With the emergence of compute-intensive and delay-sensitive applications in vehicular networks, unmanned aerial vehicles (UAVs) have emerged as a promising complement for vehicular edge computing due to the high mobility and flexible deployment. However, the existing UAV-assisted offloading strategies are insufficient in coordinating heterogeneous computing resources and adapting to dynamic network conditions. Hence, this paper proposes a dual-layer UAV-assisted edge computing architecture based on partial offloading, composed of the relay capability of high-altitude UAVs and the computing support of low-altitude UAVs. The proposed architecture enables efficient integration and coordination of heterogeneous resources. A joint optimization problem is formulated to minimize the system delay and energy consumption while ensuring the task completion rate. To solve the high-dimensional decision problem, we reformulate the problem as a Markov decision process and propose a hierarchical offloading scheme based on the soft actor-critic algorithm. The method decouples global and local decisions, where the global decisions integrate offloading ratios and trajectory planning into continuous actions, while the local scheduling is handled via designing a priority-based mechanism. Simulations are conducted and demonstrate that the proposed approach outperforms several baselines in task completion rate, system efficiency, and convergence speed, showing strong robustness and applicability in dynamic vehicular environments.
Multi-agent pathfinding (MAPF) is a common abstraction of multi-robot trajectory planning problems, where multiple homogeneous robots simultaneously move in the shared environment. While solving MAPF optimally has been proven to be NP-hard, scalable, and efficient, solvers are vital for real-world applications like logistics, search-and-rescue, etc. To this end, decentralized suboptimal MAPF solvers that leverage machine learning have come on stage. Building on the success of the recently introduced MAPF-GPT, a pure imitation learning solver, we introduce MAPF-GPT-DDG. This novel approach effectively fine-tunes the pre-trained MAPF model using centralized expert data. Leveraging a novel delta-data generation mechanism, MAPF-GPT-DDG accelerates training while significantly improving performance at test time. Our experiments demonstrate that MAPF-GPT-DDG surpasses all existing learning-based MAPF solvers, including the original MAPF-GPT, regarding solution quality across many testing scenarios. Remarkably, it can work with MAPF instances involving up to 1 million agents in a single environment, setting a new milestone for scalability in MAPF domains.
Diffusion models have demonstrated exceptional visual quality in video generation, making them promising for autonomous driving world modeling. However, existing video diffusion-based world models struggle with flexible-length, long-horizon predictions and integrating trajectory planning. This is because conventional video diffusion models rely on global joint distribution modeling of fixed-length frame sequences rather than sequentially constructing localized distributions at each timestep. In this work, we propose Epona, an autoregressive diffusion world model that enables localized spatiotemporal distribution modeling through two key innovations: 1) Decoupled spatiotemporal factorization that separates temporal dynamics modeling from fine-grained future world generation, and 2) Modular trajectory and video prediction that seamlessly integrate motion planning with visual modeling in an end-to-end framework. Our architecture enables high-resolution, long-duration generation while introducing a novel chain-of-forward training strategy to address error accumulation in autoregressive loops. Experimental results demonstrate state-of-the-art performance with 7.4\% FVD improvement and minutes longer prediction duration compared to prior works. The learned world model further serves as a real-time motion planner, outperforming strong end-to-end planners on NAVSIM benchmarks. Code will be publicly available at \href{https://github.com/Kevin-thu/Epona/}{https://github.com/Kevin-thu/Epona/}.
Diffusion models have recently emerged as a powerful approach for trajectory planning. However, their inherently non-sequential nature limits their effectiveness in long-horizon reasoning tasks at test time. The recently proposed Monte Carlo Tree Diffusion (MCTD) offers a promising solution by combining diffusion with tree-based search, achieving state-of-the-art performance on complex planning problems. Despite its strengths, our analysis shows that MCTD incurs substantial computational overhead due to the sequential nature of tree search and the cost of iterative denoising. To address this, we propose Fast-MCTD, a more efficient variant that preserves the strengths of MCTD while significantly improving its speed and scalability. Fast-MCTD integrates two techniques: Parallel MCTD, which enables parallel rollouts via delayed tree updates and redundancy-aware selection; and Sparse MCTD, which reduces rollout length through trajectory coarsening. Experiments show that Fast-MCTD achieves up to 100x speedup over standard MCTD while maintaining or improving planning performance. Remarkably, it even outperforms Diffuser in inference speed on some tasks, despite Diffuser requiring no search and yielding weaker solutions. These results position Fast-MCTD as a practical and scalable solution for diffusion-based inference-time reasoning.
