In the process of minimizing the energy consumption of a 3-RRR planar parallel manipulator (3-RRR PPM) and even general parallel kinematic manipulators, obtaining optimal results usually depends on particular functional relation between the instantaneous position of the moving platform and the kinetic time, which is called a displacement model (DM). Nevertheless, it is likely that although the movement time and path of a moving platform are the same, different amounts of energy are consumed for different DMs of the moving platform. To address this, a method of using long short-term memory neural network (LSTM-NN) instead of a complex theoretical model to predict the energy consumption of a 3-RRR PPM was presented. Subsequently, inverse dynamic equations of 3-RRR PPM were established based on the Newton–Euler method and solved using QR decomposition. Meanwhile, energy consumption between any two points in workspace of the 3-RRR PPM was programmed to provide the LSTM-NN with abundant precise training data. In view of time-varying characteristics of energy consumption prediction, the network architecture was developed based on the principle of LSTM-NN, and root-mean-square error (RMSE) was taken as the loss function. After acquiring training data, the RMSE of the LSTM-NN reached 0.00041 using whale optimization algorithm (WOA) with no need for the gradient of the loss function, so the lack of solving precision in training LSTM-NN was effectively improved. Finally, two different DMs of a moving platform with the same path and movement time were chosen to compare the total energy consumption of the 3-RRR PPM from the simulations, predictions, and experiments. The results showed that the relative error between predicted and experimental data was less than 2.50%. Therefore, the energy consumption prediction based on the LSTM-NN will be useful for achieving the intelligent application of 3-RRR PPMs.
Energy consumption prediction of cement production based on chaotic neural network-Markov chain
