Uncertainty-aware and physics-informed adaptive transformer for motion planning in autonomous driving

Purely learning-based motion planning approaches often lack verifiable safety guarantees, while traditional optimization-based methods are constrained by static parameterization, limiting their adaptability to dynamic environments. To address these limitations, we propose the Uncertainty-Aware and Physics-Informed Adaptive Transformer, a unified differentiable framework that tightly integrates data-driven interaction modeling with physics-constrained optimization. Specifically, our framework introduces a Trajectory Entropy-driven Mixture-of-Experts module to explicitly quantify interaction uncertainty and dynamically generate context-aware cost weights for the downstream planner. Furthermore, a physics-informed autoregressive decoder is designed to provide kinematically feasible initializations for the differentiable nonlinear optimizer, enabling all operations to be jointly optimized under a unified objective. To evaluate the effectiveness of the proposed framework, we conducted systematic experiments on the Waymo Open Motion Dataset and nuPlan benchmark. Empirical results demonstrate that our approach achieves state-of-the-art non-reactive performance with a 98.4% success rate on the Waymo Open Motion Dataset. In the reactive scenarios of the nuPlan Test-hard benchmark, it surpasses several representative pure learning baselines and traditional hybrid planners. Furthermore, ablation studies confirm that cost regularization prevents weight collapse, and physically feasible initialization is essential to ensure optimizer stability, while adaptive cost generation is key to maintaining desired planning performance across heterogeneous scenarios. Ultimately, the framework effectively synergizes the high adaptability of data-driven learning with the rigorous safety of optimization-based control.