Recent advancements in Vision-Language-Action (VLA) models have shown promise for end-to-end autonomous driving by leveraging world knowledge and reasoning capabilities. However, current VLA models often struggle with physically infeasible action outputs, complex model structures, or unnecessarily long reasoning. In this paper, we propose AutoVLA, a novel VLA model that unifies reasoning and action generation within a single autoregressive generation model for end-to-end autonomous driving. AutoVLA performs semantic reasoning and trajectory planning directly from raw visual inputs and language instructions. We tokenize continuous trajectories into discrete, feasible actions, enabling direct integration into the language model. For training, we employ supervised fine-tuning to equip the model with dual thinking modes: fast thinking (trajectory-only) and slow thinking (enhanced with chain-of-thought reasoning). To further enhance planning performance and efficiency, we introduce a reinforcement fine-tuning method based on Group Relative Policy Optimization (GRPO), reducing unnecessary reasoning in straightforward scenarios. Extensive experiments across real-world and simulated datasets and benchmarks, including nuPlan, nuScenes, Waymo, and CARLA, demonstrate the competitive performance of AutoVLA in both open-loop and closed-loop settings. Qualitative results showcase the adaptive reasoning and accurate planning capabilities of AutoVLA in diverse scenarios.
Low Altitude Economy (LAE) networks own transformative potential in urban mobility, emergency response, and aerial logistics. However, these networks face significant challenges in spectrum management, interference mitigation, and real-time coordination across dynamic and resource-constrained environments. After addressing these challenges, this study explores three core elements for enabling intelligent LAE networks as follows machine learning-based spectrum sensing and coexistence, artificial intelligence (AI)-optimized resource allocation and trajectory planning, and testbed-driven validation and standardization. We highlight how federated and reinforcement learning techniques support decentralized, adaptive decision-making under mobility and energy constraints. In addition, we discuss the role of real-world platforms such as AERPAW in bridging the gap between simulation and deployment and enabling iterative system refinement under realistic conditions. This study aims to provide a forward-looking roadmap toward developing efficient and interoperable AI-driven LAE ecosystems.
In this work, we provide an extended discussion of a new approach to explainable Reinforcement Learning called Diverse Near-Optimal Alternatives (DNA), first proposed at L4DC 2025. DNA seeks a set of reasonable "options" for trajectory-planning agents, optimizing policies to produce qualitatively diverse trajectories in Euclidean space. In the spirit of explainability, these distinct policies are used to "explain" an agent's options in terms of available trajectory shapes from which a human user may choose. In particular, DNA applies to value function-based policies on Markov decision processes where agents are limited to continuous trajectories. Here, we describe DNA, which uses reward shaping in local, modified Q-learning problems to solve for distinct policies with guaranteed epsilon-optimality. We show that it successfully returns qualitatively different policies that constitute meaningfully different "options" in simulation, including a brief comparison to related approaches in the stochastic optimization field of Quality Diversity. Beyond the explanatory motivation, this work opens new possibilities for exploration and adaptive planning in RL.
The rapid growth of the low-altitude economy has driven the widespread adoption of unmanned aerial vehicles (UAVs). This growing deployment presents new challenges for UAV trajectory planning in complex urban environments. However, existing studies often overlook key factors, such as urban airspace constraints and economic efficiency, which are essential in low-altitude economy contexts. Deep reinforcement learning (DRL) is regarded as a promising solution to these issues, while its practical adoption remains limited by low learning efficiency. To overcome this limitation, we propose a novel UAV trajectory planning framework that combines DRL with large language model (LLM) reasoning to enable safe, compliant, and economically viable path planning. Experimental results demonstrate that our method significantly outperforms existing baselines across multiple metrics, including data collection rate, collision avoidance, successful landing, regulatory compliance, and energy efficiency. These results validate the effectiveness of our approach in addressing UAV trajectory planning key challenges under constraints of the low-altitude economy networking.
