  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.
