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

Group-theoretic analysis of symmetry-preserving deployable structures and metamaterials

Many deployable structures in nature, as well as human-made mechanisms, preserve symmetry as their configurations evolve. Examples in nature include blooming flowers, dilation of the iris within the human eye, viral capsid maturation and molecular and bacterial motors. Engineered examples include opening umbrellas, elongating scissor jacks, variable apertures in cameras, expanding Hoberman spheres and some kinds of morphing origami structures. In these cases, the structures either preserve a discrete symmetry group or are described as an evolution from one discrete symmetry group to another of the same type as the structure deploys. Likewise, elastic metamaterials built from lattice structures can also preserve symmetry type while passively deforming and changing lattice parameters. A mathematical formulation of such transitions/deployments is articulated here. It is shown that if [Formula: see text] is Euclidean space, [Formula: see text] is a continuous group of motions of Euclidean space and [Formula: see text] is the type of the discrete subgroup of [Formula: see text] describing the symmetries of the deploying structure, then the symmetry of the evolving structure can be described by time-dependent subgroups of [Formula: see text] of the form [Formula: see text], where [Formula: see text] is a time-dependent affine transformation. Then, instead of considering the whole structure in [Formula: see text], a 'sector' of it that lives in the orbit space [Formula: see text] can be considered at each instant in time, and instead of considering all motions in [Formula: see text], only representatives from right cosets in the space [Formula: see text] need to be considered. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Bioinspiration and Biomimetic Art in Robotic Grippers

The autonomous manipulation of objects by robotic grippers has made significant strides in enhancing both human daily life and various industries. Within a brief span, a multitude of research endeavours and gripper designs have emerged, drawing inspiration primarily from biological mechanisms. It is within this context that our study takes centre stage, with the aim of conducting a meticulous review of bioinspired grippers. This exploration involved a nuanced classification framework encompassing a range of parameters, including operating principles, material compositions, actuation methods, design intricacies, fabrication techniques, and the multifaceted applications into which these grippers seamlessly integrate. Our comprehensive investigation unveiled gripper designs that brim with a depth of intricacy, rendering them indispensable across a spectrum of real-world scenarios. These bioinspired grippers with a predominant emphasis on animal-inspired solutions have become pivotal tools that not only mirror nature's genius but also significantly enrich various domains through their versatility.

Design and Fabrication of a Fiber Bragg Grating Shape Sensor for Shape Reconstruction of a Continuum Manipulator

Continuum dexterous manipulators (CDMs) are suitable for performing tasks in a constrained environment due to their high dexterity and maneuverability. Despite the inherent advantages of CDMs in minimally invasive surgery, real-time control of CDMs' shape during nonconstant curvature bending is still challenging. This study presents a novel approach for the design and fabrication of a large deflection fiber Bragg grating (FBG) shape sensor embedded within the lumens inside the walls of a CDM with a large instrument channel. The shape sensor consisted of two fibers, each with three FBG nodes. A shape-sensing model was introduced to reconstruct the centerline of the CDM based on FBG wavelengths. Different experiments, including shape sensor tests and CDM shape reconstruction tests, were conducted to assess the overall accuracy of the shape-sensing. The FBG sensor evaluation results revealed the linear curvature-wavelength relationship with the large curvature detection of 0.045 mm and a high wavelength shift of up to 5.50 nm at a 90° bending angle in both the bending directions. The CDM's shape reconstruction experiments in a free environment demonstrated the shape-tracking accuracy of 0.216 ± 0.126 mm for positive/negative deflections. Also, the CDM shape reconstruction error for three cases of bending with obstacles was observed to be 0.436 ± 0.370 mm for the proximal case, 0.485 ± 0.418 mm for the middle case, and 0.312 ± 0.261 mm for the distal case. This study indicates the adequate performance of the FBG sensor and the effectiveness of the model for tracking the shape of the large-deflection CDM with nonconstant-curvature bending for minimally invasive orthopedic applications.

