Screw theory based method to formulate local Jacobian’ magnitude estimator contours for 6 DoF robots

Abstract

Singularity prediction of Jacobian is inherently related to the design of any manipulator. Optimization of Jacobian is known to improve the joint rates and joint torques for the same set of end-effector twists and wrenches. Any mathematical entity which is an estimator of Jacobian can be used as a manifestation of the stated two schemes. It is required that online computation of Jacobian be implemented so that singular poses can be avoided and performance is maximized. We present an algorithm that relates to the determinant of the Jacobian for robotic manipulators. The algorithm developed is quicker to compute, and a strategy is developed to synthesize the local estimator contour. The contours change dynamically, henceforth optimal motor torques (in case of presence of interaction fields or system requiring force control) and optimal joint rates can be defined, depending on the control algorithm. The algorithm developed is independent of the structure of the matrix and is generalized to any six DoF manipulator structure used.