Our approach, named ORDER, uses a three-step training process. In the next parts of this section, we'll explain the methods, structures, and settings we use in each of After that, we'll talk about how we set up and carried out our experiments. In this section, we'll break down the design of the state encoder, how we decided on the best We used a grid search strategy to find the optimal hyper-parameters for our experiments. This allowed each observation dimension to match up with a state factor. We summarize the training process in Algorithm 1.

Policy network parameter sharing is a commonly used technique in advanced deep multi-agent reinforcement learning (MARL) algorithms to improve learning efficiency by reducing the number of policy parameters and sharing experiences among agents. Nevertheless, agents that share the policy parameters tend to learn similar behaviors. To encourage multi-agent diversity, prior works typically maximize the mutual information between trajectories and agent identities using variational inference. However, this category of methods easily leads to inefficient exploration due to limited trajectory visitations. To resolve this limitation, inspired by the learning of pre-trained models, in this paper, we propose a novel Contrastive Trajectory Representation (CTR) method based on learning distinguishable trajectory representations to encourage multi-agent diversity.

Urban analytics increasingly relies on AI-driven trajectory analysis, yet current approaches suffer from methodological fragmentation: trajectory learning captures movement patterns but ignores spatial context, while spatial embedding methods encode street networks but miss temporal dynamics. Three gaps persist: (1) lack of joint training that integrates spatial and temporal representations, (2) origin-agnostic treatment that ignores directional asymmetries in navigation ($A \to B \ne B \to A$), and (3) over-reliance on auxiliary data (POIs, imagery) rather than fundamental geometric properties of urban space. We introduce a conditional trajectory encoder that jointly learns spatial and movement representations while preserving origin-dependent asymmetries using geometric features. This framework decomposes urban navigation into shared cognitive patterns and origin-specific spatial narratives, enabling quantitative measurement of cognitive asymmetries across starting locations. Our bidirectional LSTM processes visibility ratio and curvature features conditioned on learnable origin embeddings, decomposing representations into shared urban patterns and origin-specific signatures through contrastive learning. Results from six synthetic cities and real-world validation on Beijing's Xicheng District demonstrate that urban morphology creates systematic cognitive inequalities. This provides urban planners quantitative tools for assessing experiential equity, offers architects insights into layout decisions' cognitive impacts, and enables origin-aware analytics for navigation systems.

Foundation models (FMs) have emerged as a powerful paradigm, enabling a diverse range of data analytics and knowledge discovery tasks across scientific fields. Inspired by the success of FMs, particularly large language models, researchers have recently begun to explore spatio-temporal foundation models (STFMs) to improve adaptability and generalization across a wide spectrum of spatio-temporal (ST) tasks. Despite rapid progress, a systematic investigation of trajectory foundation models (TFMs), a crucial subclass of STFMs, is largely lacking. This tutorial addresses this gap by offering a comprehensive overview of recent advances in TFMs, including a taxonomy of existing methodologies and a critical analysis of their strengths and limitations. In addition, the tutorial highlights open challenges and outlines promising research directions to advance spatio-temporal general intelligence through the development of robust, responsible, and transferable TFMs.

Trajectory representation learning (TRL) maps trajectories to vector embeddings and facilitates tasks such as trajectory classification and similarity search. State-of-the-art (SOTA) TRL methods transform raw GPS trajectories to grid or road trajectories to capture high-level travel semantics, i.e., regions and roads. However, they lose fine-grained spatial-temporal details as multiple GPS points are grouped into a single grid cell or road segment. To tackle this problem, we propose the BLUrred Encoding method, dubbed BLUE, which gradually reduces the precision of GPS coordinates to create hierarchical patches with multiple levels. The low-level patches are small and preserve fine-grained spatial-temporal details, while the high-level patches are large and capture overall travel patterns. To complement different patch levels with each other, our BLUE is an encoder-decoder model with a pyramid structure. At each patch level, a Transformer is used to learn the trajectory embedding at the current level, while pooling prepares inputs for the higher level in the encoder, and up-resolution provides guidance for the lower level in the decoder. BLUE is trained using the trajectory reconstruction task with the MSE loss. We compare BLUE with 8 SOTA TRL methods for 3 downstream tasks, the results show that BLUE consistently achieves higher accuracy than all baselines, outperforming the best-performing baselines by an average of 30.90%. Our code is available at https://github.com/slzhou-xy/BLUE.

Abstract-- Differential drive mobile manipulators combine the mobility of wheeled bases with the manipulation capability of multi-joint arms, enabling versatile applications but posing considerable challenges for trajectory planning due to their high-dimensional state space and nonholonomic constraints. This paper introduces T opA Y, an optimization-based planning framework designed for efficient and safe trajectory generation for differential drive mobile manipulators. The framework employs a hierarchical initial value acquisition strategy, including topological paths search for the base and parallel sampling for the manipulator . A polynomial trajectory representation with arc length-yaw parameterization is also proposed to reduce optimization complexity while preserving dynamic feasibility. Extensive simulation and real-world experiments validate that T opA Y achieves higher planning efficiency and success rates than state-of-the-art method in dense and complex scenarios. The source code is released at https://github.com/T Differential drive mobile manipulator (DDMoMa), comprising multi-joint manipulator(s) mounted on a differential drive base (DDB), integrates rich manipulation ability of manipulators and mobility of wheeled robots.

Recent learning-based methods have reduced the computational complexity of traditional trajectory similarity computation, but state-of-the-art (SOTA) methods still fail to leverage the comprehensive spectrum of trajectory information for similarity modeling. To tackle this problem, we propose \textbf{RePo}, a novel method that jointly encodes \textbf{Re}gion-wise and \textbf{Po}int-wise features to capture both spatial context and fine-grained moving patterns. For region-wise representation, the GPS trajectories are first mapped to grid sequences, and spatial context are captured by structural features and semantic context enriched by visual features. For point-wise representation, three lightweight expert networks extract local, correlation, and continuous movement patterns from dense GPS sequences. Then, a router network adaptively fuses the learned point-wise features, which are subsequently combined with region-wise features using cross-attention to produce the final trajectory embedding. To train RePo, we adopt a contrastive loss with hard negative samples to provide similarity ranking supervision. Experiment results show that RePo achieves an average accuracy improvement of 22.2\% over SOTA baselines across all evaluation metrics.