Modeling, control, and stiffness regulation of layer jamming-based continuum robots

Continuum robots with variable compliance have gained significant attention due to their adaptability in unstructured environments. Among various stiffness modulation techniques, layer jamming (LJ) provides a simple yet effective approach for achieving tunable stiffness. However, most existing LJ-based continuum robot models rely on static or quasi-static approximations, lacking a rigorous control-oriented dynamical formulation. Consequently, they are unsuitable for real-time control tasks requiring simultaneous regulation of configuration and stiffness and fail to capture the full dynamic behavior of LJ-based continuum robots. To address this gap, this paper proposes a port-Hamiltonian formulation for LJ-based continuum robots, formally characterizing the two key phenomena -- shape locking and tunable stiffness -- within a unified energy-based framework. Based on this model, we develop a passivity-based control approach that enables decoupled regulation of stiffness and configuration with provable stability guarantees. We validate the proposed framework through comprehensive experiments on the OctRobot-I continuum robotic platform. The results demonstrate consistency between theoretical predictions and empirical data, highlighting the feasibility of our approach for real-world implementation.