Occupancy Grid Map (OGM): Fundamentals

Updated 20 December 2025

Occupancy Grid Map (OGM) is a discretized spatial representation that divides an environment into cells with probabilistic occupancy values for autonomous perception and planning.
It integrates sensor data through models like Bayesian updates, TSDF, evidential methods, and hyperdimensional encoding to capture uncertainty and dynamic states.
OGMs underpin real-time robotics and vehicle navigation by fusing diverse sensor inputs, supporting SLAM, collision-checking, and advanced control strategies.

Occupancy Grid Map (OGM) is a discretized spatial representation fundamental to robotic perception, navigation, and planning. OGMs tessellate an environment into regular cells—2D or 3D—each maintaining a representation of occupancy state, typically as a probability or log-odds value, sometimes augmented with semantics or dynamic states. OGMs serve as the canonical interface between raw sensor data and downstream decision-making in autonomous systems. Research at various levels, from classical Bayesian formulations to data-driven models and neural or hyperdimensional computing approaches, reflects the evolution of OGM as both a robust real-time tool and a domain of deep algorithmic sophistication.

1. Classical Probabilistic Formulation and Variants

OGMs originated in the work of Moravec and Elfes (1980s), formalized as Bayesian update grids where each cell is a Bernoulli process conditioned on a history of measurements and poses. The key Bayesian recursion per cell $m_i$ is:

$P(m_i \mid z_{1:t},x_{1:t}) = \frac{P(z_t|m_i,x_t)P(m_i|z_{1:t-1},x_{1:t-1})}{P(z_t|x_t,z_{1:t-1},x_{1:t-1})}$

For computational efficiency, the update is performed in log-odds:

$\ell^i_t = \ell^i_{t-1} + \log{\frac{P(z_t|m_i=1,x_t)}{P(z_t|m_i=0,x_t)}} - \ell_0$

$P(m_i \mid z_{1:t},x_{1:t}) = \frac{1}{1 + \exp(-\ell^i_t)}$

Many contemporary OGM frameworks (e.g., OctoMap, HashMap, UniformMap) use this recursive structure with per-ray updates. Advanced variants include Normal Distributions Transform Occupancy Map (NDT-OM), Truncated Signed Distance Field (TSDF), and decay-rate models, which enrich the cell state beyond simple occupancy probability (Stepanas et al., 2022).

2. Sensor Integration and Inverse Sensor Models

Sensors for OGM include LiDAR, radar, and stereo vision. For LiDAR, the standard inverse sensor model marks cells along a beam as “free,” and the terminating cell as “occupied,” fusing evidence via log-odds. Advanced models compensate for unreflected beams, polygonal beam-filling (e.g., Bresenham polygon), and batch processing for efficiency (Eraqi et al., 2018, Kempen et al., 2022). Radar-centric OGMs leverage range-rate (velocity) to directly distinguish dynamic occupancy, typically requiring fewer particles for tracking dynamic cells (Ronecker et al., 2 Feb 2024).

Real-time pipelines employ pre-filtering and downsampling (such as height-filtering or odometry registration), with BEV (bird’s-eye view) grids centered on the ego-vehicle, as in RL-OGM-Parking, where a lightweight binary occupancy grid is produced by “splatting” fused LiDAR points onto the ground plane and simply marking cells as free or occupied without explicit evidence accumulation (Wang et al., 26 Feb 2025).

Table: Occupancy Update Methodologies

Method	Cell State	Evidence Fusion
Classical Bayesian	Probability/log-odds	Per-ray ISM, log-odds
NDT-OM, TSDF	Mean, covariance	Distribution-to-distribution, weighted average
Radar DOGM	State vector (+veloc)	Particle filter, Bayes
Splat-based (RL-OGM)	Binary (free/occ)	Point splat, no evidence
Deep evidential	Dirichlet/mass func	CNN, Dempster rule
VSA-OGM (hyperdim.)	Hypervector, entropy	Binding + bundling

3. Extensions: Dynamic State, Semantics, Uncertainty, and Object-Orientation

Dynamic Occupancy Grid Maps (DOGMs) augment each cell with velocity estimates, supporting representation of moving objects (vehicles, pedestrians) via RNN approaches (Schreiber et al., 2020, Schreiber et al., 2022). Some pipelines include semantic classification (vehicle, pedestrian, drivable area), allowing downstream planners to reason over object types and behavioral context (Asghar et al., 2023).

Uncertainty quantification is a major area of innovation. Evidential OGMs model first-order (aleatoric) and second-order (epistemic) uncertainty via Dempster-Shafer Theory; mass functions $m({F}), m({O}), m(\Theta)$ reflect belief and ignorance, and are mapped to Dirichlet subjective logic, with deep learning architectures jointly predicting evidential parameters (Kempen et al., 2021, Kempen et al., 2022).