We study multi-agent reinforcement learning (MARL) for tasks in complex high-dimensional environments, such as autonomous driving. MARL is known to suffer from the \textit{partial observability} and \textit{non-stationarity} issues. To tackle these challenges, information sharing is often employed, which however faces major hurdles in practice, including overwhelming communication overhead and scalability concerns. By making use of generative AI embodied in world model together with its latent representation, we develop {\it CALL}, \underline{C}ommunic\underline{a}tive Wor\underline{l}d Mode\underline{l}, for MARL, where 1) each agent first learns its world model that encodes its state and intention into low-dimensional latent representation with smaller memory footprint, which can be shared with other agents of interest via lightweight communication; and 2) each agent carries out ego-centric learning while exploiting lightweight information sharing to enrich her world model, and then exploits its generalization capacity to improve prediction for better planning. We characterize the gain on the prediction accuracy from the information sharing and its impact on performance gap. Extensive experiments are carried out on the challenging local trajectory planning tasks in the CARLA platform to demonstrate the performance gains of using \textit{CALL}.
World models are emerging as a transformative paradigm in artificial intelligence, enabling agents to construct internal representations of their environments for predictive reasoning, planning, and decision-making. By learning latent dynamics, world models provide a sample-efficient framework that is especially valuable in data-constrained or safety-critical scenarios. In this paper, we present a comprehensive overview of world models, highlighting their architecture, training paradigms, and applications across prediction, generation, planning, and causal reasoning. We compare and distinguish world models from related concepts such as digital twins, the metaverse, and foundation models, clarifying their unique role as embedded cognitive engines for autonomous agents. We further propose Wireless Dreamer, a novel world model-based reinforcement learning framework tailored for wireless edge intelligence optimization, particularly in low-altitude wireless networks (LAWNs). Through a weather-aware UAV trajectory planning case study, we demonstrate the effectiveness of our framework in improving learning efficiency and decision quality.
Visual language models (VLMs) have attracted increasing interest in autonomous driving due to their powerful reasoning capabilities. However, existing VLMs typically utilize discrete text Chain-of-Thought (CoT) tailored to the current scenario, which essentially represents highly abstract and symbolic compression of visual information, potentially leading to spatio-temporal relationship ambiguity and fine-grained information loss. Is autonomous driving better modeled on real-world simulation and imagination than on pure symbolic logic? In this paper, we propose a spatio-temporal CoT reasoning method that enables models to think visually. First, VLM serves as a world model to generate unified image frame for predicting future world states: where perception results (e.g., lane divider and 3D detection) represent the future spatial relationships, and ordinary future frame represent the temporal evolution relationships. This spatio-temporal CoT then serves as intermediate reasoning steps, enabling the VLM to function as an inverse dynamics model for trajectory planning based on current observations and future predictions. To implement visual generation in VLMs, we propose a unified pretraining paradigm integrating visual generation and understanding, along with a progressive visual CoT enhancing autoregressive image generation. Extensive experimental results demonstrate the effectiveness of the proposed method, advancing autonomous driving towards visual reasoning.
Autonomous UAV operation necessitates reliable mathematical reasoning for tasks such as trajectory planning and power management. While traditional flight control relies on hardcoded equations, recent Large Language Models (LLMs) offer potential for more flexible problem-solving but struggle with reliably selecting and applying correct mathematical formulations and executing precise multi-step arithmetic. We propose RAG-UAV, a retrieval-augmented generation framework designed to improve the mathematical reasoning of several LLMs (including GPT o1/Turbo, Llama-3.2/3.3, Mistral, and DeepSeek R1) in UAV-specific contexts by providing access to relevant domain literature. To conduct an initial assessment, we introduce the UAV-Math-Bench, a small problem set comprising 20 UAV-centric mathematical problems across four difficulty levels. Our experiments demonstrate that incorporating retrieval substantially increases exact answer accuracy (achieving up to 75% with o1), reduces instances of incorrect formulation selection (from 25% without RAG to 5% with RAG), decreases numerical errors, reducing Mean Squared Error (MSE) by orders of magnitude for the best-performing models. This pilot study indicates that RAG can enable general-purpose LLMs to function as more reliable tools for engineering analysis, although direct real-time flight control requires further investigation and validation on a larger scale. All benchmark data, question and answer are publicly available.
