Automating precision subtasks such as debridement (removing dead or diseased tissue fragments) with Robotic Surgical Assistants (RSAs) such as the da Vinci Research Kit (dVRK) is challenging due to inherent nOnlinearities in cable-driven systems. We propose and evaluate a novel two-phase coarse-to-fine calibration method. In Phase I (coarse), we place a red calibration marker on the end effector and let it randomly move through a set of open-loop trajectories to obtain a large sample set of camera pixels and internal robot end-effector configurations. This coarse data is then used to train a Deep Neural Network (DNN) to learn the coarse transformation bias. In Phase II (fine), the bias from Phase I is applied to move the end -effector toward a small set of specific target points on a printed sheet. For each target, a human operator manually adjusts the end -effector position by direct contact (not through teleoperation) and the residual compensation bias is recorded. This fine data is then used to train a Random Forest (RF) to learn the fine transformation bias. Subsequent experiments suggest that without calibration, position errors average 4.55mm. Phase I can reduce average error to 2.14mm and the combination of Phase I and Phase II can reduces average error to 1.08mm. We apply these results to debridement of raisins and pumpkin seeds as fragment phantoms. Using an endoscopic stereo camera with standard edge detection, experiments with 120 trials achieved average success rates of 94.5 %, exceeding prior results with much larger fragments (89.4%) and achieving a speedup of 2.1x, decreasing time per fragment from 15.8 seconds to 7.3 seconds. Source code, data, and videos are available at https://sites.google.com/view/calib-icra/.

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Fast and Reliable Autonomous Surgical Debridement with Cable-Driven Robots Using a Two-Phase Calibration Procedure

Haptic feedback is a critical but a clinically missing component in robotic minimally invasive surgeries. This paper proposes a Gaussian process regression (GPR) based scheme to address the gripping force estimation problem for clinically commonly used elongated cable-driven surgical instruments. Based on the cable-driven mechanism property studies, and surgical robotic system properties, four different GPR filters were designed and analyzed, including one GPR filter with two-dimensional inputs, one GPR filter with three-dimensional inputs, one GPR unscented Kalman filter (UKF) with two-dimensional inputs, and one GPR UKF with three-dimensional inputs. The four proposed methods were compared with the dynamic model based UKF filter on a 10 mm gripper on the Raven II surgical robot platform. The experimental results demonstrated that the four proposed methods outperformed the dynamic model based method on precision and reliability without parameter tuning. And surprisingly, among the four methods, the simplest GPR Filter with two-dimensional inputs has the best performance.

Gaussian Process Regression for Sensorless Grip Force Estimation of Cable-Driven Elongated Surgical Instruments

Background
Robotically assisted minimally invasive surgery can offer many benefits over open surgery and laparoscopic minimally invasive surgery. However, currently, there is no force sensing and force feedback.

Methods
This research was implemented using the da Vinci research kit. An external force estimation and implementation method was proposed based on dynamics and motor currents. The dynamics of the Patient Side Manipulator was modeled. The dynamic model was linearly parameterized. The estimation principle of external force was derived. The dynamic parameters were experimentally identified using a least squares method.

Results
Several experiments including dynamic parameter identification, joint torque estimation, and external force estimation were performed. The results showed that the proposed method could implement force estimation without using a force sensor.

Conclusions
The force estimation method was proposed and implemented and experimental results showed the method worked and was feasible. This method could be used for force sensing in minimally invasive surgical robotics in the future.

External force estimation and implementation in robotically assisted minimally invasive surgery

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 model-based sensorless grip force estimation method to address the haptic perception problem for commonly used elongated cable-driven 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 1-dimensional 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

Dynamic modeling of cable driven elongated surgical instruments for sensorless grip force estimation

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.

Hysteresis model of longitudinally loaded cable for cable driven robots and identification of the parameters

In this paper we present experimentally obtained cable-pulley Coulomb and viscous friction for cable-driven surgical robotic systems including the RAVEN II surgical robotic research platform. In the study of controlling cable-driven systems a simple mathematical model which does not capture physical behavior well is often employed. Even though control of such systems is achievable without an accurate model, fully understanding the behavior of the system will potentially realize more robust control. A surgical robot is one of the systems that often relies on cables as an actuation method as well as pulleys to guide them. Systems with such structure encounter frictional force related to conditions of cable and pulley such as cable velocity, tension, type and number of pulley, and angle of cable wrapping around pulley. Using a couple of test platforms that incorporate cable, pulleys, and other experimental conditions corresponding to the RAVEN II system, it is shown that cable-pulley friction is function of tension, wrap angle, and number of pulleys and not of magnitude of cable velocity.

Measurement of the cable-pulley Coulomb and viscous friction for a cable-driven surgical robotic system

In this article, a method of modeling robotic systems with closed-circuit cable–pulley transmissions using the independently developed hysteretic cable stretch model and cable–pulley network friction model is presented. The hysteretic cable stretch model captures the responses of the cable including elasticity, internal friction, material damping, and hysteresis. The cable–pulley network friction is a function of cable tension, average individual wrap angle of cable around pulley, and number of pulleys. For the verification of the method, these two models are integrated into the dynamic model of the first three joints of the RAVEN II robotic surgery platform. The parameters of the developed model are specifically tuned for the RAVEN II and the performance of the model is compared against the kinematic model and a previous, simplified dynamic model (a model with exponential cable stretch and linear damping model). The result showed that even though significant improvements were not observed for the first two joints, the average error and the maximum error of the third joint, which uses smaller diameter and longer cable and more guide pulleys, could be reduced by 10–20% and 5–10%, respectively, over the previous, simplified dynamic model. Also, analysis with various input trajectories indicated that cable-driven systems with very low speed, frequent change in the loading condition, and high cable tension benefit from the proposed method.

Joseph Matheson

Papers

Measurement of the cable-pulley Coulomb and viscous friction for a cable-driven surgical robotic system

Modeling Cable-Driven Robot With Hysteresis and Cable–Pulley Network Friction