Parametric curve-based State-Space Representation for Shape Control of Soft-Continuum Manipulators

Soft-Continuum Manipulators (SCMs) are robots characterized by an infinite number of degrees of freedom (DoF), giving them remarkable dexterity and adaptability, depending on their application. However, these features also make their shape modeling and control challenging. This paper explores a curve-based Reduced-Order Model (ROM) using the Pythagorean Hodograph for SCM modeling. This approach enables the authors to develop a state-space representation for controlling the shape kinematics of SCMs. The kinematics of the SCM are modeled using PH parametric curves with a predefined length. These curves are expressed in state-space configuration, leading to the design of a controller capable of driving the SCM shape in real-time while maintaining its length. Experimental validation was performed on a bio-inspired Soft Continuum Elephant Trunk Robot, demonstrating the validity of the proposed method.