This paper proposes an extension of the concept of the General Lagrangian Jacobian Inverse from driftless to control affine robotic systems, and presents the corresponding Jacobian motion planning algorithm in the parametric form. A specific choice of the Lagrangian is recommended. The motion planning algorithm is applied to the motion planning problem of a free-floating space manipulator with non-zero momentum. A conjecture is formulated that for this specific choice of the Lagrangian the motion planning algorithm outperforms the other Jacobian algorithms in terms of the length of the resulting robot trajectory.
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