Mechanical and Materials Engineering Publications

Title

A chance-constrained programming approach to preoperative planning of robotic cardiac surgery under task-level uncertainty

Document Type

Article

Publication Date

3-1-2015

Volume

19

Issue

2

Journal

IEEE Journal of Biomedical and Health Informatics

First Page

612

URL with Digital Object Identifier

10.1109/JBHI.2014.2315798

Last Page

622

Abstract

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.

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