9.4 Tracking Attached Bodies

Many tracking problems involve estimating the motion of one body relative to another attached, moving body. For example, an eye rotates inside of its socket, which is part of the skull. Although the eye may have six DOFs when treated as a rigid body in space, its position and orientation are sufficiently characterized with two or three parameters once the head pose is given. Other examples include the head relative to the torso, a hand relative to the wrist, and the tip of a finger relative to its middle bone. The entire human body can even be arranged into a tree of attached bodies, based on a skeleton. Furthermore, bodies may be attached in a similar way for other organisms, such as dogs or monkeys, and machinery, such as robots or cars. In the case of a car, the wheels rotate relative to the body. In all of these case, the result is a multibody system. The mathematical characterization of the poses of bodies relative to each other is called multibody kinematics, and the full determination of their velocities and accelerations is called multibody dynamics.