Dynamic modeling and control of an inextensible pneumatically actuated soft continuum manipulator

Modeling and control of soft continuum manipulators remain challenging due to their infinite degrees of freedom, nonlinear material properties, and demanding sensing requirements. This work presents a dynamic model-based centralized control approach for a spatially moving, inextensible soft continuum manipulator actuated by pneumatic network segments. The equations of motion are formulated using the Euler–Lagrange formalism, with segment stiffness represented by an experimentally identified spring moment model incorporating curvature, orientation, and pressure dependencies. Nonlinear system dynamics are linearized around the desired generalized coordinates, enabling a feedforward controller based on the linearized state representation combined with a PID feedback loop. State feedback is reconstructed from IMU measurements using spherical coordinates expressed in azimuth and zenith angles. The desired pressures are obtained through linear mapping from the target moments and further adapted by introducing a mean pressure, allowing simultaneous pressurization and depressurization of adjacent pneumatic networks for faster actuation. These adapted pressures are realized by an external, model-free pressure controller. The proposed method is experimentally validated, demonstrating accurate control of the continuum manipulator.