Kinematics analysis of the coupled tendon-driven robot based on the product-of-exponentials formula

Tendon-driven configurations attract extensive interest in the field of surgical robotics due to their advantages and inherent applicability in the surgical environment. However, their multiple degrees of freedom (DOF) coupling creates complications in the kinematics analysis, which further prevents the direct application of the product-of-exponentials (POE) formula. In this paper, a new method is proposed to solve this problem. It first transforms the coupled tendon-driven robot into a pure serial robot. Then several kinematics analyses are presented separately to gain forward kinematics, inverse kinematics, Jacobian and acceleration expressions for a general coupled tendon-driven robot. The presented method has also been applied in the kinematics analysis of a typical coupled tendon-driven robot to explain the configuration transformation and detailed kinematics analysis process. The analysis process shows the presented method is intuitive and convenient. Simulations and experiments prove the validity and rigor of the presented method.