Numerical computation of singular control functions for a two-link robot arm

In [ I ] Bryson and Weinreb published a model of a horizontal articulated two-link robot arm. They used this model for the computation of minimum-time movements. Here, the distance of the movement is prescribed and the robot arm has to be in rest at the begin and at the end of the motion. The i n i t i a l and the f inal position of the arm, however, are kept free, and they are determined such that the transfer time is minimized. The solutions presented in [ I ] are characterized by control functions of the bang-bang type and i t remained an open question, whether there exist singular time-optimal control functions.