A Semi-Infinite Programming Approach to Preoperative Planning of Robotic Cardiac Surgery Under Geometric Uncertainty

In this paper, a computational framework for patient-specific preoperative planning of robotics-assisted minimally invasive cardiac surgery (RAMICS) is presented. It is expected that the preoperative planning of RAMICS will improve the success rate by considering robot kinematics, patient-specific thoracic anatomy, and procedure-specific intraoperative conditions. Given the significant anatomical features localized in the preoperative computed tomography images of a patient´s thorax, port locations, and robot orientations (with respect to the patient´s body coordinate frame) are determined to optimize qualities such as dexterity, reachability, tool approach angles, and maneuverability. To address intraoperative geometric uncertainty, the problem is formulated as a generalized semi-infinite program (GSIP) with a convex lower-level problem to seek a plan that is less sensitive to geometric uncertainty in the neighborhood of surgical targets. It is demonstrated that with a proper formulation of the problem, the GSIP can be replaced by a tractable constrained nonlinear program that uses a multicriteria objective function to balance between the nominal task performance and robustness to collisions and joint limit violations. Finally, performance of the proposed formulation is demonstrated by a comparison between the plans generated by the algorithm and those recommended by an experienced surgeon for several case studies.