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Can I use graph slam to solve this problem? Yes. However, the problem with graph slam is it is an offline algorithm that requires huge memory space. So, are there any other graph-based algorithm is available which is suitable for this problem? Actually memory is less of a problem than processing speed. Secondly, If I need to implement the same problem ...

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OMPL does have Python bindings. There is a section on the site documentation explaining the differences between the Python and C++ APIs and some samples. That may provide you with a starting points, though I don't see any full tutorials using Python as of this writing (alternate long-lived link).

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As you correctly identified and mentioned, the Jacobian matrix links the joint velocities to the end effector velocities. $$\dot X = J \cdot \dot Q$$ or $$\dot Q = J^{-1} \cdot \dot X$$ What these expressions of the Jacobi Matrix do not explicitly show is their dependency of the current pose of the robot. Depending on how the Jacobi matrix has been ...

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