Configuration Space (C-Space)

The space of every possible pose a robot can be in, where each point represents one complete configuration.

A configuration is a set of numbers that uniquely pins down the position of every part of a robot; configuration space is the set of all possible configurations, with dimensionality equal to the number of degrees of freedom. For example, an object that can translate and rotate in a plane has a 3-dimensional configuration space (x, y, θ); a rigid body in 3D space has 6; a fixed-base arm with n revolute joints has an n-dimensional configuration space, using the joint angles directly as coordinates. According to Modern Robotics, Tomás Lozano-Pérez introduced this idea to motion planning in a 1980 MIT report: configurations that would collide with an obstacle are marked as obstacle regions, and everything else is called free space, which turns “steer a robot with a physical shape around obstacles” into “find a path for a single point through configuration space.” Sampling-based planners like RRT and PRM both operate in configuration space.

ExampleA planar two-link arm's configuration space consists of the two joint angles (θ1, θ2) — strictly speaking, a torus. A cup on a table becomes an irregularly shaped forbidden region on this space; planning a path means connecting a start point to a goal point on it while going around that region.

Also called

C-Space

Related

Degrees of Freedom (DoF) · Joint Space · Motion Planning · Sampling-Based Planning · Collision Checking · Generalized Coordinates

Sources

Modern Robotics（Lynch & Park, 2017 预印本）第 2 章 Configuration Space (Chinese)
Motion planning - Wikipedia
Configuration space (physics) - Wikipedia