Behavior-predefined adaptive control for heterogeneous continuum robots

This paper introduces a method for computing the shape of a continuously-flexible (continuum) robot in 3-D space which includes gravity loading by applying Cosserat rod theory to a continuum robot. With this theory, the shape of the rod can be determined using force-torque balance equations obtained from a simple free body diagram that represents the continuum robot. Real-time performance of 125 Hz makes this approach viable for the control of a continuum robot, enabled by avoiding boundary-value conditions in the solution.

Continuum robotics has become a popular area of research, with many applications derived. Though some of the designs and relative modeling have been applied in actual occasions, new modeling approaches are still required for some new designs in structure. A parallel continuum robot (PCR) prototype imitating the bionic trunk from FESTO is designed in this paper. Since the structure design of PCR adopts a cone shape to enhance stiffness, the prototype shows stronger nonlinearity than continuum robots which are modeled based on piecewise constant curvature model. Due to the structure of the PCR, this paper analyzes its nonlinearity via Euler-Bernoulli beam formulations. Three kinds of artificial neural networks (ANN) are established to identify the nonlinear parallel rod system, namely, back propagation (BP), racial basis function (RBF) and a hybrid approach using genetic algorithm (GA) to optimize the weights of BP. After training by the datum obtained from the optotrak certus 3020 active tracking system, the result shows that increasing a suitable amount of iterant training data will heighten the generation ability of the network, and the best approach to model the parallel system is the hybrid approach. For forward kinematics, the mean position error of the end-effector is 0.3%, and for inverse kinematics the mean position error is 0.43%, so, such an approach can solve the forward and inverse kinematics problem of the PCR in an acceptable precision.

This paper deals with an original combination of navigation by simultaneous localization and mapping (SLAM) and follow-the-leader (FTL) deployment for the control of concentric tube robots (CTRs). The objective is to make possible the automatic navigation of such continuum robots within an anatomical structure, by simultaneously managing both collision avoidance and map updating of the environment, i.e. , of the surrounding anatomical structures. Indeed, CTRs designed to achieve a FTL deployment to date were deployed on path identified during a planning task. In this work, this limitation is overcome by embedding, in the control scheme, an online trajectory estimation, therefore allowing an autonomous deployment of CTRs with an approximate FTL behavior. The proposed hybrid control law integrates a stability criterion to ensure at the same time CTR stability during deployment, required for a FTL deployment. The interest of the approach is demonstrated through simulation using realistic anatomical data and experiments, with a 3 degrees-of-freedom CTR.

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.

Accurate control of continuum robots is challenging, especially in the presence of external disturbances. To address this issue, reinforcement learning (RL) has been increasingly investigated in continuum robot control due to its online policy updating capability. However, the gap in Sim2Real transfer caused by inaccurate modeling results in RL implementation a dilemma. In this article, we propose a safety-critical Real2Sim2Real online RL framework, where the Real2Sim transfer is first achieved by the identification of a continuum robot using the Koopman operator. We further improve the training efficiency by introducing an imperfect demonstration into the RL framework. The offline policy is trained in simulations and then tested on a real continuum robot platform. During tests, the tracking performance is influenced by the hysteresis effect that cannot be captured by the Koopman operator. This results in a millimeter-level tracking root mean square error (RMSE). To address this issue, we online update the policy as well as the model, and the RMSE of the online controller outperforms the offline controller by 89.16% in free space and 85.70% under external payload, respectively.

Continuum Robots The cover illustrates three continuum robots accessing a nuclear facility through pipes, with a pneumatically actuated robot manipulating a radioactive component, a tendon-driven continuum robot performing a laser machining task on it, and a concentric tube robot monitoring the operation. In article number 2200367, recent advances, current limitations, and open challenges in the design, modeling, and control of continuum robots are discussed by Matteo Russo, Dragos Axinte, and colleagues.

