Shape Sensing and Kinematic Control of a Cable-Driven Continuum Robot Based on Stretchable Capacitive Sensors.

A Cable-Driven Continuum Robot (CDCR) that consists of a set of identical Cable-Driven Continuum Joint Modules (CDCJMs) is proposed in this paper. The CDCJMs merely produce 2-DOF bending motions by controlling driving cable lengths. In each CDCJM, a pattern-based flexible backbone is employed as a passive compliant joint to generate 2-DOF bending deflections, which can be characterized by two joint variables, i.e., the bending direction angle and the bending angle. However, as the bending deflection is determined by not only the lengths of the driving cables but also the gravity and payload, it will be inaccurate to compute the two joint variables with its kinematic model. In this work, two stretchable capacitive sensors are employed to measure the bending shape of the flexible backbone so as to accurately determine the two joint variables. Compared with FBG-based and vision-based shape-sensing methods, the proposed method with stretchable capacitive sensors has the advantages of high sensitivity to the bending deflection of the backbone, ease of implementation, and cost effectiveness. The initial location of a stretchable sensor is generally defined by its two endpoint positions on the surface of the backbone without bending. A generic shape-sensing model, i.e., the relationship between the sensor reading and the two joint variables, is formulated based on the 2-DOF bending deflection of the backbone. To further improve the accuracy of the shape-sensing model, a calibration method is proposed to compensate for the location errors of stretchable sensors. Based on the calibrated shape-sensing model, a sliding-mode-based closed-loop control method is implemented for the CDCR. In order to verify the effectiveness of the proposed closed-loop control method, the trajectory tracking accuracy experiments of the CDCR are conducted based on a circle trajectory, in which the radius of the circle is 55mm. The average tracking errors of the CDCR measured by the Qualisys motion capture system under the open-loop and the closed-loop control are 49.23 and 8.40mm, respectively, which is reduced by 82.94%.

Magnetic Soft Catheter Robot System for Minimally Invasive Treatments of Articular Cartilage Defects.

Articular cartilage defects are among the most common orthopedic diseases, which seriously affect patients' health and daily activities, without prompt treatment. The repair biocarrier-based treatment has shown great promise. Total joint injection and open surgery are two main methods to deliver functional repair biocarriers into the knee joint. However, the exhibited drawbacks of these methods hinder their utility. The repair effect of total joint injection is unstable due to the low targeting rate of the repair biocarriers, whereas open surgery causes serious trauma to patients, thereby prolonging the postoperative healing time. In this study, we develop a magnetic soft catheter robot (MSCR) system to perform precise in situ repair of articular cartilage defects with minimal incision. The MSCR processes a size of millimeters, allowing it to enter the joint cavity through a tiny skin incision to reduce postoperative trauma. Meanwhile, a hybrid control strategy combining neural network and visual servo is applied to sequentially complete the coarse and fine positioning of the MSCR on the cartilage defect sites. After reaching the target, the photosensitive hydrogel is injected and anchored into the defect sites through the MSCR, ultimately completing the in situ cartilage repair. The in vitro and ex vivo experiments were conducted on a 3D printed human femur model and an isolated porcine femur, respectively, to demonstrate the potential of our system for the articular cartilage repair.

Thermally Drawn-Based Microtubule Soft Continuum Robot for Cardiovascular Intervention.

Cardiovascular disease is becoming the leading cause of human mortality. In order to address this, flexible continuum robots have emerged as a promising solution for miniaturizing and automating vascular interventional equipment for diagnosing and treating cardiovascular diseases. However, existing continuum robots used for vascular intervention face challenges such as large cross-sectional sizes, inadequate driving force, and lack of navigation control, preventing them from accessing cerebral blood vessels or capillaries for medical procedures. Additionally, the complex manufacturing process and high cost of soft continuum robots hinder their widespread clinical application. In this study, we propose a thermally drawn-based microtubule soft continuum robot that overcomes these limitations. The proposed robot has cross-sectional dimensions several orders of magnitude smaller than the smallest commercially available conduits, and it can be manufactured without any length restrictions. By utilizing a driving strategy based on liquid kinetic energy advancement and external magnetic field for steering, the robot can easily navigate within blood vessels and accurately reach the site of the lesion. This innovation holds the potential to achieve controlled navigation of the robot throughout the entire blood vessel, enabling in situ diagnosis and treatment of cardiovascular diseases.

