Efficient Computation of the Jacobian for Robot Manipulators

This paper discucsses and compares six different methods for calculating the Jacobian for a general N-degree-of freedom manipulator. We enumerate the computational efficiency of each in terms of the total number of multiplications, addi tions/subtractions, and trigonometric functions required as well as in terms of the number of matrix-vector operations needed. We also give the execution times on a PDP-11/70 minicomputer for determining the Jacobian for an example seven-degree-of-freedom manipulator. This paper formulates one of the best new methods for determining the Jacobian.