Instantaneous kinematics and dexterity of mobile manipulators

We consider the kinematics of a mobile manipulator that consists of a nonholonomic (or holonomic) mobile platform and a holonomic manipulator mounted atop of the platform. At any fixed time instant and with fixed initial posture of the platform these kinematics are viewed as a map from a Hilbert space of controls and manipulator joint positions into a task-space of the mobile manipulator, and called the instantaneous kinematics. A derivative of this map is referred to as the instantaneous analytic Jacobian of the mobile manipulator. We derive an instantaneous dexterity matrix and a dexterity measure of the mobile manipulator. The dexterity matrix is used in order to introduce an instantaneous dexterity ellipsoid of the mobile manipulator. Concepts are illustrated with examples of mobile manipulators equipped with both holonomic and nonholonomic mobile platforms.