Multi-segment continuum robot shape estimation using passive cable displacement

This paper proposes a method to deform a continuum robot into a complex shape with distributed curvature using a single motor drive. This continuum robot can be deformed to a desired shape by placing tendon guides at appropriate intervals. We used several target shapes, including clothoid and sin curves, as well as a circular curve of constant curvature and confirmed that the deformed shapes match them both in the simulation and prototype. This paper proposes two models of continuum robots. One is the Plain Model in which the tendons are parallel to the rod and the Penetration Model in which the tendon penetrates to the rod. By placing the penetrating position(s), this continuum robot can be deformed into a shape with inflection point(s). We designed a mathematical model to simulate the deformed shape of the prototype to obtain the proper placement of the guides and penetration point(s). Through the optimization, it was able to find the parameters that, in most cases, result in the error of less than 4% between the target and deformed shapes on simulation. We applied these conditions to the prototype and evaluated the errors, which were approximately 10%, the same as the related works that use a conventional constant curvature model. We think that the results of this paper can be applied to reduce the number of actuators required and the size and weight of continuum or biomimetic robots.

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.

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 and soft robots have shown great potential in industrial and medical applications. Sensing the shapes of continuum robots is a challenging but significant problem for enhancing their performance during various tasks. In this letter, we present a novel method to estimate the shapes of continuum robots by capturing passive tendon displacements with image sensors. This method is reliable but low-cost. To reconstruct the shape of the continuum robot, an intuitive way based on screw theory and the material frame is also presented. The displacements of passive tendons are related to the integral of the geometric parameters of the continuum robot. By using passive tendon displacements, not only bending but also twisting of the robot can be calculated. The experiments show that our method can estimate the shapes of the robot deformed in different conditions. The mean distal position error is 3.01% of the length and the mean shape error is 1.86% of the length. The mean distal direction error is 4.1 degrees. Besides, sensing the shapes of continuum robots in real-time is also achieved.

The design and analysis of continuum robots have consistently been a prominent research focus in the field of mechanics. However, portable continuum robots with minimal spatial occupancy, which have great potential for applications such as search and rescue, are scarcely available. This paper presents a novel helical-coiled multi-segment flexible continuum robot featuring helical deployment and compact design, with an integrated framework for structural design, kinematic modeling, and experimental validation. The design of the helical-coiled multi-segment flexible continuum robot for unstructured environment detection, including a flexible body, an actuation module, a feed module, and a sensing module, is presented systematically. Kinematic models of both single- and multi-segment continuum robots were established based on the constant curvature model to analyze the parameter mapping relationship from the end-effector position and orientation to the driving inputs. Furthermore, the feedforward motion of the robot was examined, and an uncoiling strategy based on S-curve compensation was employed to complete the kinematic analysis. Finally, the accuracy of the kinematic model considering the active uncoiling feed motion was validated through experimental analysis, demonstrating the motion characteristics of the continuum robot. Altogether, this study provides a framework for the design and analysis of helical-coiled continuum robots.

Kinematic modeling is essential for planning and controlling continuum robot motion. The traditional Denavit Hartenberg (DH) model involves complex matrix multiplication operations, resulting in computationally intensive inverse solutions and trajectory planning. Solving position and orientation changes in continuum robots using the double quaternion rule can reduce computational complexity. However, existing dual quaternion methods are direct equational transformations of DH rules and do not give a complete modeling process. They usually require more interpretability when applying continuum robot kinematic modeling. This paper uses the dual quaternion method to establish a kinematic model of a continuum robot. It uses a two-section continuum robot model to compare the advantages of dual quaternion and traditional modeling methods. In addition, this paper proposes a five-polynomial interpolation algorithm based on the dual quaternion method for trajectory planning of continuum robots. This method accurately models spatial bending and torsional motions of singularity-free continuum robots.

Continuum robots have been recently used in the inspection of tight and confined spaces. State-of-the-art motion planning algorithms that are developed for rigid robots could be inadequate when applied to redundant and complainant continuum robots. In this research, a Demonstration-Guided Motion Planning (DGMP) framework is proposed to let continuum robots imitate a set of given demonstrations to plan and execute point-to-point spatial motions. A flexible interface is incorporated to allow humans to intuitively demonstrate motions for the robot via teleoperation. The Dynamic Movement Primitives (DMP) framework is adopted to learn, reproduce and generalize the given demonstrations while avoiding static or moving obstacles existing in the environment. Meanwhile, a Model Reference Adaptive Controller (MRAC) is proposed to ensure the robot robustness against perturbation while tracking the generated motions from the DGMP. The developed approach is evaluated over a simulated model of a two-section continuum robot. The obtained results show evidence that the proposed DGMP is effective in generating and tracking spatial motions for continuum robots. This could encourage a further investigation towards planning complex motions in the future for redundant continuum robots.

In this paper, neural networks are presented to solve the inverse kinematic models of continuum robots. Firstly, the forward kinematic models are calculated for variable curvature continuum robots. Then, the forward kinematic models are implemented in the neural networks which present the position of the continuum robot’s end effector. After that, the inverse kinematic models are solved through neural networks without setting up any constraints. In the same context, to validate the utility of the developed neural networks, various types of trajectories are proposed to be followed by continuum robots. It is found that the developed neural networks are powerful tool to deal with the high complexity of the non-linear equations, in particular when it comes to solving the inverse kinematics model of variable curvature continuum robots. To have a closer look at the efficiency of the developed neural network models during the follow up of the proposed trajectories, 3D simulation examples through Matlab have been carried out with different configurations. It is noteworthy to say that the developed models are a needed tool for real time application since it does not depend on the complexity of the continuum robots' inverse kinematic models.

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.

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.

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.

There is an increasingly popularity for the continuum robot in minimally invasive surgery(MIS), because of the compliance and dexterity. In the first place, a variable stiffness manipulator can resolve the two contradictions of the demands for predominant flexibility and strong payload capacity. In the second place, to control the continuum robot more precisely and avoid the collision between robot and human body, real-time tracking of the shape of the continuum robot is of great significance. A new type of flexible manipulator with variable stiffness is proposed which can track the bending shape timely. The low-melting-point-alloy (LMPA) is used to realize the variable stiffness and shape detection for the flexible manipulator. The concept design for a single module is put forward. Then the stiffness control method and finite element simulation, the method of shape detection are presented. Moreover, the presented method of shape detection is evaluated by experiments.

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

Traditional dynamic models of continuum robots are in general computationally expensive and not suitable for real-time control. Recent approaches using learning-based methods to approximate the dynamic model of continuum robots for control have been promising, although real data hungry—which may cause potential damage to robots and be time consuming—and getting poorer performance when trained with simulation data only. This paper presents a modelbased learning framework for continuum robot closed-loop control that, by combining simulation and real data, shows to require only 100 real data to outperform a real-data-only controller trained using up to 10000 points. The introduced data-efficient framework with three control policies has utilized a Gaussian process regression (GPR) and a recurrent neural network (RNN). Control policy A uses a GPR model and a RNN trained in simulation to optimize control outputs for simulated targets; control policy B retrains the RNN in policy A with data generated from the GPR model to adapt to real robot physics; control policy C utilizes policy A and B to form a hybrid policy. Using a continuum robot with soft spines, we show that our approach provides an efficient framework to bridge the sim-to-real gap in model-based learning for continuum robots.

Quasi Static Analysis of Multi-Segment Continuum Robot using Domain Decomposition Method