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The elementary transform sequence (ETS) provides a universal method ofdescribing the kinematics of any serial-link manipulator. The ETS notation isintuitive and easy to understand, while avoiding the complexity and limitationsof Denvit-Hartenberg frame assignment. In this paper, we describe a systematicmethod for computing the manipulator Jacobian and Hessian (differentialkinematics) using the ETS notation. Differential kinematics have manyapplications including numerical inverse kinematics, resolved-rate motioncontrol and manipulability motion control. Furthermore, we provide anopen-source Python library which implements our algorithm and can be interfacedwith any serial-link manipulator (available atgithub.com/petercorke/robotics-toolbox-python).

A Systematic Approach to Computing the Manipulator Jacobian and Hessian using the Elementary Transform Sequence