  The elementary transform sequence (ETS) provides a universal method of
describing the kinematics of any serial-link manipulator. The ETS notation is
intuitive and easy to understand, while avoiding the complexity and limitations
of Denvit-Hartenberg frame assignment. In this paper, we describe a systematic
method for computing the manipulator Jacobian and Hessian (differential
kinematics) using the ETS notation. Differential kinematics have many
applications including numerical inverse kinematics, resolved-rate motion
control and manipulability motion control. Furthermore, we provide an
open-source Python library which implements our algorithm and can be interfaced
with any serial-link manipulator (available at
github.com/petercorke/robotics-toolbox-python).
