Computation of the inertial and gravitational coefficients of the dynamics equations for a robot manipulator with a load

We present a method for the computation of the effective inertia, coupling inertia, and gravity loading terms for a manipulator with a load. The calculations are separated so as to consider the manipulator and the load independently. These inertial and gravity loading effects are additive and furthermore their computation need only be performed at a rate commensurate with changes in the configuration of the manipulator, not at the control sample rate. As an example we compute the terms for the PUMA manipulator. Taking advantage of the symmetries in the manipulator we need only 65 multiplications and 41 additions to compute all terms. The computations for a load requires an additional 160 multiplications and 101 additions if the load is considered as a point mass.