The Koopman operator framework has shown promising results in enabling the analysis of nonlinear dynamics into an infinite-dimensional linear representation. Koopman direct encoding (KDE) is a model-based approach that utilizes inner products and compositions in a Hilbert space to compute the Koopman operator. However, it has primarily been applied to autonomous systems and simulation environments. Here, we extend the application of KDE to nonautonomous systems and real-world environments by introducing Koopman direct encoding-based model predictive control (KDE-MPC). It was validated on nonlinear electromechanical systems with segmented dynamic conditions, such as contact-noncontact transitions, which pose challenges for modeling and control. Simulation results demonstrate a more stable and smoother position profile compared to proportional-integral-derivative control, particularly at discontinuous boundaries. KDE-MPC was also applied to real-world systems, achieving similar position tracking performance to simulation results. We anticipate that KDE-MPC will offer a viable solution for complex robotic control challenges.

Electrical impedance tomographic (EIT) tactile sensing holds great promise for whole-body coverage of contact-rich robotic systems, offering extensive flexibility in sensor geometry. However, low spatial resolution restricts its practical use, despite the existing deep-learning-based reconstruction methods. This study introduces EIT-GNN, a graph-structured data-driven EIT reconstruction framework that achieves super-resolution in large-area tactile perception on unbounded form factors of robots. EIT-GNN represents the arbitrary sensor shape into mesh connections, then employs a twofold architecture of transformer encoder and graph convolutional neural network to best manage such the geometrical prior knowledge, resulting in the accurate, generalized, and parameter-efficient reconstruction procedure. As a proof-of-concept, we demonstrate its application using large-area face-shaped sensor hardware, which represents one of the most complex geometries in human/humanoid anatomy. An extensive set of experiments, including simulation study, ablation analysis, single-touch indentation test, and latent feature analysis, confirm its superiority over alternative models. The beneficial features of the approach are demonstrated through its application in active tactile-servo control of humanoid head motion, paving the new way for integrating tactile sensors with intricate designs into robotic systems.