Grid2Guide: Hybrid Indoor Navigation

• Grid2Guide is a hybrid indoor navigation framework that separates precise spatial reasoning via A* search from natural language generation using a fine-tuned transformer.
• It employs a five-stage pipeline that converts floor plans into a binary occupancy grid and compresses A* computed paths into clear, step-by-step instructions.
• The system achieves 100% route correctness with low computational latency, offering a scalable and infrastructure-free solution for complex indoor environments.

to=arxiv_search ￣影音先锋json {"^^^^^^^^3query3 OR ti:\3^^^^Guide\"^^^^^^^^3 OR ti:\3^^^^^^^^"Grid^^^^3 OR ti:\3^^^^Guide\"","max_results":^^^^3all:\3query3^^^^,"sort_by":"relevance"} to=search_arxiv Grid^^^^3 OR ti:\3^^^^Guide is a hybrid indoor navigation framework that combines the A* search algorithm with a Small LLM (SLM) to generate clear, human-readable route instructions from an indoor floor plan in environments where GPS and dedicated positioning infrastructure are unavailable or impractical. In its original formulation, the system separates spatial reasoning from language generation: a binary occupancy matrix derived from a floor plan supports deterministic path planning, and a small instruction-tuned transformer converts terse symbolic steps into natural language (&&&^^^^3query3^^^^&&&). In later work, “Grid^^^^3 OR ti:\3^^^^Guide” is also used more broadly as a design pattern in which an explicit grid or cost field guides planning or coordinate prediction rather than leaving spatial reasoning implicit in a large generative model (&&&^^^^3all:\3^^^^&&&, &&&^^^^3 OR ti:\3^^^^&&&).

^^^^3all:\3^^^^. Problem setting and design rationale

Grid^^^^3 OR ti:\3^^^^Guide was introduced for large, complex indoor spaces such as airports, shopping malls, and hospitals, where people routinely get lost and where traditional outdoor navigation tools fail. The motivating cases are specific: airports are described as large, multi-level, and constantly changing; shopping malls as multi-floor spaces with evolving layouts and temporary kiosks; and hospitals as high-stakes settings with ad-hoc, labyrinthine layouts and poor signage. Across these settings, the paper’s central claim is that many buildings already have floor plans, but these are hard for both people and traditional rule-based systems to interpret in real time (&&&^^^^3query3^^^^&&&).

The framework is positioned against two established alternatives. The first is infrastructure-heavy indoor positioning, including Wi‑Fi fingerprinting, Bluetooth beacons, RFID, or specialized sensor arrays. These systems require installation, calibration, maintenance, and are characterized as difficult to scale across many buildings. The second is end-to-end multimodal language-model reasoning over map images. The paper argues that image-based reasoning with LLMs is computationally expensive and slow, reporting 4–5 minutes per ^^^^^^^^3query3^^^^^^^^ on current systems according to Coffrini et al.; it also emphasizes that probabilistic LLMs may invent non-existent corridors or produce suboptimal paths (&&&^^^^3query3^^^^&&&).

Grid^^^^3 OR ti:\3^^^^Guide addresses this by offloading geometric reasoning to a classical planner and restricting the LLM to a purely linguistic role. This separation yields four properties that define the system: it is infrastructure-free, computationally lightweight, deterministic in pathfinding, and still user-friendly because the final output is natural language. The key architectural principle is that the SLM never sees the image or the geometry; its task is purely linguistic, which reduces the risk of spatial hallucinations while avoiding expensive multimodal inference (&&&^^^^3query3^^^^&&&).

^^^^3 OR ti:\3^^^^. Five-stage architecture

The system is organized as a five-stage pipeline from floor plan image to human-readable instructions. A user provides a map, which is preprocessed once, and then queries routes between labeled locations such as “Southwest Gate” and “Security Checkpoint.” The system looks up grid coordinates for those landmarks, runs A* to compute an optimal path, compresses that path into symbolic commands, and sends the commands to an SLM for verbalization (&&&^^^^3query3^^^^&&&).

