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The nonlinear inverted pendulum model of a lightweight bipedal robot is identified in real-time using a reservoir-based Recurrent Neural Network (RNN). The adaptation occurs online, while a disturbance force is repeatedly applied to the robot body. The hyperparameters of the model, such as the number of neurons, connection sparsity, and number of neurons receiving feedback from the readout unit, were initialized to reduce the complexity of the RNN while preserving good performance. The convergence of the adaptation algorithm was numerically proved based on Lyapunov stability criteria. Results demonstrate that, by using a standard Recursive Least Squares (RLS) algorithm to adapt the network parameters, the learning process requires only few examples of the disturbance response. A Mean Squared Error (MSE) of 0.0048, on a normalized validation set, is obtained when 13 instances of the impulse response are used for training the RNN. As a comparison, a linear Auto Regressive eXogenous (ARX) model with the same number of adaptive parameters obtained a MSE of 0.0181, while a more sophisticated Neural Network Auto Regressive eXogenous model (NNARX), having ten time more adaptive parameters, reached a MSE of 0.0079. If only one example, one-shot, is used for identifying the RNN model, the MSE increases to 0.0329 while showing still good prediction capabilities. From a computational point of view, the RNN in combination with the RLS adaptation algorithm, presents a lower complexity compared with the NNARX model that uses the back propagation algorithm, which makes the reservoir-based RNN model more suitable for real-time applications. |
