Three dimensional statics for continuum robotics

Continuum robots have great application value and broad prospects in various fields due to their dexterity and compliance. To fully exploit their advantages, it is crucial to develop an effective, accurate and robust control system for them. However, research on continuum robot control is still in its infancy and there are many problems remaining unsolved in this field. In particular, this paper focuses on the task-space behavior and the generic control of heterogeneous continuum robots. First, a controller is proposed to achieve the kinematic motion control and visual servoing of continuum robots with predefined task-space behavior. The predefined behavior is twofold: prescribed task-space error and predefined convergence time. Then, the proposed controller is integrated with a velocity-level kinematic mapping estimator to obtain a model-free control system, which is applicable to heterogeneous continuum robots. Furthermore, a re-adjustable performance function is proposed to ensure the effectiveness and robustness of the proposed control system in the presence of external disturbance. Finally, extensive simulations and experiments are performed based on heterogeneous continuum robots, including the cable-driven continuum robot, the parallel continuum robot, the concentric-tube robot, the flexible endoscope, and the pneumatic continuum robot. Our results demonstrate that the task-space error of heterogeneous continuum robots complies with the prescribed boundaries and converges to steady state in predefined time, which reveals the efficacy of the proposed control method.

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.

Continuum robots are promising for minimally invasive surgery. They consist of thin and flexible structures whose shape can be continuously deformed using re- mote actuators, allowing them to be inserted in small tubular cavities. For safety reasons, it is important to be aware of the forces applied to surrounding tissue during deployment. Because common force sensors are too cumbersome to be embedded into continuum robots, alternative shape-based force estimation methods have been developed. Such methods estimate the contact location and the corresponding force based on the com- parison between a measured robot shape (for instance using Fiber Braggs Gratings sensors or vision sensors) and the one predicted from robot modeling (typically computed using Cosserat rod modeling and actuator po- sitions [1]). The applied force is then estimated through optimization procedures, with [2] or without [3], [4] explicit knowledge of the force application point. These algorithms have shown promising performance but are restricted to passive Cosserat rods models, whereas in practice continuum robots are active structures. Recently, Aloi et al. extended the work from [4] in the case of a 2- DOF tendon-driven robot, for which they experimentally validated their method [5]. All the previous solutions have two limitations. First, they assume contact forces to be perpendicular to the robot’s curvilinear axis: hypothesis (H1). Since con- tinuum robot shapes can be highly curved, one might question how strongly the tangential component of the force can affect the global deformation of the robot. Second, they consist of iterative optimizations during which the whole robot model is computed at each iteration using convex optimization routines. Such an approach can be computationally time-consuming and does not necessarily yield a global optimum. The present paper introduces a new Compliance-based approach to estimate an external force applied to a continuum robot in any direction. Results obtained with a simulated Concentric Tubes Continuum Robot (CTCR) are presented and discussed.

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.

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.

This paper introduces the concept of Generalized Compliance for continuum robots, specifically for those modeled with the Cosserat Rod theory. Unlike existing models based on tip compliance, the proposed approach considers interactions along the entire body of the flexible robot. The paper also presents a novel method referred to as the Low-Level Derivative Propagation Method, which is designed for the computationally efficient derivation of the Generalized Compliance matrix. The proposed method streamlines calculations and reduces integration time. The presented method, which is general and applies to various types of continuum robot models, is demonstrated on the case of a Concentric Tubes Continuum Robot. We provide detailed derivations of the equations and computation techniques leading to the derivation of the Generalized Compliance matrix, as well as a large-scale numerical validation of the method. The code used in this paper is available on the following GitHub website: https://github.com/benoitrosa/Generalized-Compliance-Computation-for-Continuum-Robots.

