Adaptive Nonparametric Kinematic Modeling of Concentric Tube Robots

A Data-Driven Model with Hysteresis Compensation for I2RIS Robot

Retinal microsurgery is a high-precision surgery performed on a delicate tissue requiring the skill of highly trained surgeons. Given the restricted range of instrument motion in the confined intraocular space, snake-like robots may prove to be a promising technology to provide surgeons with greater flexibility, dexterity, and positioning accuracy during retinal procedures such as retinal vein cannulation and epiretinal membrane peeling. Kinematics modeling of these robots is an essential step toward accurate position control. Unlike conventional manipulators, modeling these robots does not follow a straightforward method due to their complex mechanical structure and actuation mechanisms. The hysteresis problem can especially impact the positioning accuracy significantly in wire-driven snake-like robots. In this paper, we propose a data-driven kinematics model using a probabilistic Gaussian mixture model (GMM) and Gaussian mixture regression (GMR) approach with a hysteresis compensation algorithm. Experimental results on the two-degree-of-freedom (DOF) integrated robotic intraocular snake (I2RIS) show that the proposed model with the hysteresis compensation can predict the snake tip bending angle for pitch and yaw with 0.45° and 0.39° root mean square error (RMSE), respectively. This results in overall 60% and 70% improvements of accuracy for yaw and pitch over the same model without the hysteresis compensation.

Exceeding traditional curvature limits of concentric tube robots through redundancy resolution

Understanding elastic instability has been a recent focus of concentric tube robot research. Modeling advances have enabled prediction of when instabilities will occur and produced metrics for the stability of the robot during use. In this paper, we show how these metrics can be used to resolve redundancy to avoid elastic instability, opening the door for the practical use of higher curvature designs than have previously been possible. We demonstrate the effectiveness of the approach using a three-tube robot that is stabilized by redundancy resolution when following trajectories that would otherwise result in elastic instabilities. We also show that it is stabilized when teleoperated in ways that otherwise produce elastic instabilities. Lastly, we show that the redundancy resolution framework presented here can be applied to other control objectives useful for surgical robots, such as maximizing or minimizing compliance in desired directions.

Learning the Complete Shape of Concentric Tube Robots

Concentric tube robots, composed of nested pre-curved tubes, have the potential to perform minimally invasive surgery at difficult-to-reach sites in the human body. In order to plan motions that safely perform surgeries in constrained spaces that require avoiding sensitive structures, the ability to accurately estimate the entire shape of the robot is needed. Many state-of-the-art physics-based shape models are unable to account for complex physical phenomena and subsequently are less accurate than is required for safe surgery. In this work, we present a learned model that can estimate the entire shape of a concentric tube robot. The learned model is based on a deep neural network that is trained using a mixture of simulated and physical data. We evaluate multiple network architectures and demonstrate the model's ability to compute the full shape of a concentric tube robot with high accuracy.