Existing static and kinematic models of concentric tube robots are based on the ordinary differential equations of a static Cosserat rod. In this paper, we provide the first dynamic model for concentric tube continuum robots by adapting the partial differential equations of a dynamic Cosserat rod to describe the coupled inertial dynamics of precurved concentric tubes. This generates an initial-boundary-value problem that can capture robot vibrations over time. We solve this model numerically at high time resolutions using implicit finite differences in time and arc length. This approach is capable of resolving the high-frequency torsional dynamics that occur during unstable "snapping" motions and provides a simulation tool that can track the true robot configuration through such transitions. Further, it can track slower oscillations associated with bending and torsion as a robot interacts with tissue at real-time speeds. Experimental verification of the model shows that this wide range of effects is captured efficiently and accurately.

We introduce a method to optimize on a patient-specific basis the kinematic design of the Continuum Reconfigurable Incisionless Surgical Parallel (CRISP) robot, a needle-diameter medical robot based on a parallel structure that is capable of performing minimally invasive procedures. Our objective is to maximize the ability of the robot's tip camera to view tissue surfaces in constrained spaces. The kinematic design of the CRISP robot, which greatly influences its ability to perform a task, includes parameters that are fixed before the procedure begins, such as entry points into the body and parallel structure connection points. We combine a global stochastic optimization algorithm, Adaptive Simulated Annealing (ASA), with a motion planner designed specifically for the CRISP robot. ASA facilitates exploration of the robot's design space while the motion planner enables evaluation of candidate designs based on their ability to successfully view target regions on a tissue surface. By leveraging motion planning, we ensure that the evaluation of a design only considers motions which do not collide with the patient's anatomy. We analytically show that the method asymptotically converges to a globally optimal solution and demonstrate our algorithm's ability to optimize kinematic designs of the CRISP robot on a patient-specific basis.

Continuum Reconfigurable Incisionless Surgical Parallel (CRISP) robots consist of multiple needle-diameter flexible instruments that are assembled into a parallel structure inside the human body. With a camera placed at the tip of one of the instruments, the CRISP robot can be used to inspect anatomical sites in constrained body cavities in a minimally invasive manner. We introduce a motion planner for CRISP robots that computes manipulations of the flexible instruments outside the body such that the camera can visually inspect a user-specified site of clinical interest inside the body. Our sampling-based motion planner ensures avoidance of collisions with anatomical obstacles inside the body, enforces remote-center-of-motion constraints on the instrument's entry points into the body, and efficiently handles the expensive computation of CRISP robot kinematics. We also extend the motion planner to estimate the set of points inside a body cavity that can be visually inspected by the camera of a CRISP robot for a given setup. We demonstrate our method in a simulated endoscopic medical procedure in the pleural space around a lung.

We propose a new class of robotic device for minimally-invasive surgery that lies at the intersection of continuum, parallel, and reconfigurable robotics. This Continuum Reconfigurable Incisionless Surgical Parallel (CRISP) paradigm involves the use of multiple needle-diameter devices inserted through the skin and assembled into parallel structures inside the body. The parallel structure can be reconfigured inside the patient's body to satisfy changing task requirements such as reaching initially inaccessible locations or modifying mechanical stiffness for manipulation or palpation. Another potential advantage of the CRISP concept is that many small (needle-sized) entry points into the patient may be preferable in terms of both patient healing and cosmesis to the single (or multiple) larger ports needed to admit current surgical robots. This paper presents a mechanics-based model for CRISP forward and inverse kinematics, along with experimental validation.