Noah J. Cowan

Nonholonomic Modeling of Needle Steering

As a flexible needle with a bevel tip is pushed through soft tissue, the asymmetry of the tip causes the needle to bend. We propose that, by using nonholonomic kinematics, control, and path planning, an appropriately designed needle can be steered through tissue to reach a specified 3D target. Such steering capability could enhance targeting accuracy and may improve outcomes for percutaneous therapies, facilitate research on therapy effectiveness, and eventually enable new minimally invasive techniques. In this paper, we consider a first step toward active needle steering: design and experimental validation of a nonholonomic model for steering flexible needles with bevel tips. The model generalizes the standard three degree-of-freedom (DOF) nonholonomic unicycle and bicycle models to 6 DOF using Lie group theory. Model parameters are fit using experimental data, acquired via a robotic device designed for the specific purpose of inserting and steering a flexible needle. The experiments quantitatively validate the bevel-tip needle steering model, enabling future research in flexible needle path planning, control, and simulation.

Mechanics of Precurved-Tube Continuum Robots

This paper presents a new class of thin, dexterous continuum robots, which we call active cannulas due to their potential medical applications. An active cannula is composed of telescoping, concentric, precurved superelastic tubes that can be axially translated and rotated at the base relative to one another. Active cannulas derive bending not from tendon wires or other external mechanisms but from elastic tube interaction in the backbone itself, permitting high dexterity and small size, and dexterity improves with miniaturization. They are designed to traverse narrow and winding environments without relying on ldquoguidingrdquo environmental reaction forces. These features seem ideal for a variety of applications where a very thin robot with tentacle-like dexterity is needed. In this paper, we apply beam mechanics to obtain a kinematic model of active cannula shape and describe design tools that result from the modeling process. After deriving general equations, we apply them to a simple three-link active cannula. Experimental results illustrate the importance of including torsional effects and the ability of our model to predict energy bifurcation and active cannula shape.

Toward Active Cannulas: Miniature Snake-Like Surgical Robots

We have developed a new class of continuously flexible snake-like robots, called active cannulas, that consist of several telescoping pre-curved superelastic tubes. The devices derive bending actuation not from tendon wires or other external mechanisms, but from elastic energy stored in the backbone itself. This allows active cannulas to have a small diameter and a high degree of dexterity, which should enable them to navigate through complex anatomy to sites inaccessible by current surgical robotic devices. Active cannulas may also enhance patient safety because their inherent compliance mitigates potential trauma from inadvertent tool-tissue collision. A consequence of our design is that dexterity improves with miniaturization. A kinematic description of active cannula shape requires a model of the elastic interaction of telescoping pre-curved flexible tubes, and we derive a two-link beam mechanics-based model. Experiments using curved nitinol tubes and wires validate the model

Nodal dynamics, not degree distributions, determine the structural controllability of complex networks.

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167–173, 2011). Although the integration of control theory and network analysis is important, we argue that the application of the structural controllability framework to most if not all real-world networks leads to the conclusion that a single control input, applied to the power dominating set, is all that is needed for structural controllability. This result is consistent with the well-known fact that controllability and its dual observability are generic properties of systems. We argue that more important than issues of structural controllability are the questions of whether a system is almost uncontrollable, whether it is almost unobservable, and whether it possesses almost pole-zero cancellations.

Equilibrium Conformations of Concentric-tube Continuum Robots

Robots consisting of several concentric, preshaped, elastic tubes can work dexterously in narrow, constrained, and/or winding spaces, as are commonly found in minimally invasive surgery. Previous models of these “active cannulas” assume piecewise constant precurvature of component tubes and neglect torsion in curved sections of the device. In this paper we develop a new coordinate-free energy formulation that accounts for general preshaping of an arbitrary number of component tubes, and which explicitly includes both bending and torsion throughout the device. We show that previously reported models are special cases of our formulation, and then explore in detail the implications of torsional flexibility for the special case of two tubes. Experiments demonstrate that this framework is more descriptive of physical prototype behavior than previous models1 it reduces model prediction error by 82% over the calibrated bending-only model, and 17% over the calibrated transmissional torsion model in a set of experiments.