Model-based trajectory tracking of a compliant continuum robot.

Introduction: Compliant mechanisms, especially continuum robots, are becoming integral to advancements in minimally invasive surgery due to their ability to autonomously navigate natural pathways, significantly reducing collision severity. A major challenge lies in developing an effective control strategy to accurately reflect their behavior for enhanced operational precision. Methods: This study examines the trajectory tracking capabilities of a tendon-driven continuum robot at its tip. We introduce a novel feedforward control methodology that leverages a mathematical model based on Cosserat rod theory. To mitigate the computational challenges inherent in such models, we implement an implicit time discretization strategy. This approach simplifies the governing equations into space-domain ordinary differential equations, facilitating real-time computational efficiency. The control strategy is devised to enable the robot tip to follow a dynamically prescribed trajectory in two dimensions. Results: The efficacy of the proposed control method was validated through experimental tests on six different demand trajectories, with a motion capture system employed to assess positional accuracy. The findings indicate that the robot can track trajectories with an accuracy within 9.5%, showcasing consistent repeatability across different runs. Discussion: The results from this study mark a significant step towards establishing an efficient and precise control methodology for compliant continuum robots. The demonstrated accuracy and repeatability of the control approach significantly enhance the potential of these robots in minimally invasive surgical applications, paving the way for further research and development in this field.

Improving the kinematic accuracy of a collaborative continuum robot by using flexure-hinges.

Within various unstructured industrial environments, there is often the requirement to conduct remote engineering tasks, such as sampling the structure for analysis prior to decommissioning. Most existing tools are simply not dexterous enough to fulfil this task, and thus new technology is required. We describe here a simple, lightweight, and water-resistant collaborative dual-arm continuum robot system which can aid in this task. To improve the kinematic accuracy of the system, a class of flexible hinges have been combined with a conventional continuum robot configuration. The thickness and width of said flexible hinges can be adjusted to adapt to various tasks. Kinematic and stiffness models have further been developed, incorporating the influence of these flexible hinges. A set of experiments have been conducted to validate the proposed model and demonstrate the advantages of the platform. It was found that the kinematic accuracy of the continuum robot can be improved by a factor of around 10 with the aid of said hinges.

Modeling and experimental analysis of wire-driven continuum surgical robot.

A new configuration of continuum surgical robot is proposed, whose skeleton is composed of inner and outer layers. The outer layer is composed of miniature rotating modules connected in series and connected by orthogonal hinges, which can ensure the ability to resist unconventional torsion without losing the degree of freedom. The inner layer is a central support column with superelasticity. When bending, its superelasticity can make the overall configuration biased toward constant curvature bending, which is convenient for motion control and according to the new configuration, this paper establishes the kinematics model of the robot. Finally, the motion control experiment of the continuum robot is carried out. After the experiment, the average positioning error of the robot is 2.674 mm, and the average repetitive positioning error is 2.625 mm. Both are less than 2 % of the robot length, verifying the accuracy of the model.

Open continuum robotics-one actuation module to create them all.

