Signed Distance Field
- Also called: SDF, signed distance function, Euclidean signed distance field, ESDF
- Category: Planning & manipulation › Motion planning
- Tags: geometry, collision-avoidance, mapping, motion-planning, 3d-representation
A function or grid that stores, for every point in space, the distance to the nearest surface, with the sign showing whether the point lies inside or outside an object.
Definition
Signed distance fields (SDFs) assign to every point in space the distance to the nearest surface of an object or scene. The sign carries extra information: by the common convention, points outside the object have positive values, points inside have negative values, and the surface itself is the zero level set. This turns geometry into a scalar field that can be queried, differentiated and combined.
The gradient of a signed distance field points away from the nearest surface, and where the field is differentiable its magnitude is one. This property makes SDFs useful for motion planning and optimization: a planner can read off both how close a robot body point is to an obstacle and which direction moves it away. Trajectory optimizers such as CHOMP use distance fields in exactly this way, turning obstacle clearance into a smooth cost.
SDFs are stored in several forms. Voxel grids hold a value per cell and are common in mapping; the truncated signed distance field (TSDF) keeps values only near surfaces and was popularized for dense 3D reconstruction by KinectFusion, while frameworks such as Voxblox build a full Euclidean distance field for planning from incremental TSDF maps. Analytic SDFs describe primitives such as spheres, boxes and capsules in closed form. Neural SDFs represent the field with a network that maps coordinates to distance, giving a compact, continuous description of complex shapes.
The idea also extends beyond physical space. A distance field can be defined over a robot's joint space, describing how far a configuration is from collision rather than how far a point is from a surface. Such fields connect the geometry of the workspace to the planning problem the robot actually solves.
Why it matters
Collision checking alone answers yes or no, while a signed distance field also says how far away and in which direction. That extra information lets planners and controllers keep safety margins, compute smooth avoidance costs and use gradient-based optimization around obstacles.
Key applications
- Collision costs and constraints in trajectory optimization
- Dense 3D reconstruction and mapping from depth sensors
- Representing object shapes for grasp planning and contact reasoning
- Safety margins and distance-based constraints in reactive controllers
- Compact neural representations of scenes and objects
In practice
A mobile manipulator team might fuse depth camera frames into a TSDF map of the workspace, convert it into a Euclidean distance field, and approximate the robot's links with a set of spheres. During trajectory optimization, each sphere center is looked up in the field; the distance minus the sphere radius gives clearance, and the field's gradient pushes the trajectory away from obstacles. The voxel resolution is chosen as a trade-off between memory, update speed and how finely thin objects are captured.
Common misconceptions
- An SDF is the same as an occupancy grid — an occupancy grid stores whether a cell is filled, while an SDF stores distance to the nearest surface and supports gradients
- A truncated SDF gives distances everywhere — a TSDF only holds meaningful values near surfaces, so planning usually needs a full Euclidean distance field
- SDF gradients are always well defined — they are undefined at points equidistant from two surfaces, which can cause optimizers to oscillate
Who should know this
- Motion planning engineers working with trajectory optimization
- Perception engineers building 3D maps from depth data
- Researchers using neural implicit representations of geometry
Related technologies
- Occupancy Grid
- Truncated Signed Distance Field (TSDF)
- CHOMP
- Voxblox
- Neural Implicit Representations
- Collision Checking
Related terms
Related projects
- LingBot-Map: Streaming 3D reconstruction from one camera: pose and depth for every frame, live
- Cartographer: Google's real-time 2D and 3D SLAM system for multi-platform robotics
- OpenDroneMap: Open-source photogrammetry toolkit that turns drone images into maps and 3D models
- RTAB-Map: Versatile graph-based SLAM supporting RGB-D, stereo, and LiDAR with real-time operation
- LeGO-LOAM: Classic lightweight, ground-optimized lidar odometry and mapping baseline (IROS 2018)
- OMPL: Sampling-based motion planning library powering MoveIt and countless robotics applications
Videos
- introduction to Signed Distance Fields: chris biscardi