Needle Path Planning for Autonomous Robotic Surgical Suturing

Abstract

This paper develops a path plan for suture needles used with solid tissue volumes in endoscopic surgery. The path trajectory is based on the best practices that are used by surgeons. The path attempts to minimize the interaction forces between the tissue and the needle. Using surgical guides as a basis, two different techniques for driving a suture needle are developed. The two techniques are compared in hardware experiments by robotically driving the suture needle using both of the motion plans.

Fig. 1

This is an example image of a suture (adapted from [11]). Once the needle completes the suture, the suture thread (purple) will close the wound (triangle cut out of the tissue). The distance of the entry point and the exit point from the wound are approximately equal to the depth of the needle (γ). The tip of the needle is the arrow. The base of the needle is marked by a circle. To avoid clutter, the thread will be absent from other needle figures.

Fig. 2

This is the pose of the needle before it begin to bite the tissue. Notice that the tip of the needle is nearly but not quite orthogonal to the tissue. The scaler α is the initial distance between the needle tip and the needle entrance point. m is the location of the tissue break undergoing repairs. Ideally m is midway between g and f. The location defined by f is the point where the needle is supposed to exit the tissue.

Fig. 3

The depth of the needle in the tissue (d) can be calculated using the distance (p) between the needle entrance (g) and exit (f) points along with the needle radius (r). The values p and r in turn generate the height of the needle center (c) above the tissue. This value is given by h. The difference between r and h gives the needle depth in the tissue.

Fig. 4

Once the needle has penetrated the tissue, it is now possible to reorient the needle so that the needle will naturally drive to the target exit point. The point f is the location of the exit point. The dashed view of the needle is a sample orientation of needle after completing the alignment. The point c is the point that the needle center starts at. After the needle finishes the alignment, the center of the needle is now at c′. The dashed curve from c to c′ is the curve that the center of the needle will move through. Notice that this curve is a circular arc that is centered on the point g′. The scalar, ω₁, is the angular rate of rotation of the point c about g′. The angular velocity ω₂ is the speed of rotation of the body of the needle about the center point c.

Fig. 5

The non holonomic motion plan reorients the needle such that the tip velocity is exclusively tangential. The vector, v_c, is the motion of the needle center, c, towards the desired needle center, c′. Since v_c is parallel to x_n, it is not pointed directly at the target, c′. The dashed line representing the needle is one possible position of the needle after reaching the exit, f. Notice that the new needle position no longer passes through the point g′. This is due to the fact that the invariant motion of g′ must be sacrificed to maintain the non holonomic motion constraint.

Fig. 6

The images above are composite images of the needle position as it moves. The needles are colored green, yellow, and red. The green portion corresponds to the portion of the needle outside the tissue. The yellow portion is where the needle enters the tissue. Finally, the needle is colored red inside the tissue. The two different reorientations have different overall effects on the tissue. In Fig. 6a, the needle sweeps out a small area during the reorientation, but there is no area swept at the point where the needle intersects the tissue. In Fig. 6b, tissue stress at the needle tip is minimized, but the needle sweeps out a larger area. It also appears that the needle is deeper inside the tissue for the non holonomic needle motion.

Fig. 7

Shown above is a sample group of images for driving a suture needle holonomically. The tip of the gripper that actually holds the needle is touching the tissue right before the holder regrasps the needle.

Fig. 8

Shown above is a sample group of images for driving a suture needle with the non holonomic constraint. The tip of the gripper that actually holds the needle is touching the tissue right before the holder regrasps the needle.

Fig. 9

Measured force magnitudes for both the holonomic (9a) and non holonomic (9b) needle reorientation. The sensed readings are not adjusted to remove any forces due to the weight of the needle gripper.