Real-Time Kinematics of Continuum Robots: Modelling and Validation

Kinematics of flexible backbone continuum robots is highly non linear and its complexity quickly escalates with the number of sections of the robot, which is usually more than three. This paper introduces a kinematic modelling of actuation and configuration spaces that greatly simplifies the computational requirements compared to the commonly used Piecewise Constant Curvature Kinematics which results in a faster algorithm at a rate proportional to the number of sections. This new algorithm is firstly developed for Twin Pivot Compliant Joint continuum robots but then extended to a general single neutral axis backbone configuration, both achieving a very low error of approximation (0.7% for the prototype developed), which results in several advantages such as the avoidance of highly non-linear functions and singularities, great reduction of computational complexity and an user-friendly graphical representation to help operation and status monitoring of this kind of robots. Moreover, a slender, small diameter and hyper-redundant (175 mm length, 6 mm diameter, 10 Degrees of Freedom) continuum robot prototype is developed and tested in a real-case industrial application for inspection and repair of aero engines in order to validate the proposed model.