Mobile Manipulation Inverse kinematics and Trajectory Control

Our mobile manipulator is composed of a Nomad XR4000 platform on the top of which a Puma 560 arm is mounted. At kinematic level a mobile manipulator can be interpreted as a redundant open kinematic chain i.e. a classical arm manipulator with more joints than degrees of freedom. A kinematic chain can be inteded as a cascade of rigid body motions each of them describing the displacement of joint with respect to the adjacent ones. Here we use the framework of exponential coordinates to describe rigid body transformation. Such a formalism relies on the Lie group structure that can naturally be associated with the set of rotations and translations in 3D space. For an open kinematic chain, the problem of planning a motion is basically composed of two parts: the first is to find a suitable trajectory for the end effector, the second is to translate this trajectory into a corresponding trajectory for the joints of the manipulator, to be used as reference input to the system. This last problem is known as inverse kinematics and it is what is of main concern here because of the redundacy introduced by the presence of more joints than degrees of freedom. The inverse kinematics is solved by integrating an equation describing the differential kinematics of the manipulator. Indeed, this is the situation in which the formalism of exponential coordinates fits naturally since it is based on representing any motion as (explicit) integral of some linear differential equation.