In recent years, the robotics field has witnessed an unprecedented surge in the development of humanoid robots, which bear an increasingly close resemblance to human beings in appearance and functionality. This evolution has presented researchers with complex challenges, particularly in the domain of controlling the increasing number of robotic motors that animate these lifelike figures. This paper focuses on a novel approach to managing the intricate facial expressions of a humanoid face endowed with 22 degrees of freedom. We introduce a groundbreaking inverse kinematic model that leverages deep learning regression techniques to bridge the gap between the visual representation of human facial expressions and the corresponding servo motor configurations required to replicate these expressions. By mapping image space to servo motor space, our model enables precise, dynamic control over facial expressions, enhancing the robot's ability to engage in more nuanced and human-like interactions. Our methodology not only addresses the technical complexities associated with the fine-tuned control of facial motor servos but also contributes to the broader discourse on improving humanoid robots' social adaptability and interaction capabilities. Through extensive experimentation and validation, we demonstrate the efficacy and robustness of our approach, marking a significant advancement in humanoid robotics control systems.

We design a multiple-model state estimator where each filter runs a propagation model with a different source term associated to the hypothesis of the source being positioned in a specific element of the discretized domain. A null hyphotesis is added to account for the absence of the source in the domain. The decision on the propagation model (i.e., source position) that is more likely given the available acoustic measurements is taken based on the mode probabilities associated to each hypothesis. To handle the high dimension of the large-scale field estimation problem and reduce the computational complexity, the multiple-model filter is implemented by using the ensemble Kalman filter. Finally, the effectiveness of the proposed multiple-model spectral-element ensemble Kalman filter is demonstrated through simulation experiments in underwater acoustic environments with regular and irregular seabed geometry and via comparison with the standard matched-field processing method.