Manipulator Differential Kinematics: Part 2: Acceleration and Advanced Applications

This is the second and final article on tutorial manipulator differential kinematics. In Part 1, we described a method of modelling kinematics using elementary transform sequence (ETS), before formulating forward Jacobian. We then some basic applications Jacobian including resolved-rate motion control (RRMC), inverse (IK), performance measures. this article, formulate second-order kinematics, leading to definition Hessian. describe kinematics' analytical forms, which are essential dynamics applications. Subsequently, provide general formula for higher-order derivatives. The first application consider advanced velocity control. section, extend perform sub-tasks while still achieving goal redefining algorithm as quadratic program enable greater flexibility additional constraints. take another look at numerical with an emphasis adding Finally, analyse how Hessian can help escape singularities. have provided Jupyter Notebooks accompany each section within tutorial. written in Python code use Robotics Toolbox Python, Swift Simulator examples implementations algorithms. While not absolutely essential, most engaging informative experience, recommend working through reading article. setup instructions be accessed https://github.com/jhavl/dkt.