Experiments on physical continuum robot are the gold standard for evaluations. Currently, as no commercial continuum robot platform is available, a large variety of early-stage prototypes exists. These prototypes are developed by individual research groups and are often used for a single publication. Thus, a significant amount of time is devoted to creating proprietary hardware and software hindering the development of a common platform, and shifting away scarce time and efforts from the main research challenges. We address this problem by proposing an open-source actuation module, which can be used to build different types of continuum robots. It consists of a high-torque brushless electric motor, a high resolution optical encoder, and a low-gear-ratio transmission. For this article, we create three different types of continuum robots. In addition, we illustrate, for the first time, that continuum robots built with our actuation module can proprioceptively detect external forces. Consequently, our approach opens untapped and under-investigated research directions related to the dynamics and advanced control of continuum robots, where sensing the generalized flow and effort is mandatory. Besides that, we democratize continuum robots research by providing open-source software and hardware with our initiative called the Open Continuum Robotics Project, to increase the accessibility and reproducibility of advanced methods.

Fast-Response Variable-Stiffness Magnetic Catheters for Minimally Invasive Surgery.

In minimally invasive surgery, such as cardiac ablation, magnetically steered catheters made of variable-stiffness materials can enable higher dexterity and higher force application to human tissue. However, the long transition time between soft and rigid states leads to a significant increase in procedure duration. Here, a fast-response, multisegmented catheter is described for minimally invasive surgery made of variable-stiffness thread (FRVST) that encapsulates a helical cooling channel. The rapid stiffness change in the FRVST, composed of a nontoxic shape memory polymer, is achieved by an active cooling system that pumps water through the helical channel. The FRVST displays a 66 times stiffness change and a 26 times transition enhancement compare with the noncooled version. The catheter allows for selective bending of each segment up to 127° in air and up to 76° in water under an 80 mT external magnetic field. The inner working channel can be used for cooling an ablation tip during a procedure and for information exchange via the deployment of wires or surgical tools.

Design and Kinematic Modeling of a Soft Continuum Telescopic Arm for the Self-Assembly Mechanism of a Modular Robot.

In recent years, the development of mining robots has grown significantly, offering improved efficiency and safety in hazardous environments. However, there is still room for improvement in adaptability, scalability, and overall performance. The ROBOMINERS project, funded by the European Union's Horizon 2020 Research and Innovation Program, aims to facilitate Europe's access to mineral resources applying disruptive robotic concepts. One such concept is resilience, which can be achieved providing modular mining robots with the ability to reconfigure during operation. To address this challenge, this article presents the development and kinematic modeling of a soft, telescopic, continuum arm integrated into a modular robot. The arm serves as a mechanical interface for coupling different robotic modules or tools following the principle of the car crane. With a fully 3D-printed design, the arm features two sections of variable length that are driven by an innovative actuation method based on soft racks. It provides a 6 degrees of freedom (DoF) motion. The arm kinematic models are obtained by backbone parameterization assuming constant curvature and independent bending between sections for forward kinematics and applying a machine learning-based approach for inverse kinematics. The models are validated through the evaluation of two trajectories, measuring the deviation in each DoF and rack extension. Furthermore, a demonstration of the arm's coupling procedure between two robotic modules and one possible configuration of the robotic system showcases its functionality.

A Novel Extensible Continuum Robot with Growing Motion Capability Inspired by Plant Growth for Path-Following in Transoral Laryngeal Surgery.

This article presents a novel extensible continuum robot (ECR) with growing motion capability for improved flexible access in transoral laryngeal procedures. The robot uses an extensible continuum joint with a staggered V-shaped notched structure as the backbone, driven by the pushing and pulling of superelastic Nitinol rods. The notched structure is optimized to achieve a wide range of extension/contraction and bending motion for the continuum joint. The successive and uniform deflection of the notches provides the continuum joint with excellent constant curvature bending characteristics. The bidirectional rod-driven approach expands the robot's extension capabilities with both pushing and pulling operations, and the superelasticity of the driving rods preserves the robot's bending performance. The ECR significantly increases motion dexterity and reachability through its variable length, which facilitates collision-free access to deep lesions by following the anatomy. To further exploit the advantages of the ECR in path-following for flexible access, a growing motion approach inspired by the plant growth process has been proposed to minimize the path deviation error. Characterization experiments are conducted to verify the performances of the proposed ECR. The extension ratio achieves up to 225.92%, and the average distal positioning error and hysteresis error values are 2.87% and 0.51% within the ±120° bending range. Compared with the typical continuum robot with a fixed length, the path-following deviation of this robot is reduced by more than 58.30%, effectively reducing the risk of collision during access. Phantom experiments validate the feasibility of the proposed concept in flexible access procedures.

