Motion Planning

We present a novel framework for \(\varepsilon\)-optimally solving two-player zero-sum partially observable stochastic games (zs-POSGs). These games pose a major challenge due to the absence of a principled connection with dynamic programming (DP) techniques developed for two-player zero-sum stochastic games (zs-SGs). Prior attempts at transferring solution methods have lacked a lossless reduction—defined here as a transformation that preserves value functions, equilibrium strategies, and optimality structure—thereby limiting generalisation to ad hoc algorithms. This work introduces the first lossless reduction from zs-POSGs to transition-independent zs-SGs, enabling the principled application of a broad class of DP-based methods. We show empirically that point-based value iteration (PBVI) algorithms, applied via this reduction, produce \(\varepsilon\)-optimal strategies across a range of benchmark domains, consistently matching or outperforming existing state-of-the-art methods. Our results open a systematic pathway for algorithmic and theoretical transfer from SGs to partially observable settings.

Safety validation, which assesses the safety of an autonomous system's motion planning decisions, is critical for the safe deployment of autonomous vehicles. Existing input validation techniques from other machine learning domains, such as image classification, face unique challenges in motion planning due to its contextual properties, including complex inputs and one-to-many mapping. Furthermore, current output validation methods in autonomous driving primarily focus on open-loop trajectory prediction, which is ill-suited for the closed-loop nature of motion planning. We introduce REDOUBT, the first systematic safety validation framework for autonomous vehicle motion planning that employs a duo mechanism, simultaneously inspecting input distributions and output uncertainty. REDOUBT identifies previously overlooked unsafe modes arising from the interplay of In-Distribution/Out-of-Distribution (OOD) scenarios and certain/uncertain planning decisions. We develop specialized solutions for both OOD detection via latent flow matching and decision uncertainty estimation via an energy-based approach. Our extensive experiments demonstrate that both modules outperform existing approaches, under both open-loop and closed-loop evaluation settings. Our codes are available at: https://github.com/sgNicola/Redoubt.

Dense and versatile image representations underpin the success of virtually all computer vision applications. However, state-of-the-art networks, such as transformers, produce low-resolution feature grids, which are suboptimal for dense prediction tasks. To address this limitation, we present *FlowFeat*, a high-resolution and multi-task feature representation. The key ingredient behind FlowFeat is a novel distillation technique that embeds a distribution of plausible apparent motions, or *motion profiles*. By leveraging optical flow networks and diverse video data, we develop an effective self-supervised training framework that statistically approximates the apparent motion. With its remarkable level of spatial detail, FlowFeat encodes a compelling degree of geometric and semantic cues while exhibiting high temporal consistency. Empirically, FlowFeat significantly enhances the representational power of five state-of-the-art encoders and alternative upsampling strategies across three dense tasks: video object segmentation, monocular depth estimation and semantic segmentation. Training FlowFeat is computationally inexpensive and robust to inaccurate flow estimation, remaining highly effective even when using unsupervised flow networks. Our work takes a step forward towards reliable and versatile dense image representations.

The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step random walk transition kernels. In this framework, inner product or equivalently Euclidean distance between embeddings encode similarity between locations in terms of their transition probability across multiple scales, forming a cognitive map of adjacency. The combination of non-negativity and inner-product structure naturally induces sparsity, providing a principled explanation for the localized firing fields of place cells without imposing explicit constraints. The temporal parameter that defines the diffusion scale also determines field size, aligning with the hippocampal dorsoventral hierarchy. Our approach constructs global representations efficiently through recursive composition of local transitions, enabling smooth, trap-free navigation and preplay-like trajectory generation. Moreover, theta phase arises intrinsically as the angular relation between embeddings, linking spatial and temporal coding within a single representational geometry.

