Variable Curvature Modeling Method of Soft Continuum Robots with Constraints

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.

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.

Kinematics optimization and static analysis of a modular continuum robot used for minimally invasive surgery.

Compliant joints are widely used in the structural design of 3D-printed continuum robots as their monolithic structure can greatly simplify the assembly process. However, some highly flexible compliant joints, such as the leaf-spring joints, still suffer from unstable rotation centers when interfered by external forces, which greatly reduces the motion stability of the constructed continuum robots. To cope with this problem, we propose a topology-optimization-based method in this paper to achieve efficient structural design of the complaint joints in continuum robots. With our method, the rotation stability of compliant joints can be improved without causing stress concentration problems. Experiments were also carried out to evaluate the bending performance of the 3D-printed continuum robots equipped with optimized compliant joints. Results demonstrated that, compared to continuum robots with the conventional leaf-spring joints, the optimized robots showed much less twisting deformation caused by out-of-plane loads, which exhibited the high rotation stability of the optimized joints. In future work, the proposed method can be further developed to achieve optimization of other mechanical properties of the compliant joints in continuum robots.

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.

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.

In the field of robots, soft continuum robots have strong adaptability, and rigid continuum robots have large carrying capacity, but they all have some limitations. The purpose of this paper is to solve the problems of small carrying capacity of soft continuum robots and low safety of rigid continuum robots. Based on the combined action of particle jamming and fiber jamming, we use the good fluidity of spherical particles and the rigidity of spherical particles to realize the flexibility and rigidity of the robot, and put forward the requirement of flexible contact and rigid bearing. According to the large range variable stiffness actual demand, a self-locking soft continuum robot with large range variable stiffness based on the jamming phenomenon is proposed, and the principle of large range variable stiffness is explained. Then the model experiment prototype is designed and manufactured. Based on the model, the combination elastomer is defined. The basic unit is constructed and the theoretical analysis is carried out, and the equivalent of the combination elastomer stiffness model is obtained. Finally, an experimental test system is built. Through the experiment and simulation of variable stiffness, the stiffness change of combination elastomer is obtained, and the specific situation of bearing capacity change is recorded. This study provides a new method to achieve a wide range of stiffness changes, and builds a bridge from soft continuum robots to rigid continuum robots.

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 play the role of end effectors in various surgical robots and endoscopic devices. While soft continuum robots (SCRs) have proven advantages such as safety and compliance, more research and development are required to enhance their capability for specific medical scenarios. This research aims at designing a soft robot, considering the concepts of geometric and kinematic similarities. The chosen application is a semi-invasive medical application known as transesophageal echocardiography (TEE). The feasibility of fabrication of a soft endoscopic device derived from the Chorda dorsalis paragon was shown empirically by producing a three-segment pneumatic SCR. The main novelties include bioinspired design, modeling, and a navigation control strategy presented as a novel algorithm to maintain a kinematic similarity between the soft robot and the rigid counterpart. The kinematic model was derived based on the method of transformation matrices, and an algorithm based on a self-organizing map (SOM) network was developed and applied to realize kinematic similarity. The simulation results indicate that the control method forces the soft robot tip to follow the path of the rigid probe within the prescribed distance error (5 mm). The solution provides a soft robot that can surrogate and succeed the traditional rigid counterpart owing to size, workspace, and kinematics.

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.

Grasping objects in cluttered environments remains a significant challenge in robotics, particularly when dealing with novel objects that have not been previously encountered. This paper proposes a novel approach to address the problem of robustly learning object grasping in cluttered scenes, focusing on scenarios where the objects are unstructured and randomly placed. We present a unique Deep Q-learning (DQN) framework combined with a full convolutional network suitable for the end-to-end grasping of multiple adhesive objects in a cluttered environment. Our method combines the depth information of objects with reinforcement learning to obtain an adaptive grasping strategy to enable a robot to learn and generalize grasping skills for novel objects in the real world. The experimental results demonstrate that our method significantly improves the grasping performance on novel objects compared to conventional grasping techniques. Our system demonstrates remarkable adaptability and robustness in cluttered scenes, effectively grasping a diverse array of objects that were previously unseen. This research contributes to the advancement of robotics with potential applications, including, but not limited to, redundant manipulators, dual-arm robots, continuum robots, and soft robots.

The continuum robot is a soft robot with infinite degrees of freedom. Origami has a high capacity for spatial deployment. This paper proposes a flexible continuum robot based on origami and mortise-tenon structure (FCRBOM). The robot consists of some flexible hinges based on origami and mortise-tenon structure (FHBOM). The design process of the FCRBOM is given. The compliance of the FCRBOM is analyzed by the compliance matrix method. The Finite element analysis (FEA) is used to simulate and analyze the FCRBOM, and the correctness of the theoretical analysis is verified. Then a spatial FCRBOM (SFCRBOM) is designed. The impact of key dimensional parameters on the flexibility of SFCRBOM is discussed. Finally, an SFCRBOM with higher flexibility is presented.

This paper proposes a novel decentralized approach to kinematic control of soft segmented continuum robots based on a consensus strategy. The robots under consideration deform in a plane according to a multi-segment Piecewise Constant Curvature (PCC) kinematic model in which each segment is represented as an equivalent rigid-link Revolute-Prismatic-Revolute (RPR) mechanism. In our approach, we assume that each segment of the robot is equipped with sensors to measure joint variables in its local coordinate frame and can communicate with its two adjacent segments. Our consensus-based decentralized control strategy provides an alternative to conventional control methods, which solve the inverse kinematic problem by using computationally intensive numerical methods to calculate the robot's Jacobian matrix at each time instant. We investigate the stability and convergence properties of proposed controllers for position regulation and trajectory tracking tasks and provide theoretical guarantees on the controllers' performance. We evaluate the controllers in simulation for scenarios in which the robot's tip must reach a certain position or follow a specified trajectory. We compare the performance of the position regulator for different controller gains, and we find that a simulated 15-link robot can track a complex reference trajectory with an average root-mean-square error of only 0.16% of the robot's initial length.

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.