This paper presents a method to combine voice control and hybrid visual servoing for a continuum robot. In this design, the continuum robot autonomously tracks the element of interest and maintains its position in the safe region based on image information. A method of hybrid visual servoing is proposed to integrate 2D image-based visual servoing (IBVS) to ensure the elements of interests under visibility constraints and 3D position-based visual servoing (PBVS) to adjust the robot to a desired pose in the constraint region. The robotic camera thus provides stable image while tracking the element of interest. In this design, the user can move the continuum robot to acquire the desired view by voice commands. In voice control, the system can recognize connecting words to control the robot. All software modules are integrated using Robot Operating System (ROS) for controlling the continuum robot. Experimental results obtained from a prototype continuum robot verify the effectiveness of the proposed method.

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.

Continuum robots (CRs) have been developed for maxillary sinus surgery (MSS) in recent years. However, due to the anatomically curved and narrow pathway of the maxillary sinus and the deformable characteristics of the CR, it is still a challenge to accurately approach the target in the sinus. Thus, the CR-assisted MSS demands further research, whether in robotic system design or in reliable motion control. A continuum robotic system integrated with essential instruments and sensors for MSS is developed, and the path tracking control of the designed CR is studied. The differential kinematic model of the CR is constructed. By analyzing the potential problem of the traditional Jacobian-based control, an iterative Jacobian transpose-based closed-loop control method is proposed to improve the path tracking performance. To validate the design of the CR and the effectiveness of the proposed control scheme, different groups of experiments are performed. With the proposed method, the path tracking performance of the CR is improved. Compared with the open-loop Jacobian transpose-based control method, the path tracking error of the proposed method is much less. The maxillary sinus phantom tests are conducted to verify the reachability of the designed CR. Given the reference path from the nostril to the target in the maxillary sinus phantom, experiments show a mean error of 0.96mm. The designed CR is slender, flexible, and able to smoothly approach the target in a tortuous and constrained environment without colliding with or damaging the surrounding tissue. The designed continuum robotic system and the proposed iterative Jacobian transpose-based closed-loop control strategy have great potential for MSS. The limitations of the proposed method are also discussed.

Continuum robot, unlike conventional rigid-link robots, has numerous numbers of degrees of freedom, enabling it to be applied for confined space works, such as minimally invasive surgery, safe robot/objective interactions, and in-situ aero-engine detection. This study presented a cable-driven continuum robot with twin-pivot structure, which poses smaller diameter-length-ratio and torsion resistance ability compared with conventional single-pivot structure, as well as the kinematics and shape estimation. The kinematics model of the twin-pivot continuum robot is established based on the assumption of piecewise constant curvature, with which the mapping between driving space and operation space are presented. Finally, a prototype of continuum robot system with single section is constructed to verify the validation of the kinematics model and study the shape estimation. Based on the constructed prototype, the shape estimation of the continuum robot with different payloads is performed. The comparative results suggest that relative error is less than 5% for total length of the single section without payload, verifying the validity of the kinematics model. The comparison between the results with different payloads indicate that the increasing payload will increase the relative error.

The presence of a multi-segmented and malleable structure makes continuum robot (CR) promising for use in medicine, industry, space, and deep-sea research. This trend encourages researchers worldwide to create fundamentally new types of continuously deformable CR structures suitable for various applications and delicate manipulations. Despite promising achievements, the processes of design, modeling, control system development, and improvement of existing CR mechanisms remain quite complex. Taking into account the main technological features of existing solutions, this article provides a comprehensive overview of the current state of continuums robots. The analysis covers general problems arising in the design of CRs, and possible solutions are also considered, allowing the full potential of CRs for wider application to be revealed. This work aims to analyze key design and modeling methods, where the main approaches to the process of creating CRs have been classified. Taking into account the identified limitations and problems in their practical application, this review focuses on their advantages, design principles, mathematical modeling, and control strategies. Modern approaches to kinematic and dynamic modelling of CRs and CR control algorithms, including AI-based methods, were analyzed. As a result, promising directions for improving CRs for various applications were identified.

