Analytical formula for the pseudoinverse and its application for singular path tracking with a class of redundant robotic limbs

摘要

This work introduces a novel formula for calculating the right pseudoinverse, proposed for a class of kinematically redundant robotic limbs with one degree of redundancy. The formula is derived from the Singularity-Consistent method and is expressed as a sum of scalable vector fields parameterized by the desired end link twist. Pseudoinverse properties are ensured by assigning proper vector field intensities. The formula is applied to the IK problem, whereby the end link tracks a degenerate singular path, i.e. a nontangential path that penetrates the workspace boundary, and thus resulting in an unavoidable kinematic singularity. Through this method, the instability of the conventional pseudoinverse solution and the stationary point problem obtained when the solution is stripped from the ill-conditioned denominator is avoided. In addition, the appearance of the inner obstacle' algorithmic singularity problem known from a previous work can be circumvented. The performance of the method is verified via numerical simulations with an S-R-S-type structure and the Barrett WAM.