Static-to-kinematic modeling and experimental validation of tendon-driven quasi continuum manipulators with nonconstant subsegment stiffness

Continuum robots with high flexibility and compliance have the capability to operate in confined and cluttered environments. To enhance the load capacity while maintaining robot dexterity, we propose a novel non-constant subsegment stiffness structure for tendon-driven quasi continuum robots(TDQCRs) comprising rigid-flexible coupling subsegments.Aiming at real-time control applications, we present a novel static-to-kinematic modeling approach to gain a comprehensive understanding of the TDQCR model. The analytical subsegment-based kinematics for the multisection manipulator is derived based on screw theory and product of exponentials formula, and the static model considering gravity loading,actuation loading, and robot constitutive laws is established. Additionally, the effect of tension attenuation caused by routing channel friction is considered in the robot statics, resulting in improved model accuracy. The root-mean-square error between the outputs of the static model and the experimental system is less than 1.63% of the arm length(0.5 m). By employing the proposed static model, a mapping of bending angles between the configuration space and the subsegment space is established. Furthermore, motion control experiments are conducted on our TDQCR system, and the results demonstrate the effectiveness of the static-to-kinematic model.

General Kinetostatic Modeling and Deformation Analysis of a Two-Module Rod-Driven Continuum Robot with Friction Considered

Continuum robots actuated by flexible rods have large potential applications,such as detection and operation tasks in confined environments,since the push and pull actuation of flexible rods withstand tension and compressive force,and increase the structure's rigidity.In this paper,a generalized kinetostatics model for multi-module and multi-segment continuum robots considering the effect of friction based on the Cosserat rod theory is established.Then,the model is applied to a two-module rod-driven continuum robot with winding ropes to analyze its deformation and load characteristics.Four different in-plane configurations under the external load term as S1,S2,C1,and C2 are defined.Taking a bending plane as an example,the tip deformation along thex-axis of these shapes is simulated and compared,which shows that the load capacity of C1 and C2 is generally larger than that of S1 and S2.Furthermore,the deformation experiments and simulations show that the maximum error ratio without external loads relative to the total length is no more than 3%,and it is no more than 4.7%under the external load.The established kinetostatics model is proven sufficient to accurately analyze the rod-driven continuum robot with the consideration of internal friction.

Variable Curvature Modeling Method of Soft Continuum Robots with Constraints

The inherent compliance of continuum robots holds great promise in the fields of soft manipulation and safe human–robot interaction.This compliance reduces the risk of damage to the manipulated object and its surroundings.However,continuum robots possess theoretically infinite degrees of freedom,and this high flexibility usually leads to complex deformations when subjected to external forces and positional constraints.Describing these complex deformations is the main challenge in modeling continuum robots.In this study,we investigated a novel variable curvature modeling method for continuum robots,considering external forces and positional constraints.The robot configuration curve is described using the developed mechanical model,and then the robot is fitted to the curve.A ten-section continuum robot prototype with a length of 1 m was developed in order to validate the model.The feasibility and accuracy of the model were verified by the ability of the robot to reach target points and track complex trajectories with a load.This work was able to serve as a new perspective for the design analysis and motion control of continuum robots.

Path Planning of Continuum Robot Based on a New Improved Particle Swarm Optimization Algorithm

Continuum robot is a new type of biomimetic robot,which realizes the motion by bending some parts of its body.So its path planning becomes more difficult even compared with hyper-redundant robots.In this paper a circular arc spline interpolating method is proposed for the robot shape description,and a new two-stage position-selectable-updating particle swarm optimization(TPPSO)algorithm is put forward to solve this path planning problem.The algorithm decomposes the standard PSO velocity’s single-step updating formula into twostage multi-point updating,specifically adopting three points as candidates and selecting the best one as the updated position in the first half stage,and similarly taking seven points as candidates and selecting the best one as the final position in the last half stage.This scheme refines and widens each particle’s searching trajectory,increases the updating speed of the individual best,and improves the converging speed and precision.Aiming at the optimization objective to minimize the sum of all the motion displacements of every segmental points and all the axial stretching or contracting displacements of every segment,the TPPSO algorithm is used to solve the path planning problem.The detailed solution procedure is presented.Numerical examples of five path planning cases show that the proposed algorithm is simple,robust,and efficient.

