Continuum Reconfigurable Parallel Robots for Surgery: Shape Sensing and State Estimation with Uncertainty

Abstract

This paper examines shape sensing for a new class of surgical robot that consists of parallel flexible structures that can be reconfigured inside the human body. Known as CRISP robots, these devices provide access to the human body through needle-sized entry points, yet can be configured into truss-like structures capable of dexterous movement and large force application. They can also be reconfigured as needed during a surgical procedure. Since CRISP robots are elastic, they will deform when subjected to external forces or other perturbations. In this paper, we explore how to combine sensor information with mechanics-based models for CRISP robots to estimate their shapes under applied loads. The end result is a shape sensing framework for CRISP robots that will enable future research on control under applied loads, autonomous motion, force sensing, and other robot behaviors.

Keywords: Flexible Robots; Surgical Robotics: Laparoscopy; Surgical Robotics: Steerable Catheters/Needles.

Fig. 1

The Continuum Reconfigurable Incisionless Surgical Parallel (CRISP) concept lies at the intersection of parallel [5], continuum [2], and reconfigurable [6] robotics. (a) CRISP devices are parallel structures consisting of a needle-diameter flexible tool that is grasped by multiple needle-diameter snare devices. The snare devices are positioned using manipulators. (b) This paper addresses the problem of shape sensing and state estimation for CRISP systems using uncertain kinematic models and noisy sensors.

Fig. 2

An illustration of the information incorporated in (a) the posterior state estimate generated by the Kalman-Bucy filter at arc-length s₃, and (b) the smoothed estimate generated by the Rauch-Tung-Striebel smoother at arc-length s₃. Sensor observations are denoted by y_i. Constraints c_i are handled by the Kalman-Bucy filter as sensor observations.

Fig. 3

(a) A simulated two-snare CRISP structure is shown with an overlaid depiction of the smoothed position covariance as a single position sensor is moved down the length of the flexible tool. The position covariance represents the position uncertainty of the tool and snares. The placement of the sensor dramatically changes the smoothed estimate’s position uncertainty. (b) A simple CRISP structure with one snare is shown with an overlaid depiction of the smoothed position covariance as the snare and its grasp point are translated along the tool’s backbone. The snare configuration has a clear effect on the smoothed estimate’s position uncertainty, which may influence how a CRISP system is reconfigured. Note that this figure was generated with uncertainty in the snare grasp-point location on the tool’s body.

Fig. 4

(a) The experimental CRISP structure was placed into two configurations. The snare needles and flexible tool are traced for clarity. (b) Two views of the kinematic model (grey) and smoothed state estimate (blue) plotted on top of 24 data points obtained with the electromagnetic tracker. (c) The average backbone position error (17) is shown as a function of the number of uniformly-spaced sensor observations incorporated into the smoothed estimate. The average error was computed from 100 samples and the standard deviation is smaller than the plot points.

Fig. 5

(a) The experimental CRISP structure was placed into two configurations with a 20 g load applied 5 mm from the tool’s tip. The snare needles and flexible tool are traced for clarity. (b) Two views of the kinematic model (grey) and smoothed state estimate (blue) plotted on top of 24 data points obtained with the electromagnetic tracker. (c) The average backbone position error (17) is shown as a function of the number of uniformly-spaced sensor observations incorporated into the smoothed estimate. The average error was computed from 100 samples and the standard deviation is smaller than the plot points.

Fig. 6

(a) The estimated applied load with no actual load present for the configurations shown in Fig. 4(a), as a function of the number of sensor observations incorporated in the smoothed estimate. The estimator correctly reports there is virtually no load present when no load is actually applied. (b) The estimated applied load when a 20 g load is applied for the configurations of Fig. 5(a), as a function of the number of sensor observations incorporated in the smoothed estimate. In an observability study, we found that large uncertainty in the snare grasps can preclude the accurate estimation of applied load; uncertainty must be reduced through improved modeling or design.

Fig. 7

(a) The average tip position and tip heading error of the kinematic model with no sensors and the smoothed estimate measured at the tip of configuration 1 with a 20 g applied load, plotted as a function of the number of sensor observations incorporated in the smoothed estimate. (b) The average position and heading error of configuration 2 with the same load. In both examples, the state estimator does not know the direction or magnitude of the load. This demonstrates the estimator’s ability to estimate the CRISP system’s shape even in the presence of an unknown load. The average error is computed with 100 samples and the standard deviation is too small to display.