Continuum Manipulator Research Articles

Full Forward Kinematics of Lower-Mobility Planar Parallel Continuum Robots

In rigid lower-mobility parallel manipulators the motion of the end-effector is partially constrained due to a combination of passive kinematic pairs and rigid components. Translational mechanisms, such as the Delta manipulator, are the most common ones among this type of mechanisms. When flexible elements are introduced, as in Parallel Continuum Manipulators, the constraint is no longer rigid, and new challenges arise in performing certain motions depending on the degree of compliance. Mobility analysis shifts from being purely a geometric issue to one that heavily relies on force distribution within the mechanism. Simply converting classical lower-mobility rigid parallel mechanisms into Parallel Continuum Mechanisms may yield unexpected outcomes. This work, making use of a planar parallel continuum Delta manipulator, on the one hand, presents two different approaches to solve the Forward Kinematics of planar continuum manipulators, and, on the other hand, explores some challenges and issues in assessing the resultant workspace for different design alternatives of this kind of flexible manipulators.

An Anti-Interference Control Algorithm for Continuum Robot Arm

The large number of joints in a continuum manipulator complicates its dynamic modeling, making model simplification inevitable for practical motion control. However, due to external disturbances and internal noise, a controller based on the simplified dynamic model often struggles to meet the desired dynamic performance. To address this issue, this paper proposes an anti-interference control algorithm for continuum manipulators, designed to compensate for parameter uncertainties, external disturbances, and measurement noise. At the same time, the parameters of the algorithm are obtained in the form of solvability of linear matrix inequalities (LMIs). The simulation results show that the algorithm proposed in the paper provides better transient performance and is not affected by the entire disturbance. Experimental results further confirm the effectiveness and robustness of the algorithm.

Robust and Adaptive Control of a Soft Continuum Manipulator for Minimally Invasive Surgery

This article investigates the model-based control in configurations space of a soft continuum manipulator for minimally invasive surgery. The main control challenges for these types of systems are the presence of model uncertainties and nonlinearities. To this end, a sliding-mode controller, a Lyapunov redesign controller, and an adaptive controller have been designed and compared by means of simulations and experiments on a prototype. The results indicate that the adaptive controller yields better accuracy but a slower transient. Conversely, the sliding-mode controller and Lyapunov redesign yield a faster response but can result in chattering or steady-state errors.

Design, Kinematics, and Deployment of a Continuum Underwater Vehicle-Manipulator System

Abstract Underwater vehicle-manipulator systems (UVMSs) are underwater robots equipped with one or more manipulators to perform intervention missions. This article provides the mechanical, electrical, and software design of a novel UVMS equipped with a continuum manipulator, referred to as a continuum-UVMS. A kinematic model for the continuum-UVMS is derived in order to build an algorithm to resolve the robot’s redundancy and generate joint space commands. Different methods to optimize the trajectory for specific tasks are proposed using both the weighted least norm solution and the gradient projection method. Kinematic simulation results are analyzed to assess the performance of the proposed algorithm. Finally, the continuum-UVMS is deployed in an experimental demonstration in which both teleoperation and autonomous control are tested for a given reference trajectory.

Parallel Continuum Delta: On the Performance Analysis of Flexible Quasi-Translational Robots

In the field of rigid parallel manipulators, the Delta parallel robot is one of the most popular choices in the industry due to its ability to adapt to a wide range of applications, particularly pick-and-place tasks. In this paper, the authors present novel designs of Delta-type continuum parallel manipulators with flexible bars, solving both their direct and inverse kinematics, as well as obtaining the associated workspace. The continuum parallel manipulators, unlike conventional robots, incorporate certain flexible elements, such as slender rods that make up the kinematic chains of the Delta manipulators proposed in this work. As a consequence of the flexibility of these rods, a purely translational movement will not be generated, since it is necessary to analyze the zones of the workspace where a parasitic motion related to the inclination of the moving platform compromises the task devised. In addition, an experimental prototype of the Keops-Delta continuum manipulator has been built, and several experimental tests have been carried out to validate the proposed theoretical model.

