  Robot arm placements are oftentimes a limitation in surgical preoperative
procedures, relying on trained staff to evaluate and decide on the optimal
positions for the arms. Given new and different patient anatomies, it can be
challenging to make an informed choice, leading to more frequently colliding
arms or limited manipulator workspaces. In this paper, we develop a method to
generate the optimal manipulator base positions for the multi-port da Vinci
surgical system that minimizes self-collision and environment-collision, and
maximizes the surgeon's reachability inside the patient. Scoring functions are
defined for each criterion so that they may be optimized over. Since for
multi-manipulator setups, a large number of free parameters are available to
adjust the base positioning of each arm, a challenge becomes how one can
expediently assess possible setups. We thus also propose methods that perform
fast queries of each measure with the use of a proxy collision-checker. We then
develop an optimization method to determine the optimal position using the
scoring functions. We evaluate the optimality of the base positions for the
robot arms on canonical trajectories, and show that the solution yielded by the
optimization program can satisfy each criterion. The metrics and optimization
strategy are generalizable to other surgical robotic platforms so that
patient-side manipulator positioning may be optimized and solved.
