A novel inverse kinematics and shape reconstruction method for continuum robots

Purpose Continuum robots offer unique advantages in various specialized environments, particularly in confined or hard-to-reach spaces. Inverse kinematics and real-time shape estimation constitute crucial aspects of closed-loop control for continuum robots, presenting challenging problems. This paper aims to present an inverse kinematics and shape reconstruction method, which relies solely on the knowledge of base and end positions and orientations. Design/methodology/approach Based on the constant curvature assumption, continuum robots are regarded as spatial curves composed of circular arcs. Using geometric relationships, the mathematical relationships between the arc chords, points on the bisecting plane and the coordinate axes are established. On this basis, the analytical solution of the inverse kinematics of the continuum robots is derived. Using the positions and orientations of the base and end of the continuum robots, the Levenberg–Marquardt algorithm is used to solve the positions of the cubic Bezier curves, and a new method of spatial shape reconstruction of continuum robots is proposed. Findings The inverse kinematics and spatial shape reconstruction simulation of the continuum robot are carried out, and the spatial shape measurement experimental platform for the continuum robot is constructed to compare the measured and reconstructed spatial shapes. The results show that the maximum relative error between the actual shape and the reconstructed shape of the continuum robot is 2.08%, which verifies the inverse kinematics and shape reconstruction model. Additionally, when the bending angle of a single bending section of the continuum robot is less than 135°, the shape reconstruction accuracy is higher. Originality/value The proposed inverse kinematics solution method avoids iterative solving, and the shape reconstruction model does not rely on mechanical models. It has the advantages of being simple to solve, highly accurate and fast in computation, making it suitable for real-time control of continuum robots.