GoLF: Graphs over Lagrangian Fields

Robot representations for complex real spaces

GoLF: Graphs over Lagrangian Fields

GoLF helps a robot read space the way people often do: paying close attention to doors, boundaries, bottlenecks, and moving people, while keeping open space simple enough to act on quickly.

Charuvahan Adhivarahan and Karthik Dantu

Department of Computer Science & Engineering

University at Buffalo

Video abstract.

Abstract

Robots need representations that help them act, not merely store the world. A uniform grid gives every patch of space the same attention, even though a blank hallway, a doorway, a wall edge, and a moving pedestrian do not carry the same meaning for navigation. GoLF offers a different premise: a robot's map should spend its detail where the world asks for care and stay sparse where space is easy to understand. It turns spatial fields into compact graph-like maps that preserve the parts of an environment that matter for action: boundaries, narrow passages, open regions, and the local context around people. In the paper experiments, this representation supports planning across curved obstacle layouts, corridor-heavy maps, residential floor plans, and real indoor maps. Compared with dense grid-based planning, GoLF enables substantially faster planning while keeping routes close to the fine-grid reference paths. The same representation also supports socially aware navigation, where a robot must not only reach a goal but also yield, wait, and move around people in ways that make sense in shared spaces. The larger aim is to make robot maps more humane: less like exhaustive storage, more like situated understanding. GoLF treats representation as a bridge between perception and action, so that robots can move through built environments with more speed, context, and social care.

Why This Matters

Robot navigation often becomes a representational bottleneck: larger maps become expensive, cluttered spaces become fragile, and human spaces require judgments that raw geometry alone does not provide. GoLF reframes the problem around attention. Instead of asking a robot to reason over every pixel of a map, it gives the robot a smaller, structured view of what is relevant. That compact view makes navigation easier to run at scale, easier to compare across environments, and easier to interpret when behavior succeeds or fails. It also sharpens a broader question for embodied intelligence: what should a robot choose to remember about the world when it has to act in real time?

GoLF representation over smooth curved obstacle regions
Curved obstacle regions
GoLF representation over rooms connected by narrow corridors
Narrow passages
GoLF representation over a residential floor plan
Residential layouts

Applications

Faster Planning Through Indoor Space

GoLF can serve as the map a planner uses directly. In the paper's experiments, that shift changes the scale of the planning problem: planners search over a compact spatial structure instead of a dense image grid. The result is much faster planning across several kinds of environments, with only small route length tradeoffs in the reported benchmarks. The practical value is not just speed. Faster planning makes it easier to run larger sweeps, test policies across many floor plans, and study navigation behavior without letting map resolution dominate the question.

Fast path planning teaser: GoLF supports efficient routes through structured indoor environments.

Pedestrian Tracking in Shared Spaces

GoLF can also support pedestrian tracking, where the important question is not only where each person is now, but how motion unfolds through the surrounding space. The teaser below shows this idea in a shared indoor scene: people move through a structured environment while the representation keeps their motion tied to the places, passages, and nearby activity that give it context. This is useful for robotics because a robot that shares space with people needs more than isolated detections. It needs a compact view of how people are moving, where interactions may form, and which parts of the scene deserve attention as the situation changes.

Pedestrian tracking teaser: GoLF-style structure over people moving through a shared indoor scene.

Socially Aware Navigation

Shared spaces are not only geometric. Doorways, hallways, and bottlenecks carry social meaning because people move through them, pause in them, and negotiate right of way around them. GoLF gives a learning-based navigation system a structured way to relate human motion to the surrounding map context. In simulated and real-world demonstrations, the GoLF-based navigation setup supports behavior that is more than collision avoidance. The robot can follow a route when the way is clear, slow down near a constrained passage, yield to a passing person, and continue after the interaction becomes appropriate again.

Robot begins along a planned route in a shared space
Plan
Robot approaches a narrow shared passage
Approach
Robot yields to a person in a bottleneck
Yield
Robot resumes navigation after yielding
Resume

Manipulation in Contact-Rich Scenes

GoLF can also help describe manipulation, where a robot has to reason about objects, hands, surfaces, and contact at the same time. In the teaser below, the representation follows a robot arm, gripper, table, and blocks as separate but connected parts of the scene, with links appearing when objects come close enough to interact. This matters because manipulation is not only about where objects are; it is about how relationships between objects change as a robot acts. A compact, structured view of those relationships could make it easier to inspect robot behavior, compare manipulation attempts, and eventually build systems that understand when an action is starting to matter physically. This is early, unpublished work, so we present it here as an application teaser rather than a technical result.

Manipulation teaser: GoLF-style scene graphs projected onto a robot stacking episode.

A General Lens For Physical Fields

Although this project page focuses on robot navigation, the premise behind GoLF is broader. Many physical quantities are uneven: some regions are smooth and predictable, while others change sharply and deserve more attention. GoLF is a way to represent that unevenness without forcing every part of the field into the same resolution. That makes the idea relevant beyond floor plans. The paper frames GoLF as a representation for physical fields such as occupancy, motion, temperature, airflow, and related spatial quantities, with navigation as the central case study.

Resources

The paper, code, citation, and supporting materials will be added after publication.

Paper

Coming soon after publication.

Citation

BibTeX will be added with the final publication record.