Continuum robots have the potential to enable new applications in medicine, inspection, and countless other areas due to their unique shape, compliance, and size. Excellent progress has been made in the mechanical design and dynamic modeling of continuum robots, to the point that there are some canonical designs, although new concepts continue to be explored. In this paper, we turn to the problem of state estimation for continuum robots that can been modeled with the common Cosserat rod model. Sensing for continuum robots might comprise external camera observations, embedded tracking coils, or strain gauges. We repurpose a Gaussian process (GP) regression approach to state estimation, initially developed for continuous-time trajectory estimation in SE(3). In our case, the continuous variable is not time but arclength and we show how to estimate the continuous shape (and strain) of the robot (along with associated uncertainties) given discrete, noisy measurements of both pose and strain along the length. We demonstrate our approach quantitatively through simulations as well as through experiments. Our evaluations show that accurate and continuous estimates of a continuum robot’s shape can be achieved, resulting in average end-effector errors between the estimated and ground truth shape as low as 3.5 mm and 0.016° in simulation or 3.3 mm and 0.035° for unloaded configurations and 6.2 mm and 0.041° for loaded ones during experiments, when using discrete pose measurements.

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.

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, 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.

I204 recent year, the continuum robot is focused on because of its flexibility and adapt. However, the free-end vibration is a critical factor which hinder the operation stability of continuum robot. The complexity of free end vibration is main origin from the flexible structure. Hence, the vibration dynamic model is difficult to establish as an accurate solution. This paper presented a novel method for analyzing the free end vibration state of the continuum robot, and proposed the corresponding control strategy. Firstly, the prototype is built and the kinematics is established for driving the continuum robot. Secondly, the feed-back system is set up by using an acceleration sensor for acquiring the real-time acceleration date. Further, the vibration characteristic parameters of the continuum robot are calibrated based on the identification method, by which to obtain the first-order damped natural frequency and attenuation coefficient of the continuum robot under different posture. Then, the vibration function of free end is solved depend on the first-order damped natural frequency and attenuation coefficient parameters. Finally, the residual vibration of free-end is effectively attenuated by the theoretical vibration mode.

Generic and high-performance feedback control is still challenging for tendon-driven continuum robots. Conventional model-based controllers, based on the piecewise constant curvature (PCC) assumption, explicitly require the arc parameters (bending angle and direction angle) to link the task (in Cartesian coordinates) and actuation spaces. However, the approaches' effectiveness remains to be explored when robot shapes deviate from circular arcs. This paper proposed a hybrid scheme for novel kinematic control of continuum robots. The error led by the slack state has been avoided through tension supervision, while analytical differential kinematics is further developed to avoid the explicit call of arc parameters by importing Cylindrical coordinates into task space and applying accurate piecewise linear approximation. Comparison between a conventional PCC-based controller and the proposed controller has been done by implementing them in a twin-pivot joint-based continuum section. An overall tip positioning accuracy of ±0.35mm has been reached, and a result of root-mean-square-error (RMSE): 0.3mm and Max error: 0.97mm has been observed when running two predefined path tracking. Further, in order to evaluate the versatility of the proposed controller, a dual-revolute joint-based and a 3D-printed continuum section were used to test for path tracking to prove the effectiveness of the controller on a wide range of continuum robotic systems.

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.

Most existing surgical robots employ straight rigid instruments and are not compatible with imaging modalities, especially magnetic resonance imaging (MRI) that presents restrictive constraints on the robot and actuator materials. Employing continuum distal end effector and fulfilling multi-imager compatibility will potentially lead to wide adoption of surgical robots in intraoperative image-guided minimally invasive surgery (MIS). This paper introduces a 3-dimensional (3D) printed polyamide continuum robot with 2-degree of freedom, driven by modular shape memory alloy (SMA) spring actuators that enable real-time distal manipulation in 3D workspace. The multi-imager compatibility is conditionally satisfied by utilizing no ferromagnetic materials and MRI-conditional actuators in the robotic system. The use of modular SMA allows repeatable configuration setting, easy integration with active cooling strategies, and facilitates the creation of a sterile barrier between the end effector module and the actuation module. Detailed design of the robot, kinematics modeling and actuator modeling are discussed in the paper. We experimentally verified the robot kinematics and evaluated the dynamic performance of the continuum robot. It features an operating bandwidth of 0.12 Hz at -3 dB and a root-mean-square error of 0.98 mm under model predictive control when tracking sinusoidal signals, both with ±10 mm amplitude (distal bending angle of ±80^◦). As a demonstration, the robot was used as a flexible endoscope manipulator and steered under inputs from a joystick to show its real-time performance.