A Systematic Approach to Computing the Manipulator Jacobian and Hessian using the Elementary Transform Sequence
This work provides a more intuitive and less complex approach for robotics researchers and engineers to compute Jacobian and Hessian matrices, applicable in areas like inverse kinematics and motion control, but it is incremental as it builds on existing ETS notation.
The paper tackles the problem of computing differential kinematics for serial-link manipulators by introducing a systematic method using the elementary transform sequence (ETS) notation, resulting in an open-source Python library that implements the algorithm for any serial-link manipulator.
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).