In this paper, a new version of an earlier computational model of the primate saccadic system is described which has been investigated for its effectiveness in robot visuomotor control. The model consists of a recurrent neural network representing the superior colliculus, which supplies control signals to a lumped model of the burst generator. A genetic algorithm is proposed to train the lateral connective weights of the recurrent neural network, and the network is trained so that it produces dynamic activity that is very close to the observed collicular neural discharge patterns in primates. By means of a supervised training algorithm, the feedforward and feedback weights of this new model are trained, so that the model produces a wide range of saccades that are very similar to real eye movements. It has been shown mathematically that this algorithm is a close approximation of the gradient descent method of optimization. An earlier set of simulations with single and double target locations, as well as some new simulations pertaining to the robustness of the model, are then carried out. The reliability of the biological visuomotor system is demonstrated through these simulations, and theoretical issues pertaining to the reliability of this system are addressed. Finally, a novel strategy for robot visuomotor control, based on the model, is suggested.