configuratiespace

Configuratiespace, often abbreviated as C-space, is the set of all possible configurations of a mechanical system. A configuration specifies the values of all its degrees of freedom, such as joint angles, translations, or orientations. Each point in configuratiespace represents a unique arrangement of the system. In robotics, the dimensionality of C-space typically matches the number of independent parameters describing the robot.

In many problems, portions of configuratiespace are infeasible because they correspond to collisions with obstacles or to constraints being violated. These infeasible regions are called configuration-space obstacles, while the remaining regions constitute the free configuratiespace. A central idea is that planning a motion in physical space can be transformed into finding a continuous path within the free configuratiespace from a start configuration to a goal configuration.

Mapping physical-space obstacles into C-space is often achieved by expanding the obstacles by the shape of the robot, a procedure related to the Minkowski sum. This reduces collision checking to simple tests in C-space, turning motion planning into a problem of finding a path in a high-dimensional space.

Computational methods for configuratiespace planning include grid-based discretization and sampling-based planners such as probabilistic roadmaps (PRMs) and rapidly-exploring random trees (RRTs). These approaches explore the free configuratiespace without requiring a complete, explicit map.

Applications span robotics and automation, animation and simulation of articulated figures, and, more broadly, any domain involving planning over multiple coupled parameters. The concept also informs analyses in chemistry and physics where configurations of a system are of interest.