Static Modeling of a Class of Stiffness-Adjustable Snake-like Robots with Gravity Compensation

Stiffness-adjustable snake-like robots have been proposed for various applications, including minimally invasive surgery. Based on a variable neutral-line mechanism, previous works proposed a class of snake-like robots that can adjust their stiffness by changing the driving cables' tensions. A constant curvature hypothesis was used to formulate such robots' kinematics and was further verified by our previous work via rigorous force analysis and ADAMS simulations. However, all these models and analyses have ignored the effect of the robot links' gravity, resulting in significant errors in real systems. In this paper, a static model considering gravity compensation is proposed for the stiffness-adjustable snake-like robots. The proposed model adopts a nonlinear Gauss-Seidel iteration scheme and consists of two parts: gravity update and pose estimation. In each iteration, the former updates the payload of each link caused by gravity, and the latter estimates the pose of the robot by refreshing the angle and position values. This iteration stops when the change in the tip position is less than a pre-set error epsilon. During the above process, the only dependent information is each cable's tension. Simulations and experiments are carried out to verify the effectiveness of the proposed model. The impact of gravity is found to increase with growing material densities in the simulations. The experimental results further indicate that compared with a model without gravity compensation, our model reduces the tip estimation error by 91.5% on average.