Development of a continuum robot for colonoscopy

A novel continuum robot for colonoscopy is presented.The aim is to develop a robot for colonoscopywhich can provide the same functions as conventional colonoscope,but much less pain and discomfort forpatient.In contrast to traditional rigid-link robot,the robot features a continuous backbone with nojoints.The continuum robot is 300 mm in total length and 12 mm in diameter that is less than the averagediameter of human colon(20 mm).The robot has a total of 4 DOF(degrees of freedom)and is actuatedremotely by 6 hybrid step motors through super-elastic NiTi wires.Its shape can be changed with highdexterity,therefore ensuring its adaptability to the tortuous shape of human colon.The mechanical struc-ture,kinematics and DSP-based control system are discussed; prototype experiments are carried out tovalidate the kinematics model and to show the motion performances.

A New Approach to Extensible Continuum Robot Control Using the Sliding-Mode

In this paper, the authors present a new control strategy for continuous backbone （continuum） ＂trunk and tentacle＂ robots. Control of this emerging new class of robots has proved difficult due to the inherent complexity of their dynamics. Using a recently established full dynamic model, the authors introduce a new nonlinear model-based control strategy for continuum robots. The approach is applicable to continuum robots which can extend/contract as well as bend throughout their structure. Results are illustrated using the mathematical model of a three-section, six-degree of freedom planar continuum robot.

In Situ Reconfiguration of Assembling Pattern for Modular Continuum Robots

Modular continuum robots possess significant versatility across various scenarios;however,conventional assembling methods typically rely on linear connection between modules.This limitation can impede the robotic interaction capabilities,especially in specific engineering applications.Herein,inspired by the assembling pattern between the femur and tibia in a human knee,we proposed a multidirectional assembling strategy.This strategy encompasses linear,oblique,and orthogonal connections,allowing a two-module continuum robot to undergo in-situ reconfiguration into three distinct initial configurations.To anticipate the final configuration resulting from diverse assembling patterns,we employed the positional formulation finite element framework to establish a mechanical model,and the theoretical results reveal that our customizable strategy can offer an effective route for robotic interactions.We showcased diverse assembling patterns for coping with interaction requirements.The experimental results indicate that our modular continuum robot not only reconfigures its initial profile in situ but also enables on-demand regulation of the final configuration.These capabilities provide a foundation for the future development of modular continuum robots,enabling them to be adaptable to diverse environments,particularly in unstructured surroundings.

Design, modeling, and evaluation of parallel continuum robots: A survey

Parallel continuum robots(PCRs) have attracted increasing attention in the robotics community due to their simplicity in structure,inherence with compliance, and easiness of realization. Over the past decade, a variety of novel designs have been reported to enrich their diversity. However, there is a lack of systematic review of these emerging robots. To this end, this paper conducts a comprehensive survey on the mechanism design, kinetostatic modeling and analysis, and performance evaluation. For these robots, kinetostatic modeling plays a fundamental role throughout the design, analysis, and control stages. A systematic review of the existing approaches for kinetostatic modeling and analysis is provided, and a comparison is made to distinguish their differences. As well, a classification is made according to the characteristics of structure and actuation. In addition, performance evaluation on the workspace, stability, and singularity is also overviewed. Finally, the scenarios of potential applications are elaborated, and future research prospects are discussed. We believe that the information provided in this paper will be particularly useful for those who are interested in PCRs.

Detection and removal of excess materials in aircraft wings using continuum robot end-effectors

Excess materials are left inside aircraft wings due to manual operation errors,and the removal of excess materials is very crucial.To increase removal efficiency,a continuum robot(CR)with a removal end-effector and a stereo camera is used to remove excess objects.The size and weight characteristics of excess materials in aircraft wings are analyzed.A novel negative pressure end-effector and a two-finger gripper are designed based on the CR.The negative pressure end-effector aims to remove nuts,small rivets,and small volumes of aluminum shavings.A two-finger gripper is designed to remove large volumes of aluminum shavings.A stereo camera is used to achieve automatic detection and localization of excess materials.Due to poor lighting conditions in the aircraft wing compartment,supplementary lighting devices are used to improve environmental lighting.Then,You Only Look Once(YOLO)v5 is used to classify and detect excess objects,and two training data sets of excess objects in two wings are constructed.Due to the limited texture features inside the aircraft wings,this paper adopts an image-matching method based on the results of YOLO v5 detection.This matching method avoids the performance instability problem based on Oriented Fast and Rotated BRIEF feature point matching.Experimental verification reveals that the detection accuracy of each type of excess exceeds 90%,and the visual localization error is less than 2 mm for four types of excess objects.Results show the two end-effectors can work well for the task of removing excess material from the aircraft wings using a CR.

