Automatic generation of the dynamic equations of the robot manipulators using a LISP program

The decentralized control of robot manipulators at low speed needs the calculation of the inertial and gravitational coefficients of the dynamic equations. The scheme of calculation of the generalized forces can then be divided into two parts: the calculation in background of the dynamic coefficients and the calculation in real time of the generalized forces [1]. A LISP program, due to its ability for symbolic manipulation, has been created for the automatic generation of these coefficients. The input to the program is a file containing the Denavit-Hartemberg parameters, masses, centers of gravity and moments of inertia of the links. The result is a C program that calculates the coefficients. The validity of the program has been demonstrated by numerical comparison with the Newton-Euler program. Two examples, the PUMA robot and the Stanford manipulator have been tested. The former needs only 270 multiplications and 220 additions for the manipulator with an arbitrary load, and 200 multiplications and 150 additions without load; the latter needs 160 multiplications and 120 additions with an arbitrary load and 120 multiplications and 100 additions without load. The total time of calculation of the coefficients in a 8086/8087 microprocessor needs only 22 milliseconds in background.