Integrating FEM-based deformable obstacles in PRM Comp768 project presentation Mert Sedef

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

Motivation Robotic surgery: Preoperative surgery, Intraoperative surgery, Postoperative surgery Robotic surgery: Preoperative surgery, Intraoperative surgery, Postoperative surgery Preoperative surgery Preoperative surgery before the surgery before the surgery the flow of surgery is planned based on patient-specific data. 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. 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. Assessment of performance and training transfer on surgical simulators. Quantitative performance measures during a training session Quantitative performance measures during a training session task completion time task completion time hand motion economy hand motion economy path length path length work done by trainee work done by trainee amount of unnecessary tissue damage 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. 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.

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) 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. 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 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 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. 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. If the limit force is already achieved, the computed path is not acceptable.

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

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

Implementation details - PRM startgoal ExpandTree()ConnectTree()TestPath() TestPathAgainstDeformableObject() Find out if response force > limit

Implementation details – deformable obstacle in PRM Fixed here

Implementation details – deformable obstacle in PRM Fixed here

Implementation details – deformable obstacle in PRM Fixed here

Implementation details – deformable obstacle in PRM Fixed here

Implementation details – deformable obstacle in PRM Fixed here

Implementation details – deformable obstacle in PRM Collision ! Fixed here

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

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

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

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

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

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

Demo