Stability analysis and snap-through evaluation of the cable-driven continuum robots

Most of the continuum robots have flexible backbones that are deformed under the internal and external loads and a considerable amount of potential energy may be stored in the backbone. Hence, the continuum robots are exposed to instability issues such as snap-through. The snap-through instability occurs when, with changes in the applied forces, the robot reaches the boundary of its stable region and then moves toward a stable configuration in an uncontrolled manner. Snap-through instability is harmful to the continuum robots and its prediction is important for the design and control of the robot. However, most of the studies focused on design, kinematics, and dynamics of the continuum robots and there are limited studies worked on stability analysis of these robots. In this paper, the stability analysis of the cable-driven continuum robots is investigated. For this, the static equilibrium configurations of the robot are firstly determined under the internal and external loadings. Then, the stiffness matrix of the robot is obtained and the robot stability and snap-through condition are evaluated. The accuracy of the static equations of the robot is verified using the experimental results and the possibility of snap-through occurrence is modeled through simulations. Besides, the effects of the external loads, robot configuration in space, and cross-section of the backbone on the workspace and snap-through occurrence are studied.