Estimation of Position and External Force of Cable Driven Surgical Robots

Abstract

Positioning accuracy in cable driven mechanisms with motor position sensing is limited because the stiffness in these manipulators is less than rigid links. By applying Unscented Kalman Filter (UKF) and considering system dynamics in addition to motor sensing, the position estimation in these systems can be improved. To further improve the accuracy, additional observation was provided to the UKF by tracking the robot end-effector position with a camera. Furthermore, in cable driven systems the knowledge of cable's pre-tension not only improves the performance of the mechanism but can also be used as a measure to determine if the system is safe and robust to operate (e.g. too loose causes slack while too stiff causes the cable to wear and break). Thus, knowing the cable's pre-tension is important particularly in applications such as surgical robotics. To measure this initial tension, a special force gauge sensor can be used; however, these sensors are expensive and in some applications, such as surgery, it is not practical due to sterilization requirement. It is found that the stiffness parameter of cables has the highest correlation with tension. Therefore, we estimated the stiffness parameter to indirectly estimate cable's pre-tension. To estimate cable's pre-tension indirectly, first the initial tension in the cables were measured with a sensor and then the UKF was used to estimate system states and stiffness parameter simultaneously. The stiffness parameter was estimated at different tensions to find a mapping between tension and stiffness. This mapping was later used to estimate tension with UKF without a need for force sensor. Moreover, in surgery, haptic feedback is vital for surgeons. Without haptic feedback, surgeons may exert excessive force to a healthy tissue. To address this issue, we developed a novel approach to estimate external forces acting on cable driven robots by measuring the stretch in cables caused by external force similar to Series Elastic Actuators (SEA) without actually placing an elastic element in series with the motor and load. In our approach, we took advantage of the elasticity of cables. In our method, we used two encoders to precisely measure the cable stretch. The first encoder is mounted on the shaft of the motor while the second encoder is mounted on the Joint. With the first encoder, we used robot kinematics to estimate Joint angle (q_kin) and with the second encoder we measured the actual Joint angle (q). Then, by subtracting these two angles we measured the stretch. Once the stretch in cables are known, either linear Hooke's law or a non-linear spring model can be used to estimate external forces.