In this paper, the authors describe the design of a bendable robotic tip for semi-autonomous colonoscopy called COLOBOT. It is a flexible robotic manipulator made of silicone rubber in view of the compact size and biocompatibility. The outer diameter of the tip is 17 mm which is lesser than the average diameter of colon (20 mm). Three servo-valves are used to control the pressure of each chamber of this tip to obtain its flexible movement. The experimental results of this new prototype show that it can bend until 120 degrees under the pressure of 2 bar. Based on the geometric deformation and a nonlinear analysis of the silicone behavior, a direct kinematic model analogous to the forward kinematics of a conventional industrial robot kinematics chain has been put forward. The proposed kinematic model of this bendable tip is an extended model of classical models found for such a mechanism. At first a polynomial approximation is used to characterize the non linear behavior of each chamber of the actuator. Next the coupling phenomena between each chamber are highlighted through experimental tests. A new correction parameter is then proposed to take into account these interactions and a non linear optimization is made to compute this coefficient. Finally, the proposed kinematic model is experimentally validated