Stage	Operation	Output
^^^^3all:\3^^^^	Map Preprocessing and Grid Generation	Binary occupancy grid
^^^^3 OR ti:\3^^^^	Graph Encoding	Implicit graph with 8-way connectivity
3	A* Search with Diagonal Moves	Shortest path between origin and destination
4	Path Compression	Compressed symbolic route commands
5	SLM-Based Instruction Generation	Fluent, numbered directions

The implementation details are unusually explicit. The floor plan may be in PNG, JPEG, TIFF, or related formats. Each free cell in the occupancy grid becomes a node in an implicit graph with 8-way connectivity, covering the cardinal directions and diagonals. A standard A* algorithm, adapted to the 8-connected grid and using a Chebyshev heuristic, computes the shortest path. The resulting list of cells is then vectorized into directional steps, run-length encoded, and subjected to diagonal collapse so that the symbolic representation better matches plausible human movement. Finally, a small instruction-tuned transformer, identified as TinyLlama-^^^^3all:\3^^^^.^^^^3all:\3 with LoRA fine-tuning, produces numbered natural-language directions (&&&^^^^3query3^^^^&&&).

This architecture is significant because it deliberately decomposes the task into a deterministic planning core and a linguistic rendering layer. The deterministic core guarantees route structure; the SLM contributes readability rather than search. A plausible implication is that Grid^^^^3 OR ti:\3^^^^Guide belongs to a class of hybrid systems in which the correctness-critical part of the computation is delegated to an algorithm with well-understood guarantees, while the model is reserved for surface realization.

3. Binary occupancy matrix and A* path planning

The first technical representation in Grid^^^^3 OR ti:\3^^^^Guide is the binary occupancy grid

PRESERVED_PLACEHOLDER_^^^^3query3^^^^

with

PRESERVED_PLACEHOLDER_^^^^3all:\3^^^^

The floor plan is converted to grayscale and masked so that obstacles and walkable areas are visually distinguishable, then downsampled into an PRESERVED_PLACEHOLDER_^^^^3 OR ti:\3^^^^ grid chosen according to the map’s aspect ratio. Each grid cell corresponds to a block of pixels in the original image, and the paper uses a majority-voting scheme: if more than 5^^^^3query3^^^^% of the pixels in the cell correspond to obstacles, the cell is marked blocked; otherwise it is marked free (&&&^^^^3query3^^^^&&&).

The experiments report concrete grid sizes. Birmingham Airport, with aspect ratio $1292\!:\!903$, is mapped to a $90 \times 130$ grid; Bergamo Airport to $30 \times 107$; Bologna Airport to $120 \times 190$; and the Orio Center mall to $80 \times 130$. Landmark coordinates are mapped into the same grid coordinate system; the paper gives the example of the Southwest gate in Birmingham Airport being assigned $(x=53, y=16)$ in a $90 \times 130$ grid. These integer coordinates become the start and goal states for A* (&&&^^^^3query3^^^^&&&).

Path planning is performed on an 8-connected implicit graph. For each free cell PRESERVED_PLACEHOLDER_^^^^3all:\3query3^^^^, candidate neighbors are

PRESERVED_PLACEHOLDER_^^^^3all:\3all:\3^^^^

Movement costs are PRESERVED_PLACEHOLDER_^^^^3all:\3 OR ti:\3^^^^ for orthogonal moves and PRESERVED_PLACEHOLDER_^^^^3all:\33^^^^ for diagonal moves:

PRESERVED_PLACEHOLDER_^^^^3all:\3^^^^4

The heuristic is Chebyshev distance,

PRESERVED_PLACEHOLDER_^^^^3all:\3^^^^5

and the A* score is

PRESERVED_PLACEHOLDER_^^^^3all:\3^^^^6

The paper states that in this 8-connected grid with these costs, Chebyshev distance is admissible and consistent, ensuring optimality and efficient search. A min-heap priority queue stores the open set, a closed set tracks visited nodes, and a came_from map reconstructs the path PRESERVED_PLACEHOLDER_^^^^3all:\3^^^^7 once the goal is reached (&&&^^^^3query3^^^^&&&).