Nonlinear dynamic modeling and model-based AI-driven control of a magnetoactive soft continuum robot in a fluidic environment.

In recent years, magnetoactive soft continuum robots (MSCRs) with multimodal locomotion capabilities have emerged for various biomedical applications. Developments in nonlinear dynamic models and effective control methods for MSCRs are deemed vital not only to gain a better understanding of their coupled magneto-mechanical behavior but also to accurately steer the MSCRs inside the human body. This study presents a novel dynamic model and model-based AI-driven control method to guide an MSCR in a fluidic environment. The MSCR is fully exposed to fluid flows at different rates to simulate the biofluidic environment within the body. A novel nonlinear dynamic model considering the effect of damping and drag force attributed to fluidic flows is first developed to accurately and efficiently predict the response of the MSCR under varying magnetic and mechanical loading. Fairly accurate correlations were observed between the theoretical responses based on the developed magneto-viscoelastic model and the experimental data for various scenarios. A novel model-based control algorithm based on a fractional-order sliding surface and deep reinforcement learning algorithm (DRL-FOSMC) is subsequently developed to accurately steer the magnetoactive soft robot on predefined trajectories considering varying fluid flow rates. A fractional-order sliding surface and a compensator, trained using the deep deterministic policy gradient algorithm, are designed to mitigate the amount of chattering and enhance the tracking performance of the closed-loop system. The stability proof of the developed control algorithm is also presented. A hardware-in-the-loop experimental framework has been designed to assess the effectiveness of the proposed control algorithm through various case studies. The performance of the proposed DRL-FOSMC algorithm is rigorously assessed and found to be superior when compared with other control methods.

Reduced order modeling and model order reduction for continuum manipulators: an overview.

Soft robot's natural dynamics calls for the development of tailored modeling techniques for control. However, the high-dimensional configuration space of the geometrically exact modeling approaches for soft robots, i.e., Cosserat rod and Finite Element Methods (FEM), has been identified as a key obstacle in controller design. To address this challenge, Reduced Order Modeling (ROM), i.e., the approximation of the full-order models, and Model Order Reduction (MOR), i.e., reducing the state space dimension of a high fidelity FEM-based model, are enjoying extensive research. Although both techniques serve a similar purpose and their terms have been used interchangeably in the literature, they are different in their assumptions and implementation. This review paper provides the first in-depth survey of ROM and MOR techniques in the continuum and soft robotics landscape to aid Soft Robotics researchers in selecting computationally efficient models for their specific tasks.

Research on Self-Stiffness Adjustment of Growth-Controllable Continuum Robot (GCCR) Based on Elastic Force Transmission.

Continuum robots have good adaptability in unstructured and complex environments. However, affected by their inherent nature of flexibility and slender structure, there are challenges in high-precision motion and load. Thus, stiffness adjustment for continuum robots has consistently attracted the attention of researchers. In this paper, a stiffness adjustment mechanism (SAM) is proposed and built in a growth-controllable continuum robot (GCCR) to improve the motion accuracy in variable scale motion. The self-stiffness adjustment is realized by antagonism through cable force transmission during the length change of the continuum robot. With a simple structure, the mechanism has a scarce impact on the weight and mass distribution of the robot and required no independent actuators for stiffness adjustment. Following this, a static model considering gravity and end load is established. The presented theoretical static model is applicable to predict the shape deformations of robots under different loads. The experimental validations showed that the maximum error ratio is within 5.65%. The stiffness of the robot can be enhanced by nearly 79.6%.

