Deep Koopman with Control: Spectral Analysis of Soft Robot Dynamics

Abstract-- Soft robots are challenging to model and control as inherent non-linearities (e.g., elasticity and deformation), often requires complex explicit physics-based analytical modelling (e.g., a priori geometric definitions). To address this, this paper presents an approach using Koopman operator theory and deep neural networks to provide a global linear description of the non-linear control systems. Specifically, by globally linearising dynamics, the Koopman operator is analyzed using spectral decomposition to characterises important physics-based interpretations, such as functional growths and oscillations. Linear control theory is well suited to developing interpretable capturing intrinsic important global physical properties of control frameworks, through exploration of the the system. This both limits dynamics analysis of the learnt spectral components, i.e., eigenvectors and eigenvalues, of model, and reduces confidence in model generalisability. Spectral analysis can help determine system stability [1], or provide additional insight To address this, this paper proposes an approach to controlling for techniques such as filtering [2].