A Kinetostatic Model for Concentric Push-Pull Robots.

Concentric push-pull robots (CPPR) operate through the mechanical interactions of concentrically nested, laser-cut tubes with offset stiffness centers. The distal tips of the tubes are attached to each other, and relative displacement of the tube bases generates bending in the CPPR. Previous CPPR kinematic models assumed two tubes, planar shapes, no torsion, and no external loads. In this paper, we develop a new, more general CPPR model accounting for any number of tubes, describing their variable-curvature 3D shape when actuated, including the effects of torsion and external loads. To accomplish this, we employ a modified Kirchhoff rod model for each tube (with offset stiffness center) and embed the constraints of concentricity. We use an energy method to determine robot shape as a function of actuation and external loading. We experimentally validate this kinetostatic model on prototype CPPRs with two tubes and three tubes and non-constant laser-cut patterns that create variable curvature and stiffness. Experimental results agree with the model, paving the way for use of this model in design optimization, planning, and control of CPPRs.

Continuum Robots for Medical Interventions.

Continuum robots are not constructed with discrete joints but, instead, change shape and position their tip by flexing along their entire length. Their narrow curvilinear shape makes them well suited to passing through body lumens, natural orifices, or small surgical incisions to perform minimally invasive procedures. Modeling and controlling these robots are, however, substantially more complex than traditional robots comprised of rigid links connected by discrete joints. Furthermore, there are many approaches to achieving robot flexure. Each presents its own design and modeling challenges, and to date, each has been pursued largely independently of the others. This article attempts to provide a unified summary of the state of the art of continuum robot architectures with respect to design for specific clinical applications. It also describes a unifying framework for modeling and controlling these systems while additionally explaining the elements unique to each architecture. The major research accomplishments are described for each topic and directions for the future progress needed to achieve widespread clinical use are identified.

Leveraging Geometry to Enable High-Strength Continuum Robots.

Developing high-strength continuum robots can be challenging without compromising on the overall size of the robot, the complexity of design and the range of motion. In this work, we explore how the load capacity of continuum robots can drastically be improved through a combination of backbone design and convergent actuation path routing. We propose a rhombus-patterned backbone structure composed of thin walled-plates that can be easily fabricated via 3D printing and exhibits high shear and torsional stiffness while allowing bending. We then explore the effect of combined parallel and converging actuation path routing and its influence on continuum robot strength. Experimentally determined compliance matrices are generated for straight, translation and bending configurations for analysis and discussion. A robotic actuation platform is constructed to demonstrate the applicability of these design choices.

STEERABLE NEEDLE TRAJECTORY FOLLOWING IN THE LUNG: TORSIONAL DEADBAND COMPENSATION AND FULL POSE ESTIMATION WITH 5DOF FEEDBACK FOR NEEDLES PASSING THROUGH FLEXIBLE ENDOSCOPES.

Bronchoscopic diagnosis and intervention in the lung is a new frontier for steerable needles, where they have the potential to enable minimally invasive, accurate access to small nodules that cannot be reliably accessed today. However, the curved, flexible bronchoscope requires a much longer needle than prior work has considered, with complex interactions between the needle and bronchoscope channel, introducing new challenges in steerable needle control. In particular, friction between the working channel and needle causes torsional windup along the bronchoscope, the effects of which cannot be directly measured at the tip of thin needles embedded with 5 degree-of-freedom magnetic tracking coils. To compensate for these effects, we propose a new torsional deadband-aware Extended Kalman Filter to estimate the full needle tip pose including the axial angle, which defines its steering direction. We use the Kalman Filter estimates with an established sliding mode controller to steer along desired trajectories in lung tissue. We demonstrate that this simple torsional deadband model is sufficient to account for the complex interactions between the needle and endoscope channel for control purposes. We measure mean final targeting error of 1.36 mm in phantom tissue and 1.84 mm in ex-vivo porcine lung, with mean trajectory following error of 1.28 mm and 1.10 mm, respectively.

A Dynamic Model for Concentric Tube Robots.

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.