Computer generation of robot dynamics equations and the related issues

Two programs have been developed using the computer algebra system REDUCE to generate the dynamics equations of motion for robot manipulators. One of these programs is based on a Lagrange formulation and the other utilizes a recursive Newton-Euler formulation. Both programs produce equivalent scalar symbolic expressions for the generalized actuator forces, but the program based on the recursive Newton-Euler formulation is more efficient for the generation of equations. These programs have been used to generate the dynamics equations of manipulators with as many as six degrees of freedom. The efficiency of computing forces using the generated scalar symbolic expressions is compared with the efficiency of a numerical algorithm (implemented in FORTRAN '77) based on the recursive Newton-Euler formulation. Force computation by the method of symbolic equations is shown to be more efficient than the numerical recursive Newton-Euler algorithm. The technique of symbolic equations is also better adapted to multi-CPU processing.