A chance-constrained approach to preoperative planning of robotics-assisted interventions

In this paper, a planning strategy for robotics-assisted interventions is formulated in terms of uncertainty at the task level. The proposed formulation attempts to increase the chance of success by maximizing robustness with respect to the task uncertainty. It is assumed that the instrument tip pose has a Gaussian distribution in the vicinity of the desired task frame, and the planner is formulated as a chance-constrained programming problem in terms of the chance of collisions and joint limit violations based on the inverse kinematics of the arms. The proposed objective function addresses the robustness as well as the performance of the robotic arms. As an illustrative example, the planning strategy is implemented for LIMA harvesting in minimally invasive coronary artery bypass with the da Vinci robot.