Bayesian-Symbolic Integration for Uncertainty-Aware Parking Prediction

Existing end-to-end autonomous driving models rely heavily on purely data-driven inductive reasoning. This "black-box" nature leads to a lack of interpretability and absolute safety guarantees in complex, long-tail scenarios. To overcome this bottleneck, we propose a novel neuro-symbolic trajectory planning framework that seamlessly integrates rigorous deductive reasoning into end-to-end neural networks. Specifically, our framework utilizes a Large Language Model (LLM) to dynamically extract scene rules and employs an Answer Set Programming (ASP) solver for deterministic logical arbitration, generating safe and traceable discrete driving decisions. To bridge the gap between discrete symbols and continuous trajectories, we introduce a decision-conditioned decoding mechanism that transforms high-level logical decisions into learnable embedding vectors, simultaneously constraining the planning query and the physical initial velocity of a differentiable Kinematic Bicycle Model (KBM). By combining KBM-generated physical baseline trajectories with neural residual corrections, our approach inherently guarantees kinematic feasibility while ensuring a high degree of transparency. On the nuScenes benchmark, our method comprehensively outperforms the state-of-the-art baseline MomAD, reducing the L2 mean error to 0.57 m, decreasing the collision rate to 0.075%, and optimizing trajectory prediction consistency (TPC) to 0.47 m.

Trajectory prediction seeks to forecast the future motion of dynamic entities, such as vehicles and pedestrians, given a temporal horizon of historical movement data and environmental context. A central challenge in this domain is the inherent uncertainty in real-time maps, arising from two primary sources: (1) positional inaccuracies due to sensor limitations or environmental occlusions, and (2) semantic errors stemming from misinterpretations of scene context. To address these challenges, we propose a novel unified framework that jointly models positional and semantic uncertainties and explicitly integrates them into the trajectory prediction pipeline. Our approach employs a dual-head architecture to independently estimate semantic and positional predictions in a dual-pass manner, deriving prediction variances as uncertainty indicators in an end-to-end fashion. These uncertainties are subsequently fused with the semantic and positional predictions to enhance the robustness of trajectory forecasts. We evaluate our uncertainty-aware framework on the nuScenes real-world driving dataset, conducting extensive experiments across four map estimation methods and two trajectory prediction baselines. Results verify that our method (1) effectively quantifies map uncertainties through both positional and semantic dimensions, and (2) consistently improves the performance of existing trajectory prediction models across multiple metrics, including minimum Average Displacement Error (minADE), minimum Final Displacement Error (minFDE), and Miss Rate (MR). Code will available at https://github.com/JT-Sun/UATP.

Task planning often suffers from severe efficiency bottlenecks when robots must reason over long-horizon action sequences under complex logical constraints, including object affordances, spatial relationships, and sequential action dependencies. Recent neuro-symbolic methods improve planning efficiency by learning object-importance scores to prune task-irrelevant objects, but they typically rely on fixed offline supervision generated from full search spaces. This creates a train-test mismatch: at deployment, the planner operates in pruned search spaces induced by the model's own imperfect predictions, leading to exposure bias and degraded planning performance. To address this challenge, we formulate object-importance learning for task planning as an imperative learning-based bilevel optimization problem. The upper level optimizes a neural scorer, while the lower level solves a symbolic planning problem in the score-pruned search space. To stabilize this learning process, we introduce a 3R strategy into the lower-level planning, using parallel Repair, Restart, and Rollback recovery to provide reliable and adaptive feedback for upper-level learning. Experiments on three challenging benchmarks demonstrate state-of-the-art performance, including an 80.04% reduction in failure rate and a 57.14% reduction in planning time. We further validate the framework on a quadruped-based mobile manipulator in simulation and the real world, demonstrating its potential for efficient and deployable neuro-symbolic task planning.