Coupling Analysis of Compound Continuum Robots for Surgery: Another Line of Thought.

The compound continuum robot employs both concentric tube components and cable-driven continuum components to achieve its complex motions. Nevertheless, the interaction between these components causes coupling, which inevitably leads to reduced accuracy. Consequently, researchers have been striving to mitigate and compensate for this coupling-induced error in order to enhance the overall performance of the robot. This paper leverages the coupling between the components of the compound continuum robot to accomplish specific surgical procedures. Specifically, the internal concentric tube component is utilized to induce motion in the cable-driven external component, which generates coupled motion under the constraints of the cable. This approach enables the realization of high-precision surgical operations. Specifically, a kinematic model for the proposed robot is established, and an inverse kinematic algorithm is developed. In this inverse kinematic algorithm, the solution of a highly nonlinear system of equations is simplified into the solution of a single nonlinear equation. To demonstrate the effectiveness of the proposed approach, simulations are conducted to evaluate the efficiency of the algorithm. The simulations conducted in this study indicate that the proposed inverse kinematic (IK) algorithm improves computational speed by a significant margin. Specifically, it achieves a speedup of 2.8 × 103 over the Levenberg-Marquardt (LM) method. In addition, experimental results demonstrate that the coupled-motion system achieves high levels of accuracy. Specifically, the repetitive positioning accuracy is measured to be 0.9 mm, and the tracking accuracy is 1.5 mm. This paper is significant for dealing with the coupling of the compound continuum robot.

Magnetic Continuum Robot with Intraoperative Magnetic Moment Programming.

Magnetic continuum robots (MCRs), which are free of complicated structural designs for transmission, can be miniaturized and are therefore widely used in the medical field. However, the deformation shapes of different segments, including deflection directions and curvatures, are difficult to control simultaneously under an external programmable magnetic field. This is because the latest MCRs have designs with an invariable magnetic moment combination or profile of one or more actuating units. Therefore, the limited dexterity of the deformation shape causes the existing MCRs to collide readily with their surroundings or makes them unable to approach difficult-to-reach regions. These prolonged collisions are unnecessary or even hazardous, especially for catheters or similar medical devices. In this study, a novel magnetic moment intraoperatively programmable continuum robot (MMPCR) is introduced. By applying the proposed magnetic moment programming method, the MMPCR can deform under three modalities, that is, J, C, and S shapes. Additionally, the deflection directions and curvatures of different segments in the MMPCR can be modulated as desired. Furthermore, the magnetic moment programming and MMPCR kinematics are modeled, numerically simulated, and experimentally validated. The experimental results exhibit a mean deflection angle error of 3.3° and correspond well with simulation results. Comparisons between navigation capacities of the MMPCR and MCR demonstrate that the MMPCR has a higher capacity for dexterous deformation.

Design and Development of a Continuum Robot with Switching-Stiffness.

Continuum robots have the advantages of agility and adaptability. However, existing continuum robots have limitations of low stiffness and complex motion modes, and the existing variable stiffness methods cannot achieve a wide range of stiffness changes and fast switching stiffness simultaneously. A continuum robot structure, switching stiffness method, and motion principle are proposed in this article. The continuum robot is made up of three segments connected in series. Each segment comprises multiple spherical joints connected in series, and the joints can be locked by their respective airbag. A valve controls each airbag, quickly switching the segment between rigidity and flexibility. The motion of the segments is driven by three cables that run through the robot. The segment steers only when it is unlocked. When a segment becomes locked, it acts as a rigid body. As a result, by locking and unlocking each segment in sequence, the cables can alternately drive all the segments. The stiffness variation and movement of the continuum robot were tested. The segment's stiffness varies from 36.89 to 1300.95 N/m and the stiffness switching time is 0.25-0.48 s. The time-sharing control mode of segment stiffness and motion is validated by establishing a specific test platform and a mathematical model. The continuum robot's flexibility is demonstrated by controlling the fast bending of different segments sequentially.

