The Piecewise Constant Curvature Model for the Forward and Inverse Kinematics of Continuum Robot Based on Lie Theory

Continuum robots have received much attention because of their high degree of flexibility. For modeling the kinematics of continuum robots, the piecewise constant curvature model is widely used, but it has several drawbacks. Firstly, the forward kinematics calculation has high computational complexity. Secondly, the numerical solution of the inverse kinematic Jacobian matrix is difficult to describe for multi-segments continuum robots. And thirdly, the model does not take the case of torsion into account. To address the above issues, this paper proposes a piecewise constant curvature kinematic model based on Lie theory that can describe the forward and inverse kinematics of continuum robots in a more simplified form, and some simulations are performed to validate the proposed model and the simulated results show the effectiveness of the model.