Efficient Data-driven Joint-level Calibration of Cable-driven Surgical Robots

TL;DR

The paper addresses the challenge of inaccurate joint-position estimation in cable-driven robotic arms (notably RAVEN-II) due to cable stretch, which impairs safe automation of surgical tasks. It proposes an efficient data-driven joint-level calibration that uses zig-zag trajectories to collect ground-truth data and train error-correcting models (DNN, linear regression, and 2nd-order polynomial) that map robot states to the joint-position error, outputting corrections rather than end-to-end joint positions. The approach achieves high accuracy within 8–21 minutes of calibration (down to $0.104^{\circ}$, $0.120^{\circ}$, and $0.118~\mathrm{mm}$ for joints 1–3) and remains reliable over 6 hours of idle, unloaded, and loaded operation, with the DNN offering best accuracy and convergence and linear regression enabling fast, 1000 Hz servo-compatible inference. A key finding is that training on joint error yields superior performance for DNNs, while restricting inputs to essential features prevents performance degradation when operating under real-time constraints, and a Python-based CRTK controller provides a practical software backbone for deployment.

Abstract

Knowing accurate joint positions is crucial for safe and precise control of laparoscopic surgical robots, especially for the automation of surgical sub-tasks. These robots have often been designed with cable-driven arms and tools because cables allow for larger motors to be placed at the base of the robot, further from the operating area where space is at a premium. However, by connecting the joint to its motor with a cable, any stretch in the cable can lead to errors in kinematic estimation from encoders at the motor, which can result in difficulties for accurate control of the surgical tool. In this work, we propose an efficient data-driven calibration of positioning joints of such robots, in this case the RAVEN-II surgical robotics research platform. While the calibration takes only 8-21 minutes, the accuracy of the calibrated joints remains high during a 6-hour heavily loaded operation, suggesting desirable feasibility in real practice. The calibration models take original robot states as input and are trained using zig-zag trajectories within a desired sparsity, requiring no additional sensors after training. Compared to fixed offset compensation, the Deep Neural Network calibration model can further reduce 76 percent of error and achieve accuracy of 0.104 deg, 0.120 deg, and 0.118 mm in joints 1, 2, and 3, respectively. In contrast to end-to-end models, experiments suggest that the DNN model achieves better accuracy and faster convergence when outputting the error to correct original inaccurate joint positions. Furthermore, a linear regression model is shown to have 160 times faster inference speed than DNN models for application within the 1000 Hz servo control loop, with slightly compromised accuracy.

Figures (12)

• Figure 1: Workflow of the calibration. The time cost mainly depends on the collection of training data. The time cost of data processing and model training may vary for different CPUs. GPU is not necessary for the training of neural network models in this paper, unless stated otherwise. Designed for surgical purposes, the first 3 joint axes of RAVEN-II always intersect at the same location which is called the remote motion center and the surgical instrument will always pass this location as the incision site (top left). In order to possess compact and light arms, the motors and encoders are mounted on the robot base, and joints are driven by cables, which results in considerable errors in joint positions obtained by remote motor encoders (top middle). Without calibration, the average positional error of RAVEN-II's end-effector is around 20 mm (top right).
• Figure 2: The joints and cable connections of the RAVEN-II surgical robot. Compared to joints 2-7, joint 1 has a considerably short cable length (alpha wrap). Joint 3 is prismatic and has a large range for insertion, while all the rest of the joints are rotational. Joints 6 and 7 control the left and right fingers of the end-effector and can be considered as one joint in kinematics. Thus, RAVEN-II has 6 joints in kinematic models instead of 7. The left arm and the right arm of RAVEN-II are symmetric.
• Figure 3: Examples of calibration trajectories with different directions (top) and sparsity (bottom). Please note that the trajectories are defined in joint space instead of Cartesian space. Different directions cause different coverage in different joints. Smaller sparsity results in better coverage of the joint space, but also takes a longer time to execute.
• Figure 4: Model of regression-based calibration (left) and learning-based calibration (right). The outputs of the DNN model and regression model are the errors of the joint positions, these errors are added back to RAVEN-II's original inaccurate joint positions to obtain the calibrated joint positions. The output of the regression models can be either the same or end-to-end output of joint positions (details in \ref{['schar_train_on_err']}).
• Figure 5: Calibration performance with different sparsities of the calibration trajectory. For sparsity $1/2$, $1/3$, $1/4$, 5 independent calibration trajectories were recorded, and for sparsity $1/5$, $1/6$, 3 independent were recorded to prevent long-time operating. Combinations of trajectories with different sparsities, no longer than 1013 seconds to record, were also evaluated. Average RMSE is shown in solid lines and the standard deviations are shown in shades.