Extended reality (XR), blending virtual and real worlds, is a key application of future networks. While AI advancements enhance XR capabilities, they also impose significant computational and energy challenges on lightweight XR devices. In this paper, we developed a distributed queue model for multi-task DNN inference, addressing issues of resource competition and queue coupling. In response to the challenges posed by the high energy consumption and limited resources of XR devices, we designed a dual time-scale joint optimization strategy for model partitioning and resource allocation, formulated as a bi-level optimization problem. This strategy aims to minimize the total energy consumption of XR devices while ensuring queue stability and adhering to computational and communication resource constraints. To tackle this problem, we devised a Lyapunov-guided Proximal Policy Optimization algorithm, named LyaPPO. Numerical results demonstrate that the LyaPPO algorithm outperforms the baselines, achieving energy conservation of 24.79% to 46.14% under varying resource capacities. Specifically, the proposed algorithm reduces the energy consumption of XR devices by 24.29% to 56.62% compared to baseline algorithms.

Event cameras provide a compelling alternative to traditional frame-based sensors, capturing dynamic scenes with high temporal resolution and low latency. Moving objects trigger events with precise timestamps along their trajectory, enabling smooth continuous-time estimation. However, few works have attempted to optimize the information loss during event representation construction, imposing a ceiling on this task. Fully exploiting event cameras requires representations that simultaneously preserve fine-grained temporal information, stable and characteristic 2D visual features, and temporally consistent information density--an unmet challenge in existing representations. We introduce Labits: Layered Bidirectional Time Surfaces, a simple yet elegant representation designed to retain all these features. Additionally, we propose a dedicated module for extracting active pixel local optical flow (APLOF), significantly boosting the performance. Our approach achieves an impressive 49% reduction in trajectory end-point error (TEPE) compared to the previous state-of-the-art on the MultiFlow dataset. The code will be released upon acceptance. As an emerging visual modality, event cameras offer unique and practical advantages. Compared to conventional frame-based cameras, they provide higher temporal resolution, greater dynamic range, higher efficiency, and lower latency (Gallego et al. (2020)). Furthermore, under stable lighting, event cameras are primarily sensitive to the edges of moving objects, naturally filtering out stationary objects while tracking moving ones. Their ultra-high temporal resolution also enables smoother and more continuous target tracking. In recent years, numerous papers leveraging this feature of event cameras have addressed topics such as feature tracking (Messikommer et al. (2023)), optical flow generation (Wan et al. (2024)), and video interpolation (He et al. (2022)) based on events. From an event camera's perspective, each moving point generates a discrete trajectory in the xyt space, with each triggered event representing a sampled point on this trajectory, along with its timestamp.

Distance functions are crucial in robotics for representing spatial relationships between the robot and the environment. It provides an implicit representation of continuous and differentiable shapes, which can seamlessly be combined with control, optimization, and learning techniques. While standard distance fields rely on the Euclidean metric, many robotic tasks inherently involve non-Euclidean structures. To this end, we generalize the use of Euclidean distance fields to more general metric spaces by solving a Riemannian eikonal equation, a first-order partial differential equation, whose solution defines a distance field and its associated gradient flow on the manifold, enabling the computation of geodesics and globally length-minimizing paths. We show that this \emph{geodesic distance field} can also be exploited in the robot configuration space. To realize this concept, we exploit physics-informed neural networks to solve the eikonal equation for high-dimensional spaces, which provides a flexible and scalable representation without the need for discretization. Furthermore, a variant of our neural eikonal solver is introduced, which enables the gradient flow to march across both task and configuration spaces. As an example of application, we validate the proposed approach in an energy-aware motion generation task. This is achieved by considering a manifold defined by a Riemannian metric in configuration space, effectively taking the property of the robot's dynamics into account. Our approach produces minimal-energy trajectories for a 7-axis Franka robot by iteratively tracking geodesics through gradient flow backpropagation.