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(typo: all instances of "Jacobian Transform" should be replaced by "Jacobian Transpose".)

This post only scratches the surface. There are many interesting topics in IK. Joint weights, null space optimization when the robot is overactuated wrt the end effector, self-intersection, singularities, stability when reaching for unreachable points, hybrid position/force control, ...

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Another interesting point is that from a numerical optimization point of view, the Jacobian transpose method is analogous to gradient descent, while using its (pseudo) inverse is basically the Gauss-Newton algorithm.

Very interesting. I like the connections to Gradient Descent and Gauss-Newton Algorithm.

Thanks for the feedback. Can you speak more to "null space optimization", "self intersection", and "hybrid position/force control"? High level descriptions of the situations would be helpful, thanks. Or links to resources.

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