Abstract - Hierarchical and wider applications of robots, manipulators, and pick and place machines are facing challenges in industrial environments due to their insufficient intelligence for appropriately recognizing objects for grasping and handling purposes. Since robots do not posses self-consciousness, estimation of adequate grasping force for individual objects by robots or manipulators is another challenge for wider applications of robots and manipulators. This article suggests a mathematical model, recently developed, for computation of scattered energy of vibrations sensed by the stylus during an object slippage in robot grippers. The model includes in it dynamic parameters like trial grasping force, object falling velocity, and geometry of object surface irregularities. It is envisaged that using the said mathematical model, with the help of robust decision making capabilities of artificial neural network (NN), a robot memory could be able to estimate appropriate/optimal grasping force for an object considering its physiomechanical properties. On the basis of above mentioned mathematical model, this article demonstrates an experimental methodology of estimating adequate grasping forces of an object by robot grippers using Backpropagation (BP) neural networks. Four different algorithms have been explored to experiment the optimal grasping force estimation.