Robot kinematicsManipulatorkinematicsKinematics is concerned with the geometry of the articulated rigid bodies that constitute the mechanical structure of a robot. The first part of this chapter is devoted to the description of the position and orientation (pose) of a single rigid body. In particular, orientation can be represented in different ways, including rotation matrices, Euler angles, axis–angle, unit quaternions, and exponential coordinates. The notion of configuration space of a multibody robotic system is then formally established. Next, the task space is introduced, which is defined by a generic set of variables needed to describe the operations a robot should perform. The direct kinematics of a robot is the geometric relationship between these two spaces. Related to this mapping is the concept of kinematic redundancy of a robot with respect to a task, i.e., when the dimension of the configuration space of the robot is larger than that of the task space.