Multi-sensor fusion is crucial for improving the performance and robustness of end-to-end autonomous driving systems. Existing methods predominantly adopt either attention-based flatten fusion or bird's eye view fusion through geometric transformations. However, these approaches often suffer from limited interpretability or dense computational overhead. In this paper, we introduce GaussianFusion, a Gaussian-based multi-sensor fusion framework for end-to-end autonomous driving. Our method employs intuitive and compact Gaussian representations as intermediate carriers to aggregate information from diverse sensors. Specifically, we initialize a set of 2D Gaussians uniformly across the driving scene, where each Gaussian is parameterized by physical attributes and equipped with explicit and implicit features. These Gaussians are progressively refined by integrating multi-modal features. The explicit features capture rich semantic and spatial information about the traffic scene, while the implicit features provide complementary cues beneficial for trajectory planning. To fully exploit rich spatial and semantic information in Gaussians, we design a cascade planning head that iteratively refines trajectory predictions through interactions with Gaussians. Extensive experiments on the NAVSIM and Bench2Drive benchmarks demonstrate the effectiveness and robustness of the proposed GaussianFusion framework. The source code will be released at https://github.com/Say2L/GaussianFusion.
End-to-end planning systems for autonomous driving are improving rapidly, especially in closed-loop simulation environments like CARLA. Many such driving systems either do not consider uncertainty as part of the plan itself, or obtain it by using specialized representations that do not generalize. In this paper, we propose EnDfuser, an end-to-end driving system that uses a diffusion model as the trajectory planner. EnDfuser effectively leverages complex perception information like fused camera and LiDAR features, through combining attention pooling and trajectory planning into a single diffusion transformer module. Instead of committing to a single plan, EnDfuser produces a distribution of candidate trajectories (128 for our case) from a single perception frame through ensemble diffusion. By observing the full set of candidate trajectories, EnDfuser provides interpretability for uncertain, multi-modal future trajectory spaces, where there are multiple plausible options. EnDfuser achieves a competitive driving score of 70.1 on the Longest6 benchmark in CARLA with minimal concessions on inference speed. Our findings suggest that ensemble diffusion, used as a drop-in replacement for traditional point-estimate trajectory planning modules, can help improve the safety of driving decisions by modeling the uncertainty of the posterior trajectory distribution.
Embodied visual tracking is a fundamental skill in Embodied AI, enabling an agent to follow a specific target in dynamic environments using only egocentric vision. This task is inherently challenging as it requires both accurate target recognition and effective trajectory planning under conditions of severe occlusion and high scene dynamics. Existing approaches typically address this challenge through a modular separation of recognition and planning. In this work, we propose TrackVLA, a Vision-Language-Action (VLA) model that learns the synergy between object recognition and trajectory planning. Leveraging a shared LLM backbone, we employ a language modeling head for recognition and an anchor-based diffusion model for trajectory planning. To train TrackVLA, we construct an Embodied Visual Tracking Benchmark (EVT-Bench) and collect diverse difficulty levels of recognition samples, resulting in a dataset of 1.7 million samples. Through extensive experiments in both synthetic and real-world environments, TrackVLA demonstrates SOTA performance and strong generalizability. It significantly outperforms existing methods on public benchmarks in a zero-shot manner while remaining robust to high dynamics and occlusion in real-world scenarios at 10 FPS inference speed. Our project page is: https://pku-epic.github.io/TrackVLA-web.
The synthesis of Ohman's VCV sequences with intervocalic plosive consonants was first achieved 30 years ago using the DRM model. However, this approach remains primarily acoustic and lacks articulatory constraints. In this study, the same 75 VCVs are analyzed, but generated with the Maeda model, using trajectory planning that differentiates vowel-to-vowel transitions from consonantal influences. Synthetic data exhibit similar characteristics to Ohman's sequences, including the presence of S-shaped F2 trajectories. Furthermore, locus equations (LEs) for F2 and F3 are computed from synthetic CV data to investigate their underlying determinism, leading to a reassessment of conventional interpretations. The findings indicate that, although articulatory planning is structured separately for vowel and consonant groups, S-shaped F2 trajectories emerge from a composite mechanism governed by the coordinated synergy of all articulators.
