Local SVD inverse of robot Jacobians

Abstract

This study presents a fast inverse kinematics algorithm for a class of robots, including PUMA and SCARA. It decomposes a robot Jacobian into a product of sub-matrices to locate singularities. Singular value decomposition (SVD) is applied to each singular sub-matrix to find a local least-squares inverse. Perfect inverses are derived for all non-singular sub-matrices. The proposed algorithm is extremely fast. A total inverse requires 54 flops for PUMA and 43 for SCARA. Simulation and experiment are conducted to test the accuracy and real-time speed of the algorithm.