Method for determining an insertion trajectory of a tool in a deformable tissular matrix and robotic system executing the method

1. A method for determining an insertion trajectory of a tool for reaching a moving target object prior to its insertion into a tissular matrix, wherein the tissular matrix comprises obstacles, and wherein the target object has an initial position, the method comprising:

acquiring images of the tissular matrix;

constructing a three-dimensional representation of the tissular matrix from the images;

determining coordinates of the initial position of the target object and coordinates of the obstacles;

determining at least one potential trajectory of the tool from the coordinates of the obstacles of the tissular matrix and of the coordinates of the initial position of the target object, wherein in the potential trajectory, the tool encounters no obstacles up to the initial position of the target object during insertion;

simulating insertion of the tool in the three-dimensional representation of the tissular matrix to determine displacement of the target object within the tissular matrix during insertion of the tool up to the initial position of the target object along the determined potential trajectory;

determining a new position of the target object based on the determined displacement; and

determining the insertion trajectory for the new position of the target object.

2. The method of claim 1 , wherein the potential trajectory of the tool is determined by identifying a least cost trajectory among a set of trajectories along which the tool encounters no obstacle during insertion of the tool up to the initial position of the target object.

3. The method of claim 2 , wherein the least cost trajectory is the shortest trajectory up to the initial position of the target object.

4. The method of claim 1 , further comprising:

generating a set of target points to be tested around the new position of the target object; and

determining a finite family of trajectories to be tested from the generated set of target points to be tested,

wherein the trajectories to be tested are substantially colinear to the potential trajectory and wherein the trajectories to be tested arrive at one of the target points.

5. The method of claim 4 , wherein, for each of the trajectories of the family of trajectories, the method further comprises:

determining the displacement of the target object during insertion of the tool along the trajectory to be tested to obtain the position of the target object after insertion of the tool along the trajectory to be tested;

calculating an error, wherein the error is the distance between the target point of the corresponding trajectory to be tested and the position of the target object after insertion of the tool along the trajectory to be tested;

comparing the errors among the trajectories to be tested and the potential trajectory; and

selecting the insertion trajectory of the tool, wherein the insertion trajectory is the trajectory of the family of trajectories having the lowest error.

6. The method of claim 1 , wherein determining the insertion trajectory for the new position of the target object is carried out by iteration, wherein for the i th iteration the method further comprises:

determining the displacement of the target object during insertion of the tool along an i th trajectory to obtain an i th position of the target object, wherein the i th trajectory is substantially colinear to an i−1 th trajectory and wherein the i th trajectory arrives at the i−1 th position of the target object;

calculating an i th error, wherein the i th error is the distance between the i−1 th position of the target object and the i th position of the target object after insertion of the tool along the i th trajectory up to the i−1 th position of the target object.

7. The method of claim 6 , wherein determining the displacement of the target object during insertion of the tool along an i th trajectory and calculating an i th error are reiterated a finite number of times, and wherein the trajectory having the lowest error is selected to be the insertion trajectory.

8. The method of claim 6 , wherein determining the insertion trajectory for the new position of the target object further comprises:

comparing the i th error to a threshold,

wherein if the i th error is greater than the threshold, determining the displacement of the target object during insertion of the tool along an i th trajectory and calculating an i th error are reiterated, and if the i th error is less than the threshold, the i th trajectory is selected to be the insertion trajectory.

9. A robotic system for positioning a tool to be inserted into a tissular matrix to reach a moving target object within the tissular matrix, wherein the tissular matrix comprises obstacles, the system comprising:

an imaging module configured to acquire a three-dimensional image of the tissular matrix and to determine coordinates of an initial position of the target object and coordinates of the obstacles;

a tool support;

a determination module configured to:

determine an insertion trajectory of the tool from the coordinates of the initial position of the target object and the obstacles;

determine at least one potential trajectory of the tool from the coordinates of the obstacles of the tissular matrix and of the coordinates of the initial position of the target object, wherein in the potential trajectory, the tool encounters no obstacles up to the initial position of the target object during insertion;

simulate insertion of the tool in the three-dimensional representation of the tissular matrix to determine displacement of the target object within the tissular matrix during insertion of the tool up to the initial position of the target object along the determined potential trajectory;

determine a new position of the target object based on the determined displacement; and

determine the insertion trajectory for the new position of the target object; and

a positioning module configured to position the tool based on the determined insertion trajectory by displacing the tool support so that the tool is positioned according to the insertion trajectory.