Object concepts play a foundational role in human visual cognition, enabling perception, memory, and interaction in the physical world. Inspired by findings in developmental psychology—where infants are shown to acquire object understanding through observation of motion—we propose a biologically inspired framework for learning object-centric visual representations in an unsupervised manner. We were inspired by the insight that motion boundary serves as a strong signal for object-level grouping, which can be used to derive pseudo-instance supervision from raw videos. Concretely, we generate motion-based instance masks using off-the-shelf optical flow and clustering algorithms, and use them to train visual encoders via contrastive learning. Our framework is fully label-free and does not rely on camera calibration, making it scalable to large-scale unstructured video data. We evaluate our approach on three downstream tasks spanning both low-level (monocular depth estimation) and high-level (3D object detection and occupancy prediction) vision. Our models outperform previous supervised and self-supervised baselines and demonstrate strong generalization to unseen scenes. These results suggest that motion-induced object representations offer a compelling alternative to existing vision foundation models, capturing a crucial but overlooked level of abstraction: the visual instance. The implementation can be found here: https://github.com/yulemao/Object_Concepts_Emerge_from_Motion

Motion simulation, prediction and planning are foundational tasks in autonomous driving, each essential for modeling and reasoning about dynamic traffic scenarios. While often addressed in isolation due to their differing objectives, such as generating diverse motion states or estimating optimal trajectories, these tasks inherently depend on shared capabilities: understanding multi-agent interactions, modeling motion behaviors, and reasoning over temporal and spatial dynamics. Despite this underlying commonality, existing approaches typically adopt specialized model designs, which hinders cross-task generalization and system scalability. More critically, this separation overlooks the potential mutual benefits among tasks. Motivated by these observations, we propose **UniMotion**, a unified motion framework that captures shared structures across motion tasks while accommodating their individual requirements. Built on a decoder-only Transformer architecture, UniMotion employs dedicated interaction modes and tailored training strategies to simultaneously support these motion tasks. This unified design not only enables joint optimization and representation sharing but also allows for targeted fine-tuning to specialize in individual tasks when needed. Extensive experiments on the Waymo Open Motion Dataset (WOMD) demonstrate that joint training leads to robust generalization and effective task integration. With further fine-tuning, UniMotion achieves state-of-the-art performance across a range of motion tasks, establishing it as a versatile and scalable solution for autonomous driving.

World models allow agents to simulate the consequences of actions in imagined environments for planning, control, and long-horizon decision-making. However, existing autoregressive world models struggle with visually coherent predictions due to disrupted spatial structure, inefficient decoding, and inadequate motion modeling. In response, we propose Scale-wise Autoregression with Motion PrOmpt (SAMPO), a hybrid framework that combines visual autoregressive modeling for intra-frame generation with causal modeling for next-frame generation. Specifically, SAMPO integrates temporal causal decoding with bidirectional spatial attention, which preserves spatial locality and supports parallel decoding within each scale. This design significantly enhances both temporal consistency and rollout efficiency. To further improve dynamic scene understanding, we devise an asymmetric multi-scale tokenizer that preserves spatial details in observed frames and extracts compact dynamic representations for future frames, optimizing both memory usage and model performance. Additionally, we introduce a trajectory-aware motion prompt module that injects spatiotemporal cues about object and robot trajectories, focusing attention on dynamic regions and improving temporal consistency and physical realism. Extensive experiments show that SAMPO achieves competitive performance in action-conditioned video prediction and model-based control, improving generation quality with 4.4× faster inference. We also evaluate SAMPO's zero-shot generalization and scaling behavior, demonstrating its ability to generalize to unseen tasks and benefit from larger model sizes.

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of 'flows' -- one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.

Modeling and forecasting nonlinear dynamics under distribution shifts is essential for robust decision-making in real-world systems. In this work, we propose **MetaKoopman**, a Bayesian meta-learning framework for modeling nonlinear dynamics through linear latent representations. MetaKoopman learns a Matrix Normal-Inverse Wishart (*MNIW*) prior over the Koopman operator, enabling closed-form Bayesian updates conditioned on recent trajectory segments. Moreover, it provides a closed-form posterior predictive distribution over future state trajectories, capturing both epistemic and aleatoric uncertainty in the learned dynamics. We evaluate MetaKoopman on a full-scale autonomous truck and trailer system across a wide range of adverse winter scenarios—including snow, ice, and mixed-friction conditions—as well as in simulated control tasks with diverse distribution shifts. MetaKoopman consistently outperforms prior approaches in multi-step prediction accuracy, uncertainty calibration and robustness to distributional shifts. Field experiments further demonstrate its effectiveness in dynamically feasible motion planning, particularly during evasive maneuvers and operation at the limits of traction. Project website: [https://mahmoud-selim.github.io/MetaKoopman/](https://mahmoud-selim.github.io/MetaKoopman/)

