Dynamic Modeling of Bellows-Actuated Continuum Robots Using the Euler–Lagrange Formalism

In the previous decade, multiple useful approaches for kinematic models of continuum manipulators were successfully developed. However, dynamic modeling approaches needed for fast simulations and the development of model-based controller design are not powerful enough yet—especially for spatial manipulators with multiple sections. Therefore, a practicable lumped mass model similar to common dynamic models of rigid-link manipulators is needed, which can be used for simulations and model-based control design. The model incorporates mechanical interconnections of parallel and serially connected bellows and uses constant curvature kinematics and its analytical derivatives to balance forces and energies in a global reference frame. The parameters of the resulting model are identified with measurements before the simulation results are experimentally validated. The obtained dynamic model can be used to both simulate the manipulator dynamics and calculate the inverse dynamics needed for model-based controller design or path planning.