Cable-driven continuum robots find applications in bio-inspired robotics and medical robotics. Kinematics of cable-driven continuum robots, also called elephant-trunk robots, with straight cable routing is well studied in the literature. However, there are very few studies on the kinematics of continuum robots with general cable routing, despite its certain advantages. In this paper, an optimization based strategy is proposed to estimate the forward kinematics of a continuum robot with arbitrary and general cable routing. For a given displacement of the cables and cable routing, the pose of a continuum robot is obtained. Using experiments conducted on a cable driven robot, it is demonstrated that the optimization based model provides a good estimate of the forward kinematics with maximum error less than 5% of maximum tip deflection. The developed model is particularly useful since it may be possible to synthesize robots that can be deformed to desired shapes using the same theoretical framework.

The traditional surgical instruments for transnasal endoscopic skull base surgery have poor flexibility and continuum robot has attracted extensive attention for its high dexterity and safety. A new type of micro continuum surgical robot is designed. On the basis of kinematic analysis, a superposition method is proposed to analyse the reachable configuration space of the system, and the workspace is analysed. The results obtained by superposition method can provide reference for the selection of joint parameters. At last, the static model of the system is established considering friction and coupling between two segments. The simulation results show that the workspace can meet the requirements of surgery. And the validity of the static model is verified by numerical simulation and experiment, which lays a foundation for the establishment of the driving force transmission system and precise control of the robot. The research results of this study contribute to the real-time control and movement of robot. The proposed continuum robot provides convenient conditions for the clinical application.

Minimally invasive mitral valve repair offers significant advantages over traditional open-heart surgery, yet it remains a complex procedure that exposes both patients and medical staff to radiation. To address these challenges, a significant research interest is growing in automating these manual procedures. Continuum robots represent a promising approach, thanks to their ability to navigate confined spaces. However, their nonlinear behavior presents challenges in modeling and control. In this study, we developed a robust position control method for a variable-length tendon-driven continuum robot. We designed a control system that effectively tracks the desired target positions by employing a constant curvature model and a Jacobian-based control algorithm with real-time position feedback. We assessed the stability of our system through Lyapunov analysis, demonstrating reliable convergence to these target positions. Experimental validation conducted in a cardiovascular phantom demonstrated significant improvements with respect to the state of the art. Our method achieved a trajectory following error of approximately 2.43 mm [1.63, 3.23] and a target position error of about 1.92 mm [1.73, 3.13]. Moreover, the computation time per trajectory point was reduced to approximately 0.04 seconds, highlighting enhanced computational efficiency. These results showcase improved accuracy and efficiency in minimally invasive mitral valve repair procedures.

Continuum robots, owing to their inherent compliance, have become essential in endoscopic surgical procedures, such as mucosal ablation. However, the prevalent design of endoscopic manipulators, which typically features only a single active bending segment, often results in limited dexterity and accessibility. Additionally, the incorporation of variable stiffness in these robots has attracted significant interest, with the aim to improve manipulation capabilities in confined spaces. In the paper, we propose a novel variable-length continuum robot with variable stiffness for endoscopic surgery. The robot’s stiffness can be altered either by modifying the catheter’s length or solid-liquid transition of low-melting-point alloy (LMPA). The design and fabrication methods of the robot are meticulously detailed. Additionally, a quasi-static stiffness model along with a learning-based stiffness compensation approach for accurate stiffness estimation are proposed. Leveraging this model, a contact force controller is designed for ablation procedure. The experimental results show that our robot possesses good flexibility and accessibility, making it highly adept at manipulating in confined spaces. Its variable stiffness feature significantly enhances its ability to counteract external disturbance and prevent tip deformation (with a average position change of 1.1mm). Finally, through force control experiments and a surgical demonstration in a gastrointestinal model, we have further validated the robot’s applicability in surgical contexts. Note to Practitioners—This paper proposed a variable-length continuum robot with variable stiffness for endoscopic surgery. The robot can achieve axial elongation and omnidirectional bending motion, having better dexterity and accessibility than traditional medical continuum robots with one active bending segment. The robot’s stiffness can be adjusted by the length changes or solid-liquid transition of low-melting-point alloy (LMPA). Besides, an accurate stiffness model and a contact force controller are proposed for endoscopic ablation surgery. By experimental results, the robot shows high flexibility and accessibility, allowing access to confined spaces for manipulation, and good control accuracy and variable stiffness capability for endoscopic surgery.