# Trajectory Prediction

Ship trajectory forecasting no longer needs recurrent networks or repeated sampling. Earlier AIS-based models either used only the target vessel's history or relied on clustering other vessels, and approximated probability intervals through multiple forward passes. Here the vessel's past positions and a local KDE heat map are fed to a Transformer trained with quantile loss, reaching about 0.18 km average displacement error across three Danish water areas while emitting a prediction interval in a single forward pass.

Ship trajectory forecasting no longer needs recurrent networks or repeated sampling. Earlier AIS-based models either used only the target vessel's history or relied on clustering other vessels, and approximated probability intervals through multiple forward passes. Here the vessel's past positions and a local KDE heat map are fed to a Transformer trained with quantile loss, reaching about 0.18 km average displacement error across three Danish water areas while emitting a prediction interval in a single forward pass.

Autonomous-driving vision-language-action models have learned from a scalar trajectory score that flags a bad plan but cannot say whether scene understanding, behavior selection, or trajectory execution went wrong. Reflect-VLA treats reflective guidance, which pairs evaluation diagnoses with corrective suggestions, as training-time privileged information and internalizes it through dual-path on-policy self-distillation: risky trajectories align with the teacher's token-level corrective distribution, while reliable ones are preserved by self-imitation. It reaches competitive planning performance on NAVSIM v1/v2 and Bench2Drive, cuts training time by over 90% versus reinforcement learning, and generates trajectories in a single pass at inference without guidance or iterative refinement.

Autonomous-driving vision-language-action models have learned from a scalar trajectory score that flags a bad plan but cannot say whether scene understanding, behavior selection, or trajectory execution went wrong. Reflect-VLA treats reflective guidance, which pairs evaluation diagnoses with corrective suggestions, as training-time privileged information and internalizes it through dual-path on-policy self-distillation: risky trajectories align with the teacher's token-level corrective distribution, while reliable ones are preserved by self-imitation. It reaches competitive planning performance on NAVSIM v1/v2 and Bench2Drive, cuts training time by over 90% versus reinforcement learning, and generates trajectories in a single pass at inference without guidance or iterative refinement.

The authors propose Ctrl-CWM, a multi-agent controllable crowd world model that first learns and freezes an encoder via trajectory prediction on real pedestrian videos to preserve human motion dynamics, then uses an actor to propose displacements, a critic to rank imagined crowd trajectories, and a planner combining critic scores with user costs to select actions, enabling crowd generation and run-time control without retraining; on ETH–UCY, SDD, and GCS it outperforms CrowdES on most crowd realism and collision metrics and achieves the highest average compliance in avoidance and attraction scenarios.

The authors propose Ctrl-CWM, a multi-agent controllable crowd world model that first learns and freezes an encoder via trajectory prediction on real pedestrian videos to preserve human motion dynamics, then uses an actor to propose displacements, a critic to rank imagined crowd trajectories, and a planner combining critic scores with user costs to select actions, enabling crowd generation and run-time control without retraining; on ETH–UCY, SDD, and GCS it outperforms CrowdES on most crowd realism and collision metrics and achieves the highest average compliance in avoidance and attraction scenarios.