Model-based versus model-free optimal tracking for soft robots: analytical and data-driven Koopman modeling, control design and experimental validation

Soft robots, as a new type of robots, are highly flexible and deformable, which can adapt to the needs of tasks in complex environments. However, due to the complex nonlinear behaviors of soft materials and the unpredictable motion of actuators, accurate modeling and development of suitable controllers for soft robots are currently the main challenges for real applications. In this paper, we propose and compare two different modeling approaches to estimating the shape deformation of a two-dimensional pneumatic soft robot (2D-PSR): an analytical model based on the motion and air pressure dynamics and a data-driven model using Koopman operator theory and finite-dimensional approximate realization of the extended dynamic mode decomposition algorithm. The Unscented Kalman Filter (UKF) is applied to the two models to estimate the system state and filter the noises from sensors, respectively. Subsequently, based on the established models, the linear quadratic regulator (LQR) is designed to realize the precise trajectory tracking control of the 2D-PSR under two typical input signals. Both simulation and experimental results show that the proposed LQR control schemes with UKF designed based on the analytical model (A-FL-UKF-LQR) and Koopman linear model (K-UKF-LQR) can achieve the expectations in terms of tracking accuracy and robustness, in which the K-UKF-LQR framework outperforms the A-FL-UKF-LQR to a certain degree.