Object-oriented grid mapping introduces latent dependencies and semantic clustering to relax the standard independent-cell assumption. Each cell’s evidence may depend on measurements to other cells within the same object cluster, with region-growing semantic clustering determining object associations and robust adaptation/removal of dynamic objects (Pekkanen et al., 2023).

4. Data-Driven, Deep, and Hyperdimensional OGMs

Recent OGMs are learned end-to-end from point cloud sequences without explicit ground removal or handcrafted ISM, employing recurrent CNN or ConvLSTM architectures. These models achieve improved boundary fidelity, semantic richness, and velocity recovery, as well as faster run-time than classic pipelines that rely on geometric grid construction (Schreiber et al., 2022).

Brain-inspired approaches encode cell occupancy not as scalar probability but as distributed hyperdimensional vectors (Vector Symbolic Architectures), updating occupancy via algebraic binding and bundling in high-dimensional space. Fourier-based VSA-OGM methods employ spatial semantic pointers, provide deterministic algebraic update and efficient multi-agent fusion, and use entropy over hypervector readouts for principled uncertainty quantification. Memory and latency are dramatically reduced compared to classical kernel methods, with comparable accuracy and no need for domain-specific model training (Snyder et al., 13 Feb 2025, Snyder et al., 17 Aug 2024).

5. Real-Time, Memory-Bounded, and Robust OGM Architectures

Practical deployment in embedded systems, UAVs, or real-time autonomous platforms demands efficient update and memory strategies. GPU-based frameworks such as OHM exploit per-ray parallelism, region-hashed blocks, and batched updates for multi-layer (occupancy, covariance, TSDF) operations (Stepanas et al., 2022). Robocentric OGMs (“rolling” local grids) keep the grid centered on the ego-agent, using sliding windows and circular buffers to bound memory and maintain real-time updates even for high-resolution or large-scale environments. Incremental obstacle inflation based only on state changes ensures constant-time behavior even with heavy dynamic changes (Ren et al., 2023).

Hybrid planning systems integrate OGM observations directly into both classical planners (e.g., collision-checking via Reeds-Shepp curves) and learning-based planners (e.g., RL policies using OGM concatenated with target state; action masking based on OGM lookups). Performance gains in sim-to-real transfer and planning robustness directly attribute to the stability and consistency provided by the OGM-based interface (Wang et al., 26 Feb 2025).

6. Planning, Safety, and Control over OGMs

OGMs serve as foundational models for a suite of planning, localization, and control pipelines. In classical Monte Carlo localization (AMCL) and pose-graph/SLAM, OGMs extracted from structural BIM models serve as priors for robust lifelong robot navigation, especially under real-world deviations and dynamic agents (Torres et al., 2023). Control barrier function frameworks (OGM-CBF) use OGMs in conjunction with signed distance functions, enabling smooth, unified safety constraints for arbitrary obstacle shapes in constrained quadratic optimization—demonstrating real-time, collision-free tracking in both simulation and hardware (Raja et al., 17 May 2024).

Confidence- and variance-aware OGMs (e.g., SMAP) attach explicit variance estimates to each cell—ensuring consistency between reported uncertainty and map error, and supporting risk-aware, belief-space planning. Such calibration enables active perception strategies where robot trajectories are selected to reduce critical map uncertainty (Agha-mohammadi, 2016).

7. Evaluation: Metrics and Limitations

OGMs are benchmarked with metrics including Intersection-over-Union (IoU), precision/recall for occupancy/semantic classes, latency and memory usage, and downstream planning/task success rates. For example, RL-OGM-Parking demonstrates a 99.33% success rate in simulation and 87.2% in real garages, outperforming rule-based and prior hybrid approaches (Wang et al., 26 Feb 2025). Data-driven evidential models achieve soft-IoU up to 0.605 on semantic vehicle grids, with substantial gains when fusing semantics and HD map priors (Asghar et al., 2023). Hyperdimensional VSA-OGM methods achieve up to 200x latency and 1000x memory reductions compared to full-covariance kernel methods (Snyder et al., 17 Aug 2024). Object-oriented mapping cuts residual dynamic object voxels by ~35% compared to standard NDT-OM (Pekkanen et al., 2023).

Limitations include domain adaptation challenges for neural/evidential models, susceptibility to erroneous clustering/labeling in object-oriented grids, and performance trade-offs between interpretability, accuracy, and algorithmic complexity. Robustness to noise, dynamic agents, and sensor configurations is an active area of research.

In sum, OGMs remain central to autonomous robotics and vehicle planning, encompassing an array of probabilistic, evidential, deep, and hyperdimensional paradigms. Technical advances continue to refine update efficiency, semantic richness, uncertainty calibration, and real-time planning efficacy, ensuring OGMs are both a mature solution and an ongoing subject of algorithmic innovation.