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Exploring Probabilistic Distance Fields in Robotics

Lan Wu

TL;DR

Robotic missions require unified representations across localisation, mapping, planning, and interaction, but task-specific representations are costly. We propose a Gaussian Process Distance Field ($GPDF$), a probabilistic, uncertainty-aware representation that models the core properties of the Euclidean Distance Field ($EDF$) including gradients and surface normals. The approach uses a regularised $Eikonal$ equation solved by a $\log$-transformed $GP$ to approximate the $EDF$, enabling continuous predictions without post-processing, and it introduces an uncertainty proxy via a reverting GP distance field. Key contributions include a unified representation for localisation, mapping and planning; efficiency techniques via submapping ($LanRAL20$) and pseudo inputs ($wu2023pseudo$); and a roadmap toward online operation, human-robot collaboration, robust localisation, a GP-based planner, and temporal/semantic extensions.

Abstract

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.

Exploring Probabilistic Distance Fields in Robotics

TL;DR

Robotic missions require unified representations across localisation, mapping, planning, and interaction, but task-specific representations are costly. We propose a Gaussian Process Distance Field (), a probabilistic, uncertainty-aware representation that models the core properties of the Euclidean Distance Field () including gradients and surface normals. The approach uses a regularised equation solved by a -transformed to approximate the , enabling continuous predictions without post-processing, and it introduces an uncertainty proxy via a reverting GP distance field. Key contributions include a unified representation for localisation, mapping and planning; efficiency techniques via submapping () and pseudo inputs (); and a roadmap toward online operation, human-robot collaboration, robust localisation, a GP-based planner, and temporal/semantic extensions.

Abstract

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.
Paper Structure (11 sections, 2 figures)

This paper contains 11 sections, 2 figures.

Table of Contents

  1. Introduction
  2. Progress to Date
  3. Probabilistic Distance Fields
  4. Unified Representation
  5. Towards Efficiency of the Probabilistic Representation
  6. Ongoing and Future Work
  7. Online Operation of Probabilistic Distance Fields
  8. Capability for Human-Robot Collaboration
  9. Robust Performance for Localisation
  10. Theoretical New Planner Based on GP Distance Fields
  11. Vision for Future Work

Figures (2)

  • Figure 1: Block Diagram of the proposed GP-based representation architecture for multiple robotics applications and future research objectives.
  • Figure 2: a) Online GPDF framework performance for Sec. \ref{['sec:online operation']}. b) Dynamical GPDF for Human-robot collaboration application for Sec. \ref{['sec:HRI']}.