Flexible head-following motion planning for scalable and bendable continuum robots

Continuum robots,which are characterized by high length-to-diameter ratios and flexible structures,show great potential for various applications in confined and irregular environments.Due to the combination of motion modes,the existence of multiple solutions,and the presence of complex obstacle constraints,motion planning for these robots is highly challenging.To tackle the challenges of online and flexible operation for continuum robots,we propose a flexible head-following motion planning method that is suitable for scalable and bendable continuum robots.Firstly,we establish a piecewise constant curvature(PCC)kinematic model for scalable and bendable continuum robots.The article proposes an adaptive auxiliary points model and a method for updating key nodes in head-following motion to enhance the precise tracking capability for paths with different curvatures.Additionally,the article integrates the strategy for adjusting the posture of local joints of the robot into the head-following motion planning method,which is beneficial for achieving safe obstacle avoidance in local areas.The article concludes by presenting the results of multiple sets of motion simulation experiments and prototype experiments.The study demonstrates that the algorithm presented in this paper effectively navigates and adjusts posture to avoid obstacles,meeting the real-time demands of online operations.The average time for a single-step solution is 4.41×10^(-5) s,and the average tracking accuracy forcircular paths is 7.8928mm.

Design and modeling of continuum robot based on virtual-center of motion mechanism

Continuum robot has attracted extensive attention since its emergence.It has multi-degree of freedom and high compliance,which give it significant advantages when traveling and operating in narrow spaces.The flexural virtual-center of motion(VCM)mechanism can be machined integrally,and this way eliminates the assembly between joints.Thus,it is well suited for use as a continuum robot joint.Therefore,a design method for continuum robots based on the VCM mechanism is proposed in this study.First,a novel VCM mechanism is formed using a double leaf-type isosceles-trapezoidal flexural pivot(D-LITFP),which is composed of a series of superimposed LITFPs,to enlarge its stroke.Then,the pseudo-rigid body(PRB)model of the leaf is extended to the VCM mechanism,and the stiffness and stroke of the D-LITFP are modeled.Second,the VCM mechanism is combined to form a flexural joint suitable for the continuum robot.Finally,experiments and simulations are used to validate the accuracy and validity of the PRB model by analyzing the performance(stiffness and stroke)of the VCM mechanism.Furthermore,the motion performance of the designed continuum robot is evaluated.Results show that the maximum stroke of the VCM mechanism is approximately 14.2°,the axial compressive strength is approximately 1915 N/mm,and the repeatable positioning accuracies of the continuum robot is approximately±1.47°(bending angle)and±2.46°(bending direction).

Comprehensive kinetostatic modeling and morphology characterization of cable-driven continuum robots for in-situ aero-engine maintenance

In-situ maintenance is of great significance for improving the efficiency and ensuring the safety of aero-engines.The cable-driven continuum robot(CDCR)with twin-pivot compliant mechanisms,which is enabled with flexible deformation capability and confined space accessibility,has emerged as a novel tool that aims to promote the development of intelligence and efficiency for in-situ aero-engine maintenance.The high-fidelity model that describes the kinematic and morphology of CDCR lays the foundation for the accurate operation and control for in-situ maintenance.However,this model was not well addressed in previous literature.In this study,a general kinetostatic modeling and morphology characterization methodology that comprehensively contains the effects of cable-hole friction,gravity,and payloads is proposed for the CDCR with twin-pivot compliant mechanisms.First,a novel cable-hole friction model with the variable friction coefficient and adaptive friction direction criterion is proposed through structure optimization and kinematic parameter analysis.Second,the cable-hole friction,all-component gravities,deflection-induced center-of-gravity shift of compliant joints,and payloads are all considered to deduce a comprehensive kinetostatic model enabled with the capacity of accurate morphology characterization for CDCR.Finally,a compact continuum robot system is integrated to experimentally validate the proposed kinetostatic model and the concept of in-situ aero-engine maintenance.Results indicate that the proposed model precisely predicts the morphology of CDCR and outperforms conventional models.The compact continuum robot system could be considered a novel solution to perform in-situ maintenance tasks of aero-engines in an invasive manner.

Shape Sensing for Single-Port Continuum Surgical Robot Using FewMulticore Fiber Bragg Grating Sensors

We proposed a method for shape sensing using a few multicore fiber Bragg grating (FBG) sensors ina single-port continuum surgical robot (CSR). The traditional method of utilizing a forward kinematic model tocalculate the shape of a single-port CSR is limited by the accuracy of the model. If FBG sensors are used forshape sensing, their accuracy will be affected by their number, especially in long and flexible CSRs. A fusionmethod based on an extended Kalman filter (EKF) was proposed to solve this problem. Shape reconstructionwas performed using the CSR forward kinematic model and FBG sensors, and the two results were fused usingan EKF. The CSR reconstruction method adopted the incremental form of the forward kinematic model, whilethe FBG sensor method adopted the discrete arc-segment assumption method. The fusion method can eliminatethe inaccuracy of the kinematic model and obtain more accurate shape reconstruction results using only a smallnumber of FBG sensors. We validated our algorithm through experiments on multiple bending shapes underdifferent load conditions. The results show that our method significantly outperformed the traditional methodsin terms of robustness and effectiveness.

