A chance-constrained programming approach to preoperative planning of robotic cardiac surgery under task-level uncertainty.
In this paper, a novel formulation for robust surgical planning of robotics-assisted minimally invasive cardiac surgery based on patient-specific preoperative images is proposed. In this context, robustness is quantified in terms of the likelihood of intraoperative collisions and of joint limit violations. The proposed approach provides a more accurate and complete formulation than existing deterministic approaches in addressing uncertainty at the task level. Moreover, it is demonstrated that the dexterity of robotic arms can be quantified as a cross-entropy term. The resulting planning problem is rendered as a chance-constrained entropy maximization problem seeking a plan with the least susceptibility toward uncertainty at the task level, while maximizing the dexterity (cross-entropy term). By such treatment of uncertainty at the task level, spatial uncertainty pertaining to mismatches between the patient-specific anatomical model and that of the actual intraoperative situation is also indirectly addressed. As a solution method, the unscented transform is adopted to efficiently transform the resulting chance-constrained entropy maximization problem into a constrained nonlinear program without resorting to computationally expensive particle-based methods.
Hamidreza
H
Azimian
Michael D
MD
Naish
Bob
B
Kiaii
Rajni V
RV
Patel
D000465:Algorithms; D006348:Cardiac Surgical Procedures / Q000379:methods*; D001026:Coronary Artery Bypass; D006801:Humans; D065287:Robotic Surgical Procedures / Q000379:methods*