Motion planning for concentric tube robots using mechanics-based models

Abstract

Concentric tube robots have the potential to enable new minimally invasive surgical procedures by curving around anatomical obstacles to reach difficult-to-reach sites in body cavities. Planning motions for these devices is challenging in part due to their complex kinematics; concentric tube robots are composed of thin, pre-curved, telescoping tubes that can achieve a variety of shapes via extension and rotation of each of their constituent tubes. We introduce a new motion planner to maneuver these devices to clinical targets while minimizing the probability of colliding with anatomical obstacles. Unlike prior planners for these devices, we more accurately model device shape using mechanics-based models that consider torsional interaction between the tubes. We also account for the effects of uncertainty in actuation and predicted device shape. We integrate these models with a sampling-based approach based on the Rapidly-Exploring Roadmap to guarantee finding optimal plans as computation time is allowed to increase. We demonstrate our motion planner in simulation using a variety of evaluation scenarios including an anatomy-based neurosurgery case that requires maneuvering to a difficult-to-reach brain tumor at the skull base.

Can concentric tube robots follow the leader?

“…To determine conditions for concentric tube follow-the leader deployment, we first assume a deployment sequence in which no tube which ends at an arc length s < L undergoes insertion or retraction, and that all tubes which advance axially to extend the robot's tip do so together.2 Continuing from (6), we can substitute in the robot model (9) and replace j=l (10) Note that all of the rotational configuration functions 'VJi ap pear in these conditions, as well as their time derivatives. The time derivatives of the precurvature functions also appear, and are nonzero for tubes that have non-constant precurvature and are undergoing insertion.…”

“…While a great deal of the recent research in concentric tube robots has focused on the latter of these two motivations (see e.g. [7], [8]), efforts have also been made to address the former through motion planning (choosing actuator sequences to keep the shaft of the robot within anatomical bounds during deployment [9]), and in using a special case involving one curved tube and two straight tubes to hit targets in soft tissues [lO], [11].…”

“…The complexity of the equilibrium curve even for this very special and seemingly simple case raises questions as to whether follow-the-Ieader deployment is possible at all for physical robots. Based on this, recent motion planning [9] and design [21] results have used the latest mechanics-based models [5], [6], which account for bending and torsion everywhere in the device, despite formidable computational challenges in doing so. These motion planning results have revealed that curvatures and actuation sequences must be very carefully selected to enable the robot to deploy through tubular anatomical constraints (i.e.…”

A general formulation and approach to constrained, continuum manipulation

“…[13] There is also work on surgery insertion using pre-curved concentric tube robots. [14,15] More recently, an algorithm [16] was introduced for a continuum manipulator with a fixed base to perform autonomous manipulation with the tip position of the manipulator constrained to a given path as required by a task, such as an inspection task.…”

Task-constrained continuum manipulation in cluttered space

“…2 shows one example of a cluttered pipe environment, courtesy of the Electric Power Research Institute (EPRI): certain pipes in this environment can be reached by a continuum manipulator for inspection but are difficult to reach by an articulated manipulator. Continuum manipulation was mainly performed via teleoperation in the past [8], [9]; only recently, motion planning algorithms of surgery insertion using pre-curved concentric tube robots have been proposed in [10], [11]. Autonomous algorithms of grasping a target object using continuum robots have been introduced in [12], [13], while avoiding obstacles [14], [15], and in cluttered space [16].…”