Fast Computation Of Jacobian And Inverse Jacobian Of Robot Manipulators

This paper presents a computationally efficient technique for determining the Jacobian of an arbitrary robot arm as a function of its state. Fast computation of the Jacobian permits rapid determination of the new position and orientation of the end effector in base coordinates from prescribed incremental changes in the joint variables. The inverse problem is also considered in this paper. A fast efficient method for computing the differential changes in the joint variables for a given differential change in the position and orientation of the end effector is outlined. The proposed approach leads to a unique solution if the inverse solution exists. The suggested method can also quickly identify the singularities in the Jacobian. One of the main advantages of the methods proposed here is in their generality. The methods hold for any robot arm with arbitrary number of links whose states can be described by homogeneous transformations. The computational simplicity along with the generality of the approach together make the proposed methods well suited for real time applications. The proposed methods can be readily implemented on a computer.