We propose RoPECraft, a training-free video motion transfer method for diffusion transformers that operates solely by modifying their rotary positional embeddings (RoPE). We first extract dense optical flow from a reference video, and utilize the resulting motion offsets to warp the complex-exponential tensors of RoPE, effectively encoding motion into the generation process. These embeddings are then further optimized during denoising time steps via trajectory alignment between the predicted and target velocities using a flow-matching objective. To keep the output faithful to the text prompt and prevent duplicate generations, we incorporate a regularization term based on the phase components of the reference video’s Fourier transform, projecting the phase angles onto a smooth manifold to suppress high-frequency artifacts. Experiments on benchmarks reveal that RoPECraft outperforms all recently published methods, both qualitatively and quantitatively.

Motion planning in high-dimensional continuous spaces remains challenging due to complex environments and computational constraints. Although learning-based planners, especially graph neural network (GNN)-based, have significantly improved planning performance, they still struggle with inaccurate graph construction and limited structural reasoning, constraining search efficiency and path quality. The human brain exhibits efficient planning through a two-stage Perception-Decision model. First, egocentric spatial representations from visual and proprioceptive input are constructed, and then semantic–episodic synergy is leveraged to support decision-making in uncertainty scenarios. Inspired by this process, we propose NeuroMP, a brain-inspired planning framework that learns to plan like the human brain. NeuroMP integrates a Perceptive Segment Selector inspired by visuospatial perception to construct safer graphs, and a Global Alignment Heuristic guide search in weakly connected graphs by modeling semantic-episodic synergistic decision-making. Experimental results demonstrate that NeuroMP significantly outperforms existing planning methods in efficiency and quality while maintaining a high success rate.

Integrating the understanding and reasoning capabilities of Large Language Models (LLM) with the self-learning capabilities of Reinforcement Learning (RL) enables more reliable driving performance under complex driving conditions. There has been a lot of work exploring LLM-Dominated RL methods in the field of autonomous driving motion planning. These methods, which utilize LLM to directly generate policies or provide decisive instructions during policy learning of RL agent, are centrally characterized by an over-reliance on LLM outputs. However, LLM outputs are susceptible to hallucinations. Evaluations show that state-of-the-art LLM indicates a non-hallucination rate of only approximately 57.95\% when assessed on essential driving-related tasks. Thus, in these methods, hallucinations from the LLM can directly jeopardize the performance of driving policies. This paper argues that maintaining relative independence between the LLM and the RL is vital for solving the hallucinations problem. Consequently, this paper is devoted to propose a novel LLM-Hinted RL paradigm. The LLM is used to generate semantic hints for state augmentation and policy optimization to assist RL agent in motion planning, while the RL agent counteracts potential erroneous semantic indications through policy learning to achieve excellent driving performance. Based on this paradigm, we propose the HCRMP (LLM-Hinted Contextual Reinforcement Learning Motion Planner) architecture, which is designed that includes ①Augmented Semantic Representation Module to extend state space. ②Contextual Stability Anchor Module enhances the reliability of multi-critic weight hints by utilizing information from the knowledge base. ③Semantic Cache Module is employed to seamlessly integrate LLM low-frequency guidance with RL high-frequency control. Extensive experiments in CARLA validate HCRMP's strong overall driving performance. HCRMP achieves a task success rate of up to 80.3\% under diverse driving conditions with different traffic densities. Under safety-critical driving conditions, HCRMP significantly reduces the collision rate by 11.4\%, which effectively improves the driving performance in complex scenarios.