Soft robots, compared to regular rigid robots, as their multiple segments with soft materials bring flexibility and compliance, have the advantages of safe interaction and dexterous operation in the environment. However, due to its characteristics of high dimensional, nonlinearity, time-varying nature, and infinite degree of freedom, it has been challenges in achieving precise and dynamic control such as trajectory tracking and position reaching. To address these challenges, we propose a framework of Deep Koopman-based Model Predictive Control (DK-MPC) for handling multi-segment soft robots. We first employ a deep learning approach with sampling data to approximate the Koopman operator, which therefore linearizes the high-dimensional nonlinear dynamics of the soft robots into a finite-dimensional linear representation. Secondly, this linearized model is utilized within a model predictive control framework to compute optimal control inputs that minimize the tracking error between the desired and actual state trajectories. The real-world experiments on the soft robot “Chordata” demonstrate that DK-MPC could achieve highprecision control, showing the potential of DK-MPC for future applications to soft robots. More visualization results can be found at https://pinkmoon-io.github.io/DKMPC/.

This paper establishes an analytical model for a dual-pressure-actuated pneumatic linear actuator, investigating the relationship between the output force of the linear actuator and both the pressure differential and displacement. Experiments were designed to validate the model. The maximum output force of the linear actuator under negative pressure (-40 kPa) is 100 N, while under hybrid air pressure (negative pressure -40kPa combined with positive pressure 40 kPa), the maximum output force significantly increases to approximately 210 N, demonstrating that dual pressure driving can substantially enhance output performance. The analytical results exhibit excellent agreement with experimental data under low-pressure conditions, with a maximum relative error of only 5%. Furthermore, comparisons with a flexible bellows of the same dimensions confirm that the linear actuator also exhibits high stiffness. Finally, potential applications of the linear actuator in daily life are discussed.