Haptic feedback plays a key role in surgeries, but it is still a missing component in robotic Minimally Invasive Surgeries. This paper proposes a dynamic modelbased sensorless grip force estimation method to address the haptic perception problem for commonly used elongated cabledriven surgical instruments. Cable and cable-pulley properties are studied for dynamic modeling; grip forces, along with driven motor and gripper jaw positions and velocities are jointly estimated with Unscented Kalman Filter and only motor encoder readings and motor output torques are assumed to be known. A bounding filter is used to compensate for model inaccuracy and to improve method robustness. The proposed method was validated on a 10mm gripper which is driven by a Raven-II surgical robot. The gripper was equipped with 1dimensional force sensors which served as ground truth data. The experimental results showed that the proposed method provides sufficiently good grip force estimation, while only motor encoder and the motor torques are used as observations.

In this paper, we propose model of longitudinally loaded cable based on the Bouc-Wen hysteresis model and within the framework of the Duhem operator. By optimizing the 9 hysteresis model parameters with a genetic algorithm, the proposed model is shown to be capable of representing quasi-static response of two different diameter cables, 0.61 mm (thin) and 1.19 mm (thick), used for the RAVEN II surgical robotic surgery platform. The construction of the cable is 7 strands with 19 individual wires per strand. Furthermore, it is shown that the dynamic response of the cables are captured by adding a linear damping term. The hysteresis model and linear damper with the optimized parameters accurately models a longitudinal vibration test result in terms of frequency, steady state stretch, and logarithmic decrement. Energy dissipation due solely to the hysteresis term is approximately calculated to be 57 and 71% of the total energy loss for the thin and thick cables respectively. The proposed model may be used for cables with different contraction and diameter and can be applied for control of cable driven robots in which cables are stretched longitudinally without large excitation of other modes. I. INTRODUCTIONWhen actuating cable driven systems such as the RAVEN II surgical robotic research platform [1] consisting of serial links, cable is repeatedly stretched and relaxed longitudinally. Automation of such systems with high accuracy is not easily achieved due to the complicated response of cable. One approach to improve automation accuracy of such system is development of better control systems often with feedback of system's state using external observation. However, for design and control analysis, development of an accurate model becomes quite important.The significance of using a hysteresis model for modelling cable is that it eliminates the discrepancy of cable stretch force between loading and unloading phases which could introduce control inaccuracy. Moreover, a hysteresis model is able to capture the rate independent energy loss due to interwire sliding friction and plastic deformation of material, and the information of the energy loss can be used for fatigue life prediction.The Bouc-Wen hysteresis model [2] [3], a special form of the Duhem model [4], is widely used to describe non-linear hysteretic systems because of its capability to produce various shapes of hysteretic loops in analytical form. Since the Bouc-Wen model is not suitable to describe hysteresis with

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Cable driven manipulators are popular in surgical robots due to compact design, low inertia, and remote actuation. In these manipulators, encoders are usually mounted on the motor, and joint angles are estimated based on transmission kinematics. However, due to non-linear properties of cables such as cable stretch, lower stiffness, and uncertainties in kinematic model parameters, the precision of joint angle estimation is limited with transmission kinematics approach. To improve the positioning of these manipulators, we use a pair of low cost stereo camera as the observation for joint angles and we input these noisy measurements into an Unscented Kalman Filter (UKF) for state estimation. We use the dual UKF to estimate cable parameters and states offline. We evaluated the effectiveness of the proposed method on a Raven-II experimental surgical research platform. Additional encoders at the joint output were employed as a reference system. From the experiments, the UKF improved the accuracy of joint angle estimation by 33-72%. Also, we tested the reliability of state estimation under camera occlusion. We found that when the system dynamics is tuned with offline UKF parameter estimation, the camera occlusion has no effect on the online state estimation.

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