The success of intelligent robotic missions relies on integrating various research tasks, each demanding distinct representations. Designing task-specific representations for each task is costly and impractical. Unified representations suitable for multiple tasks remain unexplored. My outline introduces a series of research outcomes of GP-based probabilistic distance field (GPDF) representation that mathematically models the fundamental property of Euclidean distance field (EDF) along with gradients, surface normals and dense reconstruction. The progress to date and ongoing future works show that GPDF has the potential to offer a unified solution of representation for multiple tasks such as localisation, mapping, motion planning, obstacle avoidance, grasping, human-robot collaboration, and dense visualisation. I believe that GPDF serves as the cornerstone for robots to accomplish more complex and challenging tasks. By leveraging GPDF, robots can navigate through intricate environments, understand spatial relationships, and interact with objects and humans seamlessly.

翻译：智能机器人任务的成功依赖于整合各种研究任务，每个任务都需要不同的表示方法。为每个任务设计特定于任务的表示既成本高昂又不切实际。适用于多个任务的统一表示仍有待探索。本文概述介绍了一系列基于高斯过程的概率距离场表示的研究成果，该表示从数学上建模了欧几里得距离场的基本属性，同时包含梯度、表面法向量和密集重建。迄今为止的进展以及正在进行的未来工作表明，GPDF有潜力为定位、建图、运动规划、避障、抓取、人机协作和密集可视化等多个任务提供统一的表示解决方案。我相信，GPDF是机器人完成更复杂、更具挑战性任务的基石。通过利用GPDF，机器人能够在复杂环境中导航、理解空间关系，并无缝地与物体和人类进行交互。