VOLUME-CONSTRAINED MOTION PLANNING IN NEUROSURGERY

In my thesis work for my M.S., I worked on modifying atomic planner operations for sampling-based motion planners to enable planning in volumes. This work was in collaboration with Houston Methodist and motivated by applications in neurosurgery. After consulting surgeons, it was clear that several assistive tasks had the potential for using a high DOF robot.

In this use case, the motions executed by the robot would need to be guaranteed to be collision-free while keeping any tools the robot manipulates inside a "safety volume" near the surgical site. I framed this problem as a version of constrained motion planning where a valid solution for a robot would move a tool held by the end effector through a volume known a priori. Previous work on constrained motion planning focuses on constraints typically of lower dimensionality than the number of degrees of spatial transformations (SE(3), i.e., the space of rotations and translations). This problem – the volume-constrained motion planning problem – constrains the space of translations and rotations the end effector can take.

proposed OR set-up

Noting this insight, I proposed several modifications to several core planner operations common to all sampling-based motion planning algorithms, namely, how planners extend or connect configurations in the robot's configuration space and how random configurations are sampled. Typically, sampling-based motion planners attempt to find solutions to queries by creating a network of randomly sampled configurations that are not in collision with any obstacles and checking which connections can be made without collision. In this case, as the volumes we desire the robot to plan inside have the potential to be relatively small, this needed to change. After finding collision-free configurations inside the volume, the planning algorithm attempts first to find a path for the end effector and then finds a robot motion that tracks the same motion.

This two-step process embeds another motion planner inside sampling-based planners to better inform how connections are drawn. To find paths for the robot's end effector, I connected states using a dual-quaternion interpolation (which had the convenient property of being parametric – neglecting the need for an explicit representation). To find robot motions that tracked this end-effector path, I designed a resolution-complete algorithm that uses the inverse kinematics of the robot to find solutions.