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