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Integrating FEM-based deformable obstacles in PRM Comp768 project presentation

Integrating FEM-based deformable obstacles in PRM Comp768 project presentation. Mert Sedef. Laparoscopic Surgery & Abdominal Region. Abdominal region Highly dynamic environment Very little free space - organs and tissues placed on top of each other

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Integrating FEM-based deformable obstacles in PRM Comp768 project presentation

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  1. Integrating FEM-based deformable obstacles in PRMComp768 project presentation Mert Sedef

  2. Laparoscopic Surgery & Abdominal Region • Abdominal region • Highly dynamic environment • Very little free space - organs and tissues placed on top of each other • In laparoscopic surgery settings, surgeon has to • Deform and move the organs on the way • But implicitly knows how much force to apply not to harm the tissues! Laparoscopic tool

  3. Motivation • Robotic surgery: Preoperative surgery, Intraoperative surgery, Postoperative surgery • Preoperative surgery • before the surgery • the flow of surgery is planned based on patient-specific data. • During this part, a motion planning algorithm can be used to find out the ultimate path of the surgical tool and the most efficient and least harmful maneuvers to follow during the Intraoperative part, which is the part where actual surgery takes place. • Assessment of performance and training transfer on surgical simulators. • Quantitative performance measures during a training session • task completion time • hand motion economy • path length • work done by trainee • amount of unnecessary tissue damage • With a motion planning algorithm designed for a specific virtual surgical task, the optimum values of measures can be calculated and the values of a trainee’s performance can be compared with the optimum ones for a realistic and correct assessment.

  4. Summary of my project • A simple model of the abdominal area with rigid obstacles (should not be touched) and deformable obstacles (can be touched and deformed until some limit) • The spherical robot is a rigid free-flying object. It aims to go from start position to a goal position in the abdominal region. • A modified motion planning algorithm (PRM) for the spherical robot to find a path in which • The robot cannot collide with the rigid obstacles • The robot can touch and deform the deformable obstacles (FEM-based organs) until it feels some limit response force from the obstacle. • If the limit force is already achieved, the computed path is not acceptable.

  5. Prior work • Bayazit, Lien, and Amato (2002). • A motion planning algorithm in a geometrically deformable environment based on Probabilistic Road Map (PRM) method • Gayle et al. (2005). • A constraint based planning algorithm for a deformable robot in complex environments. • Rodriguez, Lien, and Amato (2005). • A motion planning algorithm based on Rapidly-Exploring Random Tree technique for a deformable robot in a completely deformable environment.

  6. Implementation • PRM for planning (MPK-PRM environment) • Extended with linear elastostatic FEM deformation

  7. Implementation details - PRM TestPathAgainstDeformableObject() Find out if response force > limit ExpandTree() ConnectTree() TestPath() start goal

  8. Implementation details – deformable obstacle in PRM Fixed here

  9. Implementation details – deformable obstacle in PRM Fixed here

  10. Implementation details – deformable obstacle in PRM Fixed here

  11. Implementation details – deformable obstacle in PRM Fixed here

  12. Implementation details – deformable obstacle in PRM Fixed here

  13. Implementation details – deformable obstacle in PRM Collision ! Fixed here

  14. Implementation details – deformable obstacle in PRM Closest vertex Input displacement vector given to closest vertex

  15. Implementation details – deformable obstacle in PRM KU = Fext U = Kinv Fext = U (dof x 1) Kinv (dof x dof) Fext (dof x 1)

  16. Implementation details – deformable obstacle in PRM KU = Fext U = Kinv Fext Unknown response force at closest vertex 0 ? ? 0 ? 0 = known 0 ? 0 ? 0 ? 0 ? U (dof x 1) Kinv (dof x dof) Fext (dof x 1)

  17. Implementation details – deformable obstacle in PRM Solve for the external force on closest vertex Linear set of equations = If magnitude of computed force vector > limit try a different path ( expandTree() ) Else continue deforming and calculating

  18. Implementation details – deformable obstacle in PRM KU = Fext U = Kinv Fext Known response force at closest vertex 0 ? ? 0 ? 0 = Solve for the displacements at other vertices 0 ? 0 ? 0 ? 0 ? U (dof x 1) Kinv (dof x dof) Fext (dof x 1)

  19. Implementation details – deformable obstacle in PRM KU = Fext U = Kinv Fext Known response force at closest vertex 0 0 0 = Solve for the displacements at other vertices 0 0 0 0 U (dof x 1) Kinv (dof x dof) Fext (dof x 1)

  20. Demo

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