Computer-aided Generation of Kinematic Equations in Symbolic Form

Abstract

Symbolic kinematic equations of robotic manipulators play an important role in contemporary robot control. The use of symbolic equations instead of numeric ones, speeds up the computation of the control signals necessary to guide a manipulator along a desired path. On the other hand, on-line motion generation, by means of low-cost microcomputers, becomes an important feature of modern industrial robots. In order to achieve this feature, the least computationally expensive algorithms should be applied. Such algorithms certainly make use of the symbolic kinematic model. The kinematic equations in symbolic form are equations which describe manipulator hand position and orientation as explicit trigonometric functions of the joint coordinates. These equations can be obtained by hand using the equations derived in the preceding chapter. The same is true in the case of the derivation of the symbolic Jacobian matrix. However, this tiresome process is subjected to human errors. Besides, once the symbolic equations have been obtained, a computer program must be written to compute these kinematic variables optimally, i.e. with the minimal number of multiplications and additions. In this chapter we will do this automatically, by means of a computer.