Optimal Control of Dielectric Elastomer Actuated Multibody Dynamical Systems.

In this work, a simulation model for the optimal control of dielectric elastomer actuated flexible multibody dynamics systems is presented. The dielectric elastomer actuator (DEA) behaves like a flexible artificial muscle in soft robotics. It is modeled as an electromechanically coupled geometrically exact beam, where the electric charges serve as control variables. The DEA-beam is integrated as an actuator into multibody systems consisting of rigid and flexible components. The model also represents contact interaction via unilateral constraints between the beam actuator and, for example, a rigid body during the grasping process of a soft robot. With a mathematically concise and physically representative formulation, a reduced free energy function is developed for the electromechanically coupled beam. In the optimal control problem, an objective function is minimized while the electromechanically coupled dynamic balance equations for the multibody system have to be fulfilled together with the complementarity conditions for the contact and boundary conditions. The optimal control problem is solved via a direct transcription method, transforming it into a constrained nonlinear optimization problem. The electromechanically coupled geometrically exact beam is firstly semidiscretized with one-dimensional finite elements and then the multibody dynamics is temporally discretized with a variational integrator leading to the discrete Euler-Lagrange equations, which are further reduced with the null space projection. The discrete Euler-Lagrange equations and the boundary conditions serve as equality constraints, whereas the contact constraints are treated as inequality constraints in the optimization of the discretized objective. The constrained optimization problem is solved using the Interior Point Optimizer solver. The effectiveness of the developed model is demonstrated by three numerical examples, including a cantilever beam, a soft robotic worm, and a soft robotic grasper.

End-Point Position Estimation of a Soft Continuum Manipulator Using Embedded Linear Magnetic Encoders.

Soft continuum robots are compliant mechanisms that rely on a deformable structure in order to achieve a desired posture. One of the challenges in designing and controlling this type of robot is to obtain the necessary proprioceptive information without resorting to external sensors, like cameras or 3D positioning devices. This requires a reliable and repeatable sensor that can be embedded in the highly deformable structure, distributed along its length, without imposing a significant change to the overall stiffness. This paper presents design considerations and practical results of estimating the tip position of a soft continuum manipulator module using embedded linear magnetic encoders. Three flexible scales with incremental tracks and a magnetic pole pitch of 2 mm are embedded in the robot structure as passive tendons, and six pairs of Hall effect linear sensors are used to measure the relative displacement between points along the outer surface of the structure. The curvature and tip position are then estimated from these measurements. Results are compared with the ground truth measurement of the tip position provided by a commercial optical tracker system. Average error estimates lower than 2.0 mm, with 8.7 mm peak value, were obtained for a robot module with a motion span of approximately 100 mm.

A Preprogrammable Continuum Robot Inspired by Elephant Trunk for Dexterous Manipulation.

Cable-driven continuum robots with hyper-redundant deformable backbones show great promise in applications, such as inspection in unstructured environments, where traditional rigid robots with discrete links and joints fail to operate. However, the motion of existing continuum robots is still constrained by their homogeneous backbones, and limited to environments with modest geometrical complexity. In this study, inspired by highly deformable elephant trunks, we presented a modular tensegrity structure with preprogrammable stiffness for continuum robots. Then we derived a mechanical model based on a positional formulation finite element method for predicting the configuration of the structure in different deformation scenarios. Theoretical predictions revealed that the curvature of each segment could be regulated by preprogramming their spring stiffness. Hence, our customizable design could offer an effective route for efficient robotic interactions. We further fabricated a continuum robot consisting of 12 modules, and showcased its deformation patterns under multiple scenarios. By regulating the distribution of spring stiffness, our robot could move through channels with varying curvatures, exhibiting its potential for applications where varying curvature, and conformal and efficient interactions are needed. Leveraging the inherent intelligence, this robotic system could simplify the complexity of the required actuation and control systems.