Decision Transformer (DT) has recently demonstrated strong generalizability in dynamic resource allocation within unmanned aerial vehicle (UAV) networks, compared to conventional deep reinforcement learning (DRL). However, its performance is hindered due to zero-padding for varying state dimensions, inability to manage long-term energy constraint, and challenges in acquiring expert samples for few-shot fine-tuning in new scenarios. To overcome these limitations, we propose an attention-enhanced prompt Decision Transformer (APDT) framework to optimize trajectory planning and user scheduling, aiming to minimize the average age of information (AoI) under long-term energy constraint in UAV-assisted Internet of Things (IoT) networks. Specifically, we enhance the convenional DT framework by incorporating an attention mechanism to accommodate varying numbers of terrestrial users, introducing a prompt mechanism based on short trajectory demonstrations for rapid adaptation to new scenarios, and designing a token-assisted method to address the UAV's long-term energy constraint. The APDT framework is first pre-trained on offline datasets and then efficiently generalized to new scenarios. Simulations demonstrate that APDT achieves twice faster in terms of convergence rate and reduces average AoI by $8\%$ compared to conventional DT.
Safe and feasible trajectory planning is essential for real-world autonomous driving systems. However, existing learning-based planning methods often rely on expert demonstrations, which not only lack explicit safety awareness but also risk inheriting unsafe behaviors such as speeding from suboptimal human driving data. Inspired by the success of large language models, we propose Plan-R1, a novel two-stage trajectory planning framework that formulates trajectory planning as a sequential prediction task, guided by explicit planning principles such as safety, comfort, and traffic rule compliance. In the first stage, we train an autoregressive trajectory predictor via next motion token prediction on expert data. In the second stage, we design rule-based rewards (e.g., collision avoidance, speed limits) and fine-tune the model using Group Relative Policy Optimization (GRPO), a reinforcement learning strategy, to align its predictions with these planning principles. Experiments on the nuPlan benchmark demonstrate that our Plan-R1 significantly improves planning safety and feasibility, achieving state-of-the-art performance. Our code will be made public soon.
While autonomous driving (AD) stacks struggle with decision making under partial observability and real-world complexity, human drivers are capable of commonsense reasoning to make near-optimal decisions with limited information. Recent work has attempted to leverage finetuned Vision-Language Models (VLMs) for trajectory planning at inference time to emulate human behavior. Despite their success in benchmark evaluations, these methods are often impractical to deploy (a 70B parameter VLM inference at merely 8 tokens per second requires more than 160G of memory), and their monolithic network structure prohibits safety decomposition. To bridge this gap, we propose VLM-Embedded Reasoning for autonomous Driving (VERDI), a training-time framework that distills the reasoning process and commonsense knowledge of VLMs into the AD stack. VERDI augments modular differentiable end-to-end (e2e) AD models by aligning intermediate module outputs at the perception, prediction, and planning stages with text features explaining the driving reasoning process produced by VLMs. By encouraging alignment in latent space, VERDI enables the modular AD stack to internalize structured reasoning, without incurring the inference-time costs of large VLMs. We demonstrate the effectiveness of our method on the NuScenes dataset and find that VERDI outperforms existing e2e methods that do not embed reasoning by 10% in $\ell_{2}$ distance, while maintaining high inference speed.
Ensuring safe and human-like trajectory planning for automated vehicles amidst real-world uncertainties remains a critical challenge. While existing car-following models often struggle to consistently provide rigorous safety proofs alongside human-like acceleration and deceleration patterns, we introduce a novel multi-phase projection-based car-following model. This model is designed to balance safety and performance by incorporating bounded acceleration and deceleration rates while emulating key human driving principles. Building upon a foundation of fundamental driving principles and a multi-phase dynamical systems analysis (detailed in Part 1 of this study \citep{jin2025WA20-02_Part1}), we first highlight the limitations of extending standard models like Newell's with simple bounded deceleration. Inspired by human drivers' anticipatory behavior, we mathematically define and analyze projected braking profiles for both leader and follower vehicles, establishing safety criteria and new phase definitions based on the projected braking lead-vehicle problem. The proposed parsimonious model combines an extended Newell's model for nominal driving with a new control law for scenarios requiring projected braking. Using speed-spacing phase plane analysis, we provide rigorous mathematical proofs of the model's adherence to defined safe and human-like driving principles, including collision-free operation, bounded deceleration, and acceptable safe stopping distance, under reasonable initial conditions. Numerical simulations validate the model's superior performance in achieving both safety and human-like braking profiles for the stationary lead-vehicle problem. Finally, we discuss the model's implications and future research directions.