The broader significance of this design lies in its explicit rejection of learned spatial inference for a problem that already admits a compact discrete model. Grid^^^^3 OR ti:\3^^^^Guide’s navigation correctness is therefore inherited from classical graph search rather than from prompt engineering or multimodal generalization.

4. Path compression and SLM-based instruction generation

The raw A* path is a sequence of grid cells, which Grid^^^^3 OR ti:\3^^^^Guide converts into textual navigation steps through a three-stage symbolic compression procedure. First, it computes displacements

PRESERVED_PLACEHOLDER_^^^^3all:\3^^^^8

maps each displacement to one of eight compass codes, and represents the route as a sequence such as PRESERVED_PLACEHOLDER_^^^^3all:\3^^^^9. Second, it applies run-length encoding, turning repeated directions into tuples such as PRESERVED_PLACEHOLDER_^^^^3 OR ti:\3query3^^^^. Third, it performs diagonal collapse: local zig-zag patterns such as PRESERVED_PLACEHOLDER_^^^^3 OR ti:\3all:\3^^^^ followed by PRESERVED_PLACEHOLDER_^^^^3 OR ti:\3 OR ti:\3^^^^ are replaced by a single diagonal command such as PRESERVED_PLACEHOLDER_^^^^3 OR ti:\33^^^^, followed by a second RLE pass to merge consecutive diagonals. The paper gives the example

PRESERVED_PLACEHOLDER_^^^^3 OR ti:\3^^^^4

corresponding to symbolic commands like “Go SE 5 steps,” “Go N 3 steps,” and “Go E ^^^^3 OR ti:\3^^^^ steps” (&&&^^^^3query3^^^^&&&).

This compression stage is linear in path length PRESERVED_PLACEHOLDER_^^^^3 OR ti:\3^^^^5, with time PRESERVED_PLACEHOLDER_^^^^3 OR ti:\3^^^^6, and is described as negligible compared to even modest language-model inference times. The paper also notes that the symbolic commands can later be mapped to approximate distances such as steps or meters using a known scale factor between grid cells and physical space. That statement does not imply that such a scale factor is fully integrated in the reported system; rather, it identifies an available extension point (&&&^^^^3query3^^^^&&&).

The linguistic component uses TinyLlama-^^^^3all:\3^^^^.^^^^3all:\3 approximately ^^^^3all:\3^^^^.^^^^3all:\3^^^^ billion parameters, fine-tuned with parameter-efficient fine-tuning using LoRA on a dataset of approximately ^^^^3all:\3query3query3query3^^^^ examples that map terse commands to conversational instructions. The SLM is described as instruction-tuned, efficient enough to run on CPU with reasonable latency, and model-agnostic in concept. Inputs consist of a system prompt plus a list of terse commands such as “Go East 3 steps” and “Go North ^^^^3all:\3^^^^ step.” The output is a numbered route description, for example: “Start by walking east for 3 steps” followed by “Finally, walk north for ^^^^3all:\3^^^^ step and you will reach your destination” (&&&^^^^3query3^^^^&&&).

Prompt design is treated as a control mechanism. The system prompt instructs the model to act as a precise navigation assistant, to convert terse commands into a numbered guide, to use specified phrasings for the first, intermediate, and final steps, to output exactly one numbered line per input command, and not to change the order or number of steps. The article’s argument is therefore not that the SLM reasons about the map, but that it performs constrained text formatting over a correct symbolic route. Although the paper does not report dedicated human user studies on phrasing quality, it presents the short, structured instruction-generation task as a good fit for small instruction-tuned models (&&&^^^^3query3^^^^&&&).

