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The Jacobian is the matrix of partial derivatives of a function. For robot arms, the Jacobian relates joint velocities to end-effector velocity. Jacobian Inverse Kinematic method is one method to solve inverse kinematic problems.

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Cartesian control for $z$ vector of end effector frame to point towards a specific direction

Final step is to compute the joint velocities by using the pseudoinverse of the manipulator's jacobian, like so: $ \dot{q} = J^{-1}(q) \cdot D $. …