Variable stiffness methods of flexible robots for minimally invasive surgery:A review

With high flexibility and slim body,flexible robots have been widely used in minimally invasive surgery because they can safely reach the lesion deep inside the human body through small incisions or natural orifices.However,high stiffness of robot body is also required for transferring force and maintaining the motion accuracy.To meet these two contradictory requirements,various methods have been implemented to enable adjustable stiffness for flexible surgical robots.In this review,we first summarize the anatomic constraints of common natural tracts of human body to provide a guidance for the design of variable stiffness flexible robots.And then,the variable stiffness methods have been categorized based on their basic principles of varying the stiffness.In the end,two variable stiffness methods with great potential and the moving strategy of variable stiffness flexible robots are discussed.

Geometrically Exact Finite Element Formulation for Tendon-Driven Continuum Robots

Tendon-driven continuum robots achieve continuous deformations through the contraction of tendons embedded inside the robotic arms.For some continuum robots,the constant curvature assumption-based kinematic modeling can be accurate and effective.While for other cases,such as soft robots or robot-environment interactions,the constant curvature assumption can be inaccurate.To model the complex deformation of continuum robots,the geometrically exact beam theory(may also be called the Cosserat rod theory)has been used to develop computational mechanics models.Different from previous computational models that used finite difference schemes for the spatial discretization,here we develop a three-dimensional geometrically exact beam theory-based finite element model for tendon-driven continuum robots.Several numerical examples are presented to show the accuracy,efficiency,and applicability of our new computational model for tendon-driven continuum robots.

Bio-inspired design of alternate rigid-flexible segments to improve the stiffness of a continuum manipulator

Intrinsic flexible structures enable a continuum manipulator to exhibit attractive dexterity and intrinsic compliance over traditional hyper-redundant robots.However,its insufficient stiffness makes the performance of continuum manipulators unsatisfactory and thus limits the applications in many fields.A significant challenge is how to make a trade-off among dexterity,compliance and stiffness.From an evolutionary perspective,this paper compares several biological structures that enable the continuum manipulator function,and intends to reveal the mechanism on how the biological structures can improve the stiffness.The notochord and the vertebral column with acoelous centra are abstracted and physically implemented.A fundamental roddriven continuum manipulator is also introduced as a comparison.The stiffness models of these three continuum manipulators are proposed,and comparative experiments are conducted to verify their stiffness properties.Our results demonstrate that the rigid-flexible segmental structure can improve the stiffness properties of a continuum manipulator.

A novel obstacle avoidance heuristic algorithm of continuum robot based on FABRIK

Obstacle avoidance and path planning of continuum robots are challenging tasks due to the hyper-redundant degree of freedoms(DOFs)and restricted working environments.Meanwhile,most current heuristic algorithm-based obstacle avoidance algorithms exist with low computational efficiency,complex solution process,and inability to add global constraints.This paper proposes a novel obstacle avoidance heuristic algorithm based on the forward and backward reaching inverse kinematics(FABRIK)algorithm.The update of key nodes in this algorithm is modeled as the movement of charges in an electric field,avoiding complex nonlinear operations.The algorithm achieves the robustness of inverse kinematics and path tracking in complex environments by imposing constraints on key nodes and determining the location of obstacles in advance.This algorithm is characterized by a high convergence rate,low computational cost,and can be used for real-time applications.The proposed approach also has wide applicability and can be applied to both mobile and fixed-base continuum robots.And it can be further extended to the field of hyper-redundant robots.The algorithm's effectiveness is further validated by simulating the path tracking and obstacle avoidance of a five-segment continuum robot in various environments and comparisons with classical methods.

Motion Control and Optimal Design of a Biomimetic Manipulator Based on Snake Coiling and Stretching

The traditionally articulated manipulator had a single control method,and the limited motion trajectory space was unsuitable for working in an unstructured environment.This paper introduces a control method and optimization for a multijoint manipulator Inspired by snakes'curling and stretching motions.First,we analyze the manipulator’s connection mode and motion planning and propose a new motion method.In addition,we calculated the relevant positions and angles and subdivided the motion of some joints based on the principle of the meta-heuristic algorithm.Ultimately,the manipulator in this mode has a larger workspace and more flexible motion trajectories.The experimental results are consistent with the theoretical analysis,which further proves the feasibility and scalability of the scheme.