Visual servoing of continuum robots: Methods, challenges, and prospects

BACKGROUND

Recent advancements in continuum robotics have accentuated developing efficient and stable controllers to handle shape deformation and compliance. The control of continuum robots (CRs) using physical sensors attached to the robot, particularly in confined spaces, is difficult due to their limited accuracy in three-dimensional deflections and challenging localisation. Therefore, using non-contact imaging sensors finds noticeable importance, particularly in medical scenarios. Accordingly, given the need for direct control of the robot tip and notable uncertainties in the kinematics and dynamics of CRs, many papers have focussed on the visual servoing (VS) of CRs in recent years.

METHODS

The significance of this research towards safe human-robot interaction has fuelled our survey on the previous methods, current challenges, and future opportunities.

RESULTS

Beginning with actuation modalities and modelling approaches, the paper investigates VS methods in medical and non-medical scenarios.

CONCLUSIONS

Finally, challenges and prospects of VS for CRs are discussed, followed by concluding remarks.

Can the Shape of a Planar Pathway Be Estimated Using Proximal Forces of Inserting a Flexible Shaft?

The shape information of flexible endoscopes or other continuum structures, e.g., intro-vascular catheters, is needed for accurate navigation, motion compensation, and haptic feedback in robotic surgical systems. Existing methods rely on optical fiber sensors, electromagnetic sensors, or expensive medical imaging modalities such as X-ray fluoroscopy, magnetic resonance imaging, and ultrasound to obtain the shape information of these flexible medical devices. Here, we propose to estimate the shape/curvature of a continuum structure by measuring the force required to insert a flexible shaft into the internal channel/pathway of the continuum. We found that there is a consistent correlation between the measured insertion force and curvature of the planar continuum pathway. A testbed was built to insert a flexible shaft into a planar continuum pathway with adjustable shapes. The insertion forces, insertion displacement, and the shapes of the pathway were recorded. A neural network model was developed to model this correlation based on the training data collected on the testbed. The trained model, tested on the testing data, can accurately estimate the curvature magnitudes and the accumulated bending angles of the pathway simply based on the measured insertion force at the proximal end of the shaft. The approach may be used to estimate the curvature magnitudes and accumulated bending angles of flexible endoscopic surgical robots or catheters for accurate motion compensation, haptic force feedback, localization, or navigation. The advantage of this approach is that the employed proximal force can be easily obtained outside the pathway or continuum structure without any embedded sensor in the continuum structure. Future work is needed to further investigate the correlation between insertion forces and the pathway and enhance the capability of the model in estimating more complex shapes, e.g., spatial shapes with multiple bends.

The Path to Surgical Robotics in Neurosurgery

Robotic systems may help efficiently execute complicated tasks that require a high degree of accuracy, and this, in large part, explains why robotics have garnered widespread use in a variety of neurosurgical applications, including intracranial biopsies, spinal instrumentation, and placement of intracranial leads. The use of robotics in neurosurgery confers many benefits, and inherent limitations, to both surgeons and their patients. In this narrative review, we provide a historical overview of robotics and its implementation across various surgical specialties, and discuss the various robotic systems that have been developed specifically for neurosurgical applications. We also discuss the relative advantages of robotic systems compared to traditional surgical techniques, particularly as it pertains to integration of image guidance with the ability of the robotic arm to reliably execute pre-planned tasks. As more neurosurgeons adopt the use of robotics in their practice, we postulate that further technological advancements will become available that will help achieve improved technical capabilities, user experience, and overall patient clinical outcomes.

Continuous body 3-D reconstruction of limbless animals

Limbless animals such as snakes, limbless lizards, worms, eels and lampreys move their slender, long bodies in three dimensions to traverse diverse environments. Accurately quantifying their continuous body's 3-D shape and motion is important for understanding body-environment interactions in complex terrain, but this is difficult to achieve (especially for local orientation and rotation). Here, we describe an interpolation method to quantify continuous body 3-D position and orientation. We simplify the body as an elastic rod and apply a backbone optimization method to interpolate continuous body shape between end constraints imposed by tracked markers. Despite over-simplifying the biomechanics, our method achieves a higher interpolation accuracy (∼50% error) in both 3-D position and orientation compared with the widely used cubic B-spline interpolation method. Beyond snakes traversing large obstacles as demonstrated, our method applies to other long, slender, limbless animals and continuum robots. We provide codes and demo files for easy application of our method.

