Editing Configuration space (physics) (section)

===Robotic arm===
{{See also|Configuration space (mathematics)#Configuration spaces of mechanical linkages}}

For a robotic arm consisting of numerous rigid linkages, the configuration space consists of the location of each linkage (taken to be a rigid body, as in the section above), subject to the constraints of how the linkages are attached to each other, and their allowed range of motion. Thus, for <math>n</math> linkages, one might consider the total space
<math display="block">\left[\mathbb{R}^3\times \mathrm{SO}(3)\right]^n</math>
except that all of the various attachments and constraints mean that not every point in this space is reachable.  Thus, the configuration space <math>Q</math> is necessarily a subspace of the <math>n</math>-rigid-body configuration space. 

Note, however, that in robotics, the term ''configuration space'' can also refer to a further-reduced subset: the set of reachable positions by a robot's [[end-effector]].<ref>John J. Craig, ''Introduction to Robotics: Mechanics and Control'', 3rd Ed. Prentice-Hall, 2004</ref> This definition, however, leads to complexities described by the [[holonomy]]: that is, there may be several different ways of arranging a robot arm to obtain a particular end-effector location, and it is even possible to have the robot arm move while keeping the end effector stationary. Thus, a complete description of the arm, suitable for use in kinematics, requires the specification of ''all'' of the joint positions and angles, and not just some of them.

The joint parameters of the robot are used as generalized coordinates to define configurations.  The set of joint parameter values is called the ''joint space''.  A robot's [[forward kinematics|forward]] and [[inverse kinematics]] equations define [[Map (mathematics)|maps]] between configurations and end-effector positions, or between joint space and configuration space.  Robot [[motion planning]] uses this mapping to find a path in joint space that provides an achievable route in the configuration space of the end-effector.