Math & Kinematics

Configuration Space (C-Space)

Configuration space is the set of all possible configurations of a robot, with each point specifying the values of every degree of freedom, such as the joint angles of a manipulator. Formalized for robotics by Lozano-Perez (1983), it transforms motion planning into finding a path for a point through the free subset of C-space, with obstacles mapped into C-space obstacles. Its dimension equals the robot's degrees of freedom, making high-DOF planning computationally demanding.

Why it matters for physical AI

Sampling-based planners, collision checking, and the joint-space action representations of many learned policies all operate in configuration space, making it the mathematical substrate of motion generation.