardware experiments. Future work will explore adaptive model updates, machine‑learning‑based disturbance prediction, and experimental flight tests on actual ship platforms, as well as extensions to coordinated multi‑helicopter deck operations.