Closed-form redundancy solving of serial chain robots with a weak generalized inverse approach

•A pseudoinverse weaker than the Moore–Penrose pseudoinverse is used for redundancy solving.•Formal compact solution including projector onto null space is developed.•The method can be applied for optimizing a criterion or multiple task performance.•A redundancy degree of 1 induces very simple expression of the projector onto null space.•A general inverse model is given for any nnR-planar robot whatever nn.

Redundancy solving of robot-limbs is generally made at the velocity level by means of sophisticated matrix tools. We attempt to develop an alternative approach based on a right-inverse of the robot Jacobian which is not the Moore–Penrose inverse with, as a goal, to generate closed-form and compact expressions of the joint velocities. Considering the definition of the determinant of a rectangular m×nm×n matrix (m