Occupancy Grid

Each cell in an occupancy grid stores a belief state, typically a probability between 0 (free) and 1 (occupied). This is updated over time using Bayesian filtering (e.g., log-odds) as new sensor data arrives. This probabilistic nature explicitly models sensor uncertainty and noise, allowing the system to distinguish between transient sensor artifacts and persistent obstacles. For example, a LiDAR reflection from a moving person creates a temporary high probability that fades as they walk away.

The grid resolution—the physical size of each cell (e.g., 5cm x 5cm)—is a critical design parameter. A finer resolution provides more accurate obstacle boundaries but exponentially increases memory consumption and processing time. A coarse resolution reduces computational load but can cause collision checking errors for small obstacles. In practice, multi-resolution or hierarchical grids are often used, where high-resolution is applied only in critical areas like near the robot.

Occupancy grids are the primary data structure for multi-sensor fusion. Data from heterogeneous sensors like LiDAR (precise range), radar (velocity, works in poor weather), stereo cameras (dense depth), and ultrasonic sensors (close-range) are all converted into a common probabilistic observation model to update the grid. This creates a unified, robust environmental model that is more complete and reliable than any single sensor's output.

Advanced implementations often maintain multiple grid layers. A static layer models permanent infrastructure (walls, racks). A dynamic layer tracks moving obstacles (other robots, people). These are updated at different rates and with different persistence models. This separation allows for efficient long-term mapping while enabling fast reactive avoidance of dynamic agents, a core requirement for heterogeneous fleet orchestration.

The grid acts as a cost map for global and local planners. Global planners (e.g., A*, Dijkstra) use the grid to find an initial, statically safe path. Local planners (e.g., Dynamic Window Approach, Model Predictive Control) perform fine-grained, real-time collision checking against the grid to adjust the trajectory. The grid's probabilistic values can be converted into traversal costs, penalizing paths through high-probability occupied cells.

To handle dynamic environments, occupancy values are not permanent. Temporal decay mechanisms gradually reduce the occupancy probability of cells that are not re-observed. This prevents 'ghost obstacles'—persistent marks from temporary objects like a parked pallet that has been moved. The decay rate is a tuned parameter balancing map stability and adaptability. This is essential for accurate long-term operation in warehouses and logistics centers.

A path planning technique that artificially expands the geometric representation of obstacles by a predefined safety margin. This is often applied directly to an occupancy grid by marking additional cells as occupied around detected obstacles. The process:

• Simplifies collision checking by creating a buffer zone.
• Accounts for system uncertainties like sensor noise, localization error, and agent footprint.
• Ensures planned paths maintain a minimum clearance distance, providing robustness against unexpected deviations.

The algorithmic combination of data from multiple heterogeneous sensors (e.g., LiDAR, radar, cameras, ultrasonic) to create a unified, reliable representation of the environment for populating an occupancy grid. Key aspects:

• Reduces false positives/negatives inherent to any single sensor modality.
• Improves accuracy and completeness of the grid, especially in challenging conditions (low light, dust, rain).
• Common fusion methods include Kalman filters and Bayesian inference, which update cell occupancy probabilities by combining new sensor evidence with prior grid estimates.

A reactive, local motion planning algorithm that uses a short-term occupancy grid to evaluate achievable velocities within an agent's dynamic constraints. It operates by:

• Sampling velocity space (v, ω) limited by acceleration and braking capabilities.
• Simulating trajectories over a short time horizon for each sample.
• Scoring trajectories based on progress toward goal, clearance from occupied cells, and speed.
• Selecting the optimal velocity command that avoids imminent collisions represented in the local grid.

An optimization-based control strategy that repeatedly solves a finite-horizon optimal control problem, using an occupancy grid as a constraint to ensure collision-free motion. The process:

• Predicts the agent's future state over a receding horizon using a dynamic model.
• Formulates constraints that the predicted trajectory must not intersect occupied grid cells.
• Solves for optimal control inputs (e.g., steering, acceleration) that satisfy constraints while minimizing a cost function (e.g., deviation from path, energy).
• Executes the first control input and repeats, enabling proactive avoidance.

A deliberately added buffer—in distance, time, or probability—applied within collision avoidance systems that use occupancy grids. It is a critical engineering parameter for robustness.

• Distance Margin: Added to agent footprint or obstacle boundaries during collision checking.
• Probability Margin: A threshold higher than 0.5 (e.g., 0.65) for declaring a grid cell 'occupied' to be conservative.
• Time Margin: Planning to avoid obstacles earlier than the strict Time to Collision (TTC) would dictate.
• These margins account for latency, actuation delays, localization error, and unmodeled dynamics to prevent edge-case failures.

The process of forecasting the future states (position, velocity) of dynamic obstacles, which is essential for maintaining an accurate and predictive occupancy grid. Methods include:

• Kinematic Models: Assuming constant velocity or acceleration to extrapolate obstacle motion.
• Machine Learning Models: Using recurrent neural networks (RNNs) or transformers to predict complex pedestrian or vehicle trajectories.
• The predicted future positions of obstacles are used to update or create a temporal series of occupancy grids, allowing the planning system to anticipate and avoid moving hazards proactively.