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.

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