Abstract

In this thesis, a novel semi-analytical method is proposed for the pseudo-rigid body (PRB) modeling of highly flexible slender continuum robots (CRs) with no constraint on the number of degrees of freedom of the PRB model. The proposed method has a simple formulation and high precision. Furthermore, it can describe initially-curved variable-length CRs having a variable stiffness along the length. The versatility of the method is investigated for the PRB modeling of the slender CRs, such as steerable catheters and concentric tubes. A new analytical formulation is also introduced for the Cartesian stiffness of the CRs using the proposed PRB model. The existing formulations for the Cartesian stiffness in the literature, such as enhanced stiffness and constant stiffness models, fail to properly describe CRs force/deflection behavior with large nonlinear deformation. However, it is shown that the proposed method gives a high precision estimation of the applied force at the CR tip. Additionally, the proposed Cartesian stiffness is a function of deflection and allows indirect force estimation using the knowledge of only the tip point deflection, which makes it ideal for concentric tube robots (CTR) in vitreoretinal surgeries. The formulation of the stiffness is then used for the simultaneous force/position control of the CTRs interacting with a soft environment. The governing equation is a boundary value problem, and the existing control architectures for the simultaneous force/position control in rigid robotics cannot be directly used. Furthermore, in CTRs, the distributed friction force among the tubes and also at the entry port in vitreoretinal surgeries is beyond the desired force at the robot tip. Thus, the conventional method to map the task space forces to that of the joint space, which is fundamental in the existing force control methods, cannot be used. Therefore, a new control architecture is devised for the indirect hybrid force/position control of a variable-length initially-curved CTR. The proposed method uses displacement as the control input to the robot and proves effective for environments with a wide range of stiffness.