Axis-Aligned Bounding Box

• Also called: AABB
• Category: Planning & manipulation › Motion planning
• Tags: collision-detection, computational-geometry, motion-planning, bounding-volume, simulation

The smallest box with edges parallel to the coordinate axes of a chosen frame that encloses an object, stored as minimum and maximum corners and used for fast overlap and distance tests.

Definition

An axis-aligned bounding box (AABB) is a box that encloses an object and whose faces are parallel to the axes of a chosen coordinate frame. In 3D it is fully described by six numbers: the minimum and maximum x, y and z of the object, or equivalently a center and three half-extents. In 2D it is a rectangle, and the boxes drawn by most image object detectors are AABBs in pixel coordinates.

The value of an AABB is that tests on it are very cheap. Two AABBs overlap only if their intervals overlap on every axis, which takes a handful of comparisons. The distance between two boxes is found by computing, on each axis, the gap between the intervals (zero if they overlap) and taking the Euclidean norm of the three gaps. Because of this, AABBs are the standard first stage in collision detection: physics engines and collision libraries use them in the broad phase, often organized into a tree called a bounding volume hierarchy, to discard pairs of objects that cannot be touching before running exact tests on the remaining pairs.

The price is a loose fit. An AABB is defined relative to a frame, so when an object rotates its world-frame AABB must be recomputed and generally grows; a long, thin tool held at 45 degrees has a box much larger than the tool itself. Tests on AABBs are therefore conservative: if two boxes do not overlap, the objects do not either, but overlapping boxes do not prove contact, and the box-to-box distance is a lower bound on the true distance. Oriented bounding boxes (OBBs), bounding spheres, capsules, convex hulls and signed distance fields give tighter answers at higher cost.

Why it matters

AABBs are the cheapest geometric proxy for collision checking, workspace limits and spatial queries, and they appear in almost every motion planner, simulator and perception pipeline. Knowing that they are conservative and frame-dependent explains both why they are used so widely and why checks based on them can report false collisions or overestimate how close two objects are.

Key applications

• Broad-phase collision detection in simulators and motion planners
• Bounding volume hierarchies for fast distance and ray queries
• Cropping point clouds to a region of interest or workspace
• 2D object detection boxes in images
• Fast clearance checks on generated robot programs and trajectories

In practice

A tool that checks robot programs generated by a language model steps through each planned waypoint. At each one it transforms the gripper's collision mesh into the world frame, computes its AABB from the minimum and maximum vertex coordinates, and computes the distance to the AABB of each object on the table. Any waypoint where the distance falls below a clearance threshold is flagged with the object involved, so the program can be revised. Because the boxes are conservative, a rotated gripper passing close to a tall bottle may be flagged even when there is room; for flagged cases the tool falls back to an exact mesh distance query in a collision library before reporting a real problem.

Common misconceptions

• Overlapping AABBs mean the objects collide — overlap only shows that contact is possible; an exact test is needed to confirm it
• An AABB is a fixed property of an object — it depends on the frame and the object's orientation, and must be recomputed when the object rotates
• AABB distance is the true distance between objects — it is a lower bound, often much smaller than the real gap for rotated or irregular shapes
• Any box around an object is an AABB — a box aligned with the object's own principal axes is an oriented bounding box (OBB)

Who should know this

• Motion planning and collision-checking engineers
• Simulation and game physics developers
• Perception engineers working with point clouds and detections
• Developers of program verification tools for robots

Related technologies

• Oriented Bounding Box
• Bounding Volume Hierarchy
• Flexible Collision Library (FCL)
• GJK Distance Algorithm
• Sweep and Prune
• Bullet Physics

Related terms

• Obstacle Avoidance
• Motion Planning
• Signed Distance Field
• Octree
• Point Cloud
• End-User Robot Programming

Related projects

• GENESIS: World's fastest physics engine: 43M FPS for embodied AI learning
• LeRobot: HuggingFace ML library for real-world robotics in PyTorch
• PyBullet: Python physics simulator for robotics and RL research with fast CPU-based simulation
• RLinf: Scalable infrastructure for post-training foundation models via RL
• Webots: Cross-platform robot simulator with built-in models, sensors, and development environment
• NVIDIA Isaac Sim: NVIDIA Omniverse app for AI-driven robot simulation and testing

Videos

• COMP4300 - Game Programming - Lecture 08 - Collision Detection & AABB: Dave Churchill