5. Evaluation, runtime, and baseline comparison

The experimental platform is a desktop with an AMD Ryzen 7 57^^^^3query3query3^^^^X CPU with 8 cores and ^^^^3all:\3^^^^6 threads, 3^^^^3 OR ti:\3^^^^ GB RAM, and no GPU. All processing and inference are performed on CPU. The evaluation uses four maps: Birmingham–Shuttlesworth International Airport, Milan Bergamo Airport, Bologna Guglielmo Marconi Airport, and the Orio Center shopping mall. The paper reports 8^^^^3query3^^^^ test cases, ^^^^3 OR ti:\3query3^^^^ per map, with different origin–destination pairs (&&&^^^^3query3^^^^&&&).

Map	Average A* runtime	Average A* + SLM runtime
Birmingham	PRESERVED_PLACEHOLDER_^^^^3 OR ti:\3^^^^7	PRESERVED_PLACEHOLDER_^^^^3 OR ti:\3^^^^8
Bergamo	PRESERVED_PLACEHOLDER_^^^^3 OR ti:\3^^^^9	$1292\!:\!903$^^^^3query3^^^^
Bologna	$1292\!:\!903$^^^^3all:\3^^^^	$1292\!:\!903$^^^^3 OR ti:\3^^^^
Orio Center	$1292\!:\!903$3	$1292\!:\!903$4

The average overall full-pipeline runtime is approximately $1292\!:\!903$5 per ^^^^^^^^3query3^^^^^^^^ on CPU. The A* contribution is negligible, with most latency coming from SLM inference. The paper also states that A* is deterministic, so the same input yields the same optimal route every time, and characterizes pathfinding as effectively real-time at the tested grid sizes (&&&^^^^3query3^^^^&&&).

The principal comparison is with Coffrini et al. (^^^^3 OR ti:\3query3 OR ti:\3^^^^5), which uses ChatGPT to process simplified map images plus prompts and generate instructions end-to-end. The reported route-generation accuracies for that baseline are 76.36% for Bergamo, 8^^^^3 OR ti:\3^^^^.^^^^3query3^^^^9% for Bologna, and 6^^^^3 OR ti:\3^^^^.5^^^^3query3^^^^% for Orio Center, with an average response time of 4–5 minutes per ^^^^^^^^3query3 Grid^^^^3 OR ti:\3^^^^Guide, by contrast, reports ^^^^3all:\3query3query3^^^^% route correctness across all 8^^^^3query3^^^^ test cases, on the condition that a path exists, because A* finds the optimal route under the stated cost model. The comparison is thus framed around three axes: higher reliability, dramatically lower computation and latency, and greater suitability for real-time use and resource-constrained devices (&&&^^^^3query3^^^^&&&).

These results should be interpreted with the paper’s decomposition in mind. The measured correctness pertains to route computation under the grid model; it does not constitute a claim that the binarized map always matches physical reality. The paper itself treats map accuracy, localization, and dynamic obstacles as separate concerns.

6. Deployment assumptions, limitations, and failure modes

Grid^^^^3 OR ti:\3^^^^Guide is described as infrastructure-free because it requires no Wi‑Fi fingerprinting, no Bluetooth beacons, RFID tags, or external localization systems, and no specialized sensors beyond what is used to generate or obtain the floor plan. Its assumptions are instead front-loaded: a floor plan image must exist, the plan must be preprocessed once into an occupancy grid, and points of interest such as rooms, gates, or shops must be mapped to grid coordinates through a one-time labeling step (&&&^^^^3query3^^^^&&&).

The system focuses on route planning and instruction generation from a known start cell to a known goal cell. It assumes that the user’s origin is already known in grid coordinates, as in the example “you are at Southwest Gate.” Real-time localization of the user as they move is explicitly outside the scope of the current work. The deployment stack is correspondingly modest: Python for preprocessing and A*, plus a local inference stack for the SLM; a CPU-only machine is sufficient, and the paper states that a mid-range smartphone or embedded platform with enough RAM and compute could host a quantized SLM (&&&^^^^3query3^^^^&&&).

