This paper addresses autonomous landing of unmanned aerial vehicle (UAV) rotorcrafts on a heaving ship deck using a recurrent policy trained via asymmetric actor-critic reinforcement learning: the critic sees 6 s of future deck height during training, while the actor sees only what the onboard sensors provide in flight, a 17-dimensional state made of the vehicle's position, velocity and attitude relative to the deck and outputs world-frame velocity and yaw-rate commands. Training is performed across 4096 parallel simulated environments, followed by fine-tuning in 16 environments with an onboard vision pipeline in the loop. A control-barrier-function (CBF) stopping margin on the deck-relative vertical state is incorporated at two stages: as a reward term during training, where it halves the median simulated contact speed relative to a policy trained without it, and as a runtime safety filter at deployment, evaluated at every control step to abort and retry the descent when the margin is violated. Because the autopilot's disarm logic cannot detect the vehicle resting on a moving deck, proximity-based thrust cutoff at touchdown is commanded directly in the landing pipeline. The proposed approach is validated using a parallel-manipulator-platform-based deck emulator that reproduces the heaving motion of the ship deck (scaled to 0.70 m peak-to-peak, 7.5 s mean period) and a quadcopter UAV with an onboard camera. Across 31 motion-capture and 20 vision-based trials, the UAV landed every time, with median times to contact of 6.5 and 7.3 s; 77% and 50% landed on the first attempt, with mean deck-relative speeds of 0.29 and 0.27 m/s, respectively, at the instant of thrust cutoff, which is the last speed under the policy's control. Supplementary video: https://youtu.be/S5hDkrSZJt4

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