Diffusion-Based Motion Planning for a Nonholonomic Flexible Needle Model

Fine needles facilitate diagnosis and therapy because they enable minimally invasive surgical interventions. This paper formulates the problem of steering a very flexible needle through firm tissue as a nonholonomic kinematics problem, and demonstrates how planning can be accomplished using diffusion-based motion planning on the Euclidean group, SE(3). In the present formulation, the tissue is treated as isotropic and no obstacles are present. The bevel tip of the needle is treated as a nonholonomic constraint that can be viewed as a 3D extension of the standard kinematic cart or unicycle. A deterministic model is used as the starting point, and reachability criteria are established. A stochastic differential equation and its corresponding Fokker-Planck equation are derived. The Euler-Maruyama method is used to generate the ensemble of reachable states of the needle tip. Inverse kinematics methods developed previously for hyper-redundant and binary manipulators that use this probability density information are applied to generate needle tip paths that reach the desired targets.

Robot-Assisted Needle Steering

Needle insertion is a critical aspect of many medical treatments, diagnostic methods, and scientific studies, and is considered to be one of the simplest and most minimally invasive medical procedures. Robot-assisted needle steering has the potential to improve the effectiveness of existing medical procedures and enable new ones by allowing increased accuracy through more dexterous control of the needle-tip path and acquisition of targets not accessible by straight-line trajectories. In this article, we describe a robot-assisted needle-steering system that uses three integrated controllers: a motion planner concerned with guiding the needle around obstacles to a target in a desired plane, a planar controller that maintains the needle in the desired plane, and a torsion compensator that controls the needle-tip orientation about the axis of the needle shaft.

Task-level control of rapid wall following in the American cockroach

SUMMARY The American cockroach, Periplaneta americana, is reported to follow walls at a rate of up to 25 turns s–1. During high-speed wall following, a cockroach holds its antenna relatively still at the base while the flagellum bends in response to upcoming protrusions. We present a simple mechanosensory model for the task-level dynamics of wall following. In the model a torsional, mass-damper system describes the cockroachs turning dynamics, and a simplified antenna measures distance from the cockroachs centerline to a wall. The model predicts that stabilizing neural feedback requires both proportional feedback (difference between the actual and desired distance to wall) and derivative feedback (velocity of wall convergence) information from the antenna. To test this prediction, we fit a closed-loop proportional-derivative control model to trials in which blinded cockroaches encountered an angled wall (30° or 45°) while running. We used the average state of the cockroach in each of its first four strides after first contacting the angled wall to predict the state in each subsequent stride. Nonlinear statistical regression provided best-fit model parameters. We rejected the hypothesis that proportional feedback alone was sufficient. A derivative (velocity) feedback term in the control model was necessary for stability.

Image Guidance of Flexible Tip-Steerable Needles

Image guidance promises to improve targeting accuracy and broaden the scope of medical procedures performed with needles. This paper takes a step toward automating the guidance of a flexible tip-steerable needle as it is inserted into the human tissue. We build upon a previously proposed nonholonomic model of needles that derive steering from asymmetric bevel forces at the tip. The bevel-tip needle is inserted and rotated at its base in order to steer it in 6 DOF. As a first step for control, we show that the needle tip can be automatically guided to a planar slice of the tissue as it is inserted. Our approach keeps the physician in the loop to control insertion speed. The distance of the needle tip position from the plane of interest is used to drive an observer-based feedback controller that we prove is locally asymptotically stable. Numerical simulations demonstrate a large domain of attraction and robustness of the controller in the face of parametric uncertainty and measurement noise. Physical experiments with tip-steerable nitinol needles inserted into a transparent plastisol tissue phantom under stereo image guidance validate the effectiveness of our approach.

Integrated planning and image-guided control for planar needle steering

Flexible, tip-steerable needles promise to enhance physicianspsila abilities to accurately reach targets and maneuver inside the human body while minimizing patient trauma. Here, we present a functional needle steering system that integrates two components: (1) a patient-specific 2D pre- and intraoperative planner that finds an achievable route to a target within a planar slice of tissue (Stochastic Motion Roadmap), and (2) a low-level image-guided feedback controller that keeps the needle tip within that slice. The planner generates a sequence of circular arcs that can be realized by interleaving pure insertions with 180deg rotations of the needle shaft. This pre-planned sequence is updated in realtime at regular intervals. Concurrently, the low-level image-based controller servos the needle to remain close to the desired plane between plan updates. Both planner and controller are predicated on a previously developed kinematic nonholonomic model of beveltip needle steering. We use slighly different needles here that have a small bend near the tip, so we extend the model to account for discontinuities of the tip position caused by 180deg rotations. Further, during large rotations of the needle base, we maintain the desired tip angle by compensating for torsional compliance in the needle shaft, neglected in previous needle steering work. By integrating planning, control, and torsion compensation, we demonstrate both accurate targeting and obstacle avoidance.