How to Model Tendon-Driven Continuum Robots and Benchmark Modelling Performance

Tendon actuation is one of the most prominent actuation principles for continuum robots. To date, a wide variety of modelling approaches has been derived to describe the deformations of tendon-driven continuum robots. Motivated by the need for a comprehensive overview of existing methodologies, this work summarizes and outlines state-of-the-art modelling approaches. In particular, the most relevant models are classified based on backbone representations and kinematic as well as static assumptions. Numerical case studies are conducted to compare the performance of representative modelling approaches from the current state-of-the-art, considering varying robot parameters and scenarios. The approaches show different performances in terms of accuracy and computation time. Guidelines for the selection of the most suitable approach for given designs of tendon-driven continuum robots and applications are deduced from these results.

Lateral Oscillation and Body Compliance Help Snakes and Snake Robots Stably Traverse Large, Smooth Obstacles

Snakes can move through almost any terrain. Similarly, snake robots hold the promise as a versatile platform to traverse complex environments such as earthquake rubble. Unlike snake locomotion on flat surfaces which is inherently stable, when snakes traverse complex terrain by deforming their body out of plane, it becomes challenging to maintain stability. Here, we review our recent progress in understanding how snakes and snake robots traverse large, smooth obstacles such as boulders and felled trees that lack "anchor points" for gripping or bracing. First, we discovered that the generalist variable kingsnake combines lateral oscillation and cantilevering. Regardless of step height and surface friction, the overall gait is preserved. Next, to quantify static stability of the snake, we developed a method to interpolate continuous body in three dimensions (3D) (both position and orientation) between discrete tracked markers. By analyzing the base of support using the interpolated continuous body 3-D kinematics, we discovered that the snake maintained perfect stability during traversal, even on the most challenging low friction, high step. Finally, we applied this gait to a snake robot and systematically tested its performance traversing large steps with variable heights to further understand stability principles. The robot rapidly and stably traversed steps nearly as high as a third of its body length. As step height increased, the robot rolled more frequently to the extent of flipping over, reducing traversal probability. The absence of such failure in the snake with a compliant body inspired us to add body compliance to the robot. With better surface contact, the compliant body robot suffered less roll instability and traversed high steps at higher probability, without sacrificing traversal speed. Our robot traversed large step-like obstacles more rapidly than most previous snake robots, approaching that of the animal. The combination of lateral oscillation and body compliance to form a large, reliable base of support may be useful for snakes and snake robots to traverse diverse 3-D environments with large, smooth obstacles.

Separation method of bending and torsion in shape sensing based on FBG sensors array

This paper presents a theoretical method for separating bending and torsion of shape sensing sensor to improve sensing accuracy during its deformation. We design a kind of shape sensing sensor by encapsulating three fibers on the surface of a flexible rod and forming a triangular FBG sensors array. According to the configuration of FBG sensors array, we derive the relationship between bending curvature and bending strain, and set up a function about the packaging angle of FBG sensor and strain induced by torsion under different twist angles. Combined with the influence of bending and torsion on strain, we establish a nonlinear matrix equation resolving three unknown parameters including maximum strain, bending direction and wavelength shift induced by torsion and temperature. The three parameters are sufficient to separate bending and torsion, and acquire two scalar functions including curvature and torsion, which could describe 3D shape of rod according to Frenet-Serret formulas. Experimental results show that the relative average error of measurement about maximum strain, bending direction is respectively 2.65% and 0.86% when shape-sensing sensor is bent into an arc with a radius of 260 mm. The separating method also applied to 2D shape and 3D shape of reconstruction, and the absolute spatial position maximum error is respectively 3.79mm and 11.10mm when shape-sensing sensor with length 500mm is bent into arc shape with a radius 260mm and helical curve. The experiment results verify the feasibility of separating method, which would provide effective parameters for precise 3D reconstruction model of shape sensing sensor.

