Kinematics modeling and performance optimization of a kinematic-mechanics coupled continuum manipulator

Abstract

An optimization design of a notched continuum manipulator is proposed in this paper, which is based on our defined performance evaluation indices. By experimental testing the mechanics-based forward kinematics and the curve-fitting-based inverse kinematics, our proposed kinematic-mechanics coupled continuum manipulator is equivalent to a robot that features discrete joints and rigid links. Based on the mechanics and the kinematics models, two kinematic performance evaluation indices are developed to comprehensively describe the performance distribution characteristics in the workspace. Firstly, the global stiffness performance index of the proposed manipulator is established based on the 3-dimensional 2-node Timoshenko beam element. Secondly, the equivalent Jacobian matrix, a linear mapping from the joint space to the task space of the continuum manipulator, is analyzed, and equivalent dexterity performance index is determined. Finally, the optimal design for our proposed continuum manipulator considering the stiffness performance and kinematics performance simultaneously is implemented as a case study utilizing the NAGA-II genetic algorithm. The results demonstrate that the optimized geometric parameters can improve the kinematic performance evaluation indices simultaneously, and our proposed kinematic performance evaluation indices can be applied and extended to the kinematic evaluation and the kinematic optimization of this kind of notched continuum manipulator.