configuration space (C-space)

The configuration space, almost always shortened to C-space, is an imaginary map that captures every possible pose a robot can strike, with one point on the map standing for one complete pose. Here "pose" means the full set of numbers needed to pin the robot down: for a simple arm, the angle of each joint; for a wheeled robot rolling on a floor, its x and y position plus which way it faces. If a robot has, say, six joints, then one point in its C-space is just a list of six numbers, and the whole space has six dimensions — impossible to picture, but perfectly easy to compute with. The key mental switch is this: in C-space you stop thinking about the robot's metal body moving through a room and start thinking about a single dot gliding through this map of poses.

Why bother with such an abstraction? Because planning a motion is enormously simpler when the robot is shrunk to a single point. In the real room the robot is a bulky shape with arms and corners that can clip a wall in complicated ways; tracking all of that during planning is a nightmare. But in C-space the entire robot becomes one dot, and the question "can the robot move from here to there without hitting anything?" turns into the much cleaner question "can this dot travel from one point of the map to another along a clear route?" Almost every path-planning method in robotics quietly does its work in C-space, not in the physical workspace you can see — that is the central trick that makes motion planning tractable.