The limitations are direct. The occupancy grid is static, so temporary obstacles such as crowds or construction are not modeled. Multi-floor navigation, including elevators, stairs, and floor transitions, is not developed. Instructions are based on directions and step counts rather than rich landmarks, even though coordinate labels for points of interest exist. The paper also identifies failure modes: outdated or inaccurately binarized maps may block valid corridors or create paths that do not match reality, and the SLM could in principle deviate from the required output format, although the authors mention simple regex-based post-processing to enforce structure (&&&^^^^3query3^^^^&&&).

The proposed future work follows from those constraints. It includes automated grid-map creation and update using sensor data such as cameras, LiDAR, and crowd density; more customized and context-aware phrasing, including landmark-based instructions; accessibility features such as text-to-speech for visually impaired users; and integration of the deterministic A* core with optional visual or semantic cues from richer models when resources permit (&&&^^^^3query3^^^^&&&).

7. Broader Grid^^^^3 OR ti:\3^^^^Guide interpretations and related research lines

Subsequent work extends the phrase “Grid^^^^3 OR ti:\3^^^^Guide” beyond indoor route description to a more general grid-guidance pattern. In autonomous driving, G^^^^3 OR ti:\3^^^^DP defines an explicit spatio-temporal cost volume by fusing probabilistic future occupancy distributions with a route-progress map, converts that volume into a continuous safety energy over trajectories through footprint sampling and Top‑K aggregation, and injects the resulting gradient into a diffusion planner during denoising. The paper explicitly summarizes this as a general Grid^^^^3 OR ti:\3^^^^Guide recipe: build a spatio-temporal grid, define a fused cost field, convert it into a continuous energy functional, and use that energy as an exponential reweighting of the diffusion distribution (&&&^^^^3all:\3^^^^&&&).

In GUI grounding, a closely related use of the idea appears in explicit position-to-coordinate mapping. There, RULER tokens serve as explicit coordinate markers, allowing a model to reference positions like gridlines on a map, while Interleaved MRoPE balances spatial frequency coverage across width and height. The paper’s description is that the screen is turned into an explicit, learnable grid that guides coordinate prediction instead of requiring implicit inference of pixel values from positional embeddings alone. This suggests a different but structurally similar notion of Grid^^^^3 OR ti:\3^^^^Guide: an explicit grid provides coordinate anchors, and the model performs bounded local adjustment rather than unconstrained global coordinate generation (&&&^^^^3 OR ti:\3^^^^&&&).

A plausible antecedent for this broader interpretation is constraint-based graph layout with soft and hard grid-like constraints. "Incremental Grid-like Layout Using Soft and Hard Constraints" introduces Node-Snap, Grid-Snap, edge-node separation, and Adaptive Constrained Alignment within a force-directed framework, making grid-like structure emerge from tunable penalties and incrementally added constraints rather than from a rigid orthogonal-layout pipeline. That work is not named Grid^^^^3 OR ti:\3^^^^Guide, but it exemplifies the same underlying motif: an explicit grid or alignment structure guides an optimization process while coexisting with other constraints and interactive updates (&&&^^^^3 OR ti:\3^^^^4&&&).

Across these lines of work, the unifying principle is stable. Grid^^^^3 OR ti:\3^^^^Guide denotes either a specific indoor navigation system or, more broadly, a family of architectures in which an external grid representation carries the burden of spatial structure and a separate model or optimizer handles expression, refinement, or generation. In indoor navigation this grid is a binary occupancy matrix; in diffusion planning it is a spatio-temporal cost field; in GUI grounding it is an explicit coordinate ruler embedded in the token sequence. The recurring claim is that explicit grids improve reliability, control, and computational tractability in settings where purely implicit neural spatial reasoning is either too costly or too error-prone (&&&^^^^3query3^^^^&&&, &&&^^^^3all:\3^^^^&&&, &&&^^^^3 OR ti:\3^^^^&&&).