Kinematics and Manipulability Analysis of a Highly Articulated Soft Robotic Manipulator

Recently, the idea of applying “jamming” of appropriate media has been exploited for a novel continuum robot design. It is completed by applying vacuum in a robot structure filled with granular media. The backbone deformation and motion are achieved by controlling the fluid pressure. A jammable robotic manipulator does not certainly follow constant curvature during bending, that is, gravitational loads cause section sag. The kinematics describes the deformation of continuum manipulators. This formulation is expected to facilitate additional synthesis and analysis on workspace. This paper presents a Jacobian-based approach to obtain the forward kinematics solution. The proposed kinematic formulation in this paper tries to combine the key advantages of the techniques in constant curvature and variable curvature models. Hence, the deformation of any arbitrary bending is modeled. The workspace synthesis is continued by kinematic analysis, and in this regard, the manipulability measure is computed. This is an important improvement when compared with existing work for this kind of manipulators. It shows how manipulability measure can determine the workspace quality, where usually reachability is used for robot’s capabilities representation. As a result, the forward kinematics and manipulability analysis based on a piecewise-constant-curvature approximation are discussed in the simulation. The simulation has been carried out according to the fabricated experimental robot.

Discrete modular serpentine robotic tail: design, analysis and experimentation

This paper presents the design, analysis and experimentation of a Discrete Modular Serpentine Tail (DMST). The mechanism is envisioned for use as a robotic tail integrated onto mobile legged robots to provide a means, separate from the legs, to aid stabilization and maneuvering for both static and dynamic applications. The DMST is a modular two-degree-of-freedom (DOF) articulated, under-actuated mechanism, inspired by continuum and serpentine robotic structures. It is constructed from rigid links with cylindrical contoured grooves that act as pulleys to route and maintain equal displacements in antagonistic cable pairs that are connected to a multi-diameter pulley. Spatial tail curvatures are produced by adding a roll-DOF to rotate the bending plane of the planar tail curvatures. Kinematic and dynamic models of the cable-driven mechanism are developed to analyze the impact of trajectory and design parameters on the loading profiles transferred through the tail base. Experiments using a prototype are performed to validate the forward kinematic and dynamic models, determine the mechanism's accuracy and repeatability, and measure the mechanism's ability to generate inertial loading.

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

This paper examines shape sensing for a new class of surgical robot that consists of parallel flexible structures that can be reconfigured inside the human body. Known as CRISP robots, these devices provide access to the human body through needle-sized entry points, yet can be configured into truss-like structures capable of dexterous movement and large force application. They can also be reconfigured as needed during a surgical procedure. Since CRISP robots are elastic, they will deform when subjected to external forces or other perturbations. In this paper, we explore how to combine sensor information with mechanics-based models for CRISP robots to estimate their shapes under applied loads. The end result is a shape sensing framework for CRISP robots that will enable future research on control under applied loads, autonomous motion, force sensing, and other robot behaviors.

Large-deflection statics analysis of active cardiac catheters through co-rotational modelling

This paper presents a co-rotational concept for large-deflection formulation of cardiac catheters. Using this approach, the catheter is first discretized with a number of equal length beam elements and nodes, and the rigid body motions of an individual beam element are separated from its deformations. Therefore, it is adequate for modelling arbitrarily large deflections of a catheter with linear elastic analysis at the local element level. A novel design of active cardiac catheter of 9 Fr in diameter at the beginning of the paper is proposed, which is based on the contra-rotating double helix patterns and is improved from the previous prototypes. The modelling section is followed by MATLAB simulations of various deflections when the catheter is exerted different types of loads. This proves the feasibility of the presented modelling approach. To the best knowledge of the authors, it is the first to utilize this methodology for large-deflection static analysis of the catheter, which will enable more accurate control of robot-assisted cardiac catheterization procedures. Future work would include further experimental validations.