PH-Gauss-Lobatto Reduced-Order-Model for Shape Control of Soft-Continuum Manipulators

Soft and hyperelastic materials possess properties of resilience and flexibility, characterizing a class of soft-continuum manipulators (SCMs). The latter describes a robot structure with an infinite number of degrees of freedom (DoF), useful for mobility and manipulation. However, these geometric characteristics are a source of modeling and control problems. In this article, a Pythagorean hodograph (PH) curve-based reduced order model (ROM) relying on the Gauss-Lobatto quadrature is investigated for the modeling and the control of SCM. This allows, first, reducing the dimension of the SCM kinematics based on the PH parametric curves with a predefined length, and second, developing the shape kinematics control from its control polygon. The use of the Gauss-Lobatto quadrature allows to move independently the PH curve control points, while preserving PH features of length and minimum curve energy. These features are important to control in real-time the shape of the SCM. The proposed approach has been validated numerically and experimentally, carried out on a bioinspired soft continuum elephant trunk robot.