Conformational Modeling of Continuum Structures in Robotics and Structural Biology: A Review

Abstract

Hyper-redundant (or snakelike) manipulators have many more degrees of freedom than are required to position and orient an object in space. They have been employed in a variety of applications ranging from search-and-rescue to minimally invasive surgical procedures, and recently they even have been proposed as solutions to problems in maintaining civil infrastructure and the repair of satellites. The kinematic and dynamic properties of snakelike robots are captured naturally using a continuum backbone curve equipped with a naturally evolving set of reference frames, stiffness properties, and mass density. When the snakelike robot has a continuum architecture, the backbone curve corresponds with the physical device itself. Interestingly, these same modeling ideas can be used to describe conformational shapes of DNA molecules and filamentous protein structures in solution and in cells. This paper reviews several classes of snakelike robots: (1) hyper-redundant manipulators guided by backbone curves; (2) flexible steerable needles; and (3) concentric tube continuum robots. It is then shown how the same mathematical modeling methods used in these robotics contexts can be used to model molecules such as DNA. All of these problems are treated in the context of a common mathematical framework based on the differential geometry of curves, continuum mechanics, and variational calculus. Both coordinate-dependent Euler-Lagrange formulations and coordinate-free Euler-Poincaré approaches are reviewed.

Continuum Reconfigurable Parallel Robots for Surgery: Shape Sensing and State Estimation With Uncertainty

“…The Continuum Reconfigurable Incisionless Surgical Parallel (CRISP) concept lies at the intersection of parallel [5], continuum [2], and reconfigurable [6] robotics. (a) CRISP devices are parallel structures consisting of a needle-diameter flexible tool that is grasped by multiple needle-diameter snare devices.…”

“…Continuum robots are largely motivated by the problem of manipulation in confined, hard-to-reach workspaces. Unlike rigid-link robots, continuum robots can continuously deform along their body [2]. Continuum devices have been applied to the applications of exploration [3] and medicine [4].…”

Autonomous Control of Continuum Robot Manipulators for Complex Cardiac Ablation Tasks

“…Because the environment can distort continuum robots into irregular and unpredictable configurations, it is difficult to model these robot manipulators accurately [21].…”

Medical Technologies and Challenges of Robot-Assisted Minimally Invasive Intervention and Diagnostics

“…[48,34]), with the exception of recent growth on continuum robots (e.g. [49,50,51]). These robots locate their actuators remotely from their end effectors in order to facilitate miniaturization.…”