Repeatable approximation of the Jacobian pseudo-inverse

For the redundant robot kinematics we construct an extended Jacobian inverse that approximates the Jacobian pseudo-inverse. Our construction relies on the approximation of a codistribution associated with the Jacobian pseudo-inverse by an integrable codistribution, spanned by differentials of certain functions that serve as components of the augmenting kinematics map in the extended Jacobian inverse. The procedure is applied to the kinematics of a 7 degree-of-freedom manipulator POLYCRANK, and to the kinematics of a mobile robot in the chained form.