Recently, continuum robots have attracted many researchers in the field of robotics and biomimetics. In comparison to the conventional rigid robots, this type of robots that are made of flexible links can bend along their arm continuously. This flexibility enables them conform themselves to the shape of the objects to grasp and carry them. This allows them pass through the narrow and winding holes and tubes with no collision. Due to infinite degrees of freedom (DOF), they have kinematic redundancy. Using this redundancy, extra tasks can be defined for the robot while the robot is tracking the desired trajectory. The application of these robots has been developed in the fields of surgery, nuclear industries and investigation missions. Especially in surgery, two cooperative continuum robots can work together to perform a surgery in some areas of body having enough space for operation. Previous studies in the area of continuum robots are followed by the assumption of constant curvature in each robot section. In the current study, by considering this assumption and using transformation matrices, the direct and inverse kinematic equations of the robot are derived. According to the fact that the curvature plane of lateral backbones is parallel to that of central backbone, the relation between tensions of the lateral backbones and configuration space variables are obtained. Consequently, using the relation between workspace and configuration variables obtained from inverse kinematics, tensions of lateral backbones are determined as a function of workspace variables. Designing a desired trajectory for the end-effector of the robot and obtaining the configuration space variables through the inverse kinematics, the desired tensions of the actuators are calculated. A two-section continuum robot is designed and constructed. Using the relation between the voltage and the rotational speed of the motor, a kinematic controller is designed. The calculated tensions along with the designed controller are implemented to the aforementioned two-section continuum robot. The end-effector position is detected by a stereo-vision system. Assumption of constant curvature is acceptable only when all of the actuators are in use. If one of the actuators is out of control (e.g. when a motor is failed and the backbone connected to it can move freely) then the curvature will not be constant. In this case, we can equal the tensions of two actuators to that of one assumptive wire having been in the curvature plane. If the shape of this assumptive wire is specified, the shape of those two actuators can be obtained through the geometrical relations. This shape is obtained from simulating each section separately in ABAQUS software. Having this relation between tension of assumptive wire and the position of end point of each section and using the transformation matrices, the desired workspace variables’ trajectory can be transformed to the desired tensions of those two actuators. Using the same aforementioned kinematic controller, these tensions have implemented to the faulty robot which one actuator of each section is failed and their backbones can move freely. Key Words: Continuum robot, Faulty systems, Kinematics control, Vision