Redesign of a Balance Rehabilitation Device Based on a Parallel Continuum Mechanism

In the present work, a parallel continuum manipulator for trunk rehabilitation tasks for patients who have suffered a stroke was analyzed and redesigned. The manipulator had to perform active assistance exercises for the motor recovery of the patient. Based on this background, a series of requirements were defined, which determined the design framework during the modeling of the manipulator. Finally, an improved prototype was built and tested to verify that the model can properly characterize the behavior of the manipulator. Such tests were carried out using a self-made dummy that replicates the simplifying hypotheses and conditions assumed in the mathematical model.

YoMo: Yoshimura Continuum Manipulator for MR Environment.

Origami robots have garnered attention due to their versatile deformation and potential applications, particularly for medical applications. In this article, we propose a Yoshimura continuum manipulator (YoMo) that can achieve accurate control of the tip position for the magnetic resonance (MR) environment. The YoMo made of a single piece of paper is cable-actuated to generate the bending and shortening deformation. The paper-based YoMo attached to an arc frame can readily function under different orientations in the MR environment. The design and fabrication of YoMo were formulated according to the Yoshimura folding pattern. The kinematics model based on constant curvature assumption was derived as a benchmark method to predict the tip position of the YoMo. The Koopman operator theory was applied to describe the relationship between the tip position and the length change under different orientations. The linear quadratic regulator integrated into the Koopman-based model (K-LQR) was adopted to achieve the trajectory tracking. Comprehensive experiments were carried out to examine the proposed YoMo, its modeling and control methods. The performance of the YoMo including stiffness and workspace was characterized via a customized test setup. The Koopman-based method demonstrates the superiority over the constant curvature-based model to predict the tip position. The K-LQR control method was examined with different trajectories, and the impact of the orientation, speed, and different trajectories were taken into consideration. The results demonstrate the YoMo is capable of achieving trajectory tracking with satisfied accuracy, indicating its potential for medical applications in the MR environment.

Design and kinematics analysis of a cable-stayed notch manipulator for transluminal endoscopic surgery

The friction between the joints of the continuum manipulator with discrete joints brings great difficulties to kinematic modeling. The traditional driving wire arrangement limits the load capacity of the manipulator. A cable-stayed notch manipulator for transluminal endoscopic surgery is proposed, and a driving force coupling kinematic mode is established. The manipulator is fabricated from a superelastic Nitinol tube with bilaterally cut rectangular notches and is actuated by a stay cable. By applying the comprehensive elliptic integral solution (CEIS) for large deformation beams, the bending angle of each elastic beam is obtained, and the kinematics from the driving space to the joint space is formed. According to the bending angle of each elastic beam, the expression of the manipulator in Cartesian space can be obtained by geometric analysis. The kinematics from the joint space to the Cartesian space is established. The outer diameter of the manipulator is only 3.5 mm, and the inner diameter can reach 2 mm, allowing instruments to pass through. The maximum error of the manipulator movement is less than 5%. The load capacity of the manipulator has been verified through the stiffness experiments, and the maximum load of the manipulator can reach 400 g. The cable-stayed notch manipulator can be accurately modeled on the base of CEIS, and its motion accuracy can meet the needs of engineering applications. The compact size and excellent load capacity of the manipulator make it potential for application in transluminal endoscopic surgical robots.

Differential-algebraic equation-based model predictive control for trajectory tracking of spacecraft-mounted continuum manipulators

Spacecraft-mounted continuum manipulators (SMCMs) exhibit great potential for performing dexterous operations in unstructured environments due to their inherent compliance and dexterity. However, the dynamic model of the rigid-flexible coupling SMCM is highly nonlinear and typically formulated as a set of implicit differential-algebraic equations (DAEs), posing significant challenges for precise trajectory tracking control. This paper proposes a novel model predictive control (MPC) framework specifically designed for generic DAEs to achieve precise trajectory tracking of the SMCM under uncertain disturbances and input limitations. The DAE model of the SMCM is discretized into a set of nonlinear algebraic equations. By performing implicit differentiation of these equations with respect to the system state, the state transition matrix (STM) for the DAE model is derived. The optimal control action for the SMCM can be further determined based on the derived STM. Additionally, nonlinear complementary functions are introduced to address the issue of input limitations, allowing the problem of determining the optimal control sequence to be equivalently transformed into a set of nonlinear algebraic equations for solving. Numerical simulations demonstrate that the proposed approach can achieve precise trajectory tracking of the SMCM while strictly adhering to input limitations.

Simultaneous position and force control of a SMA-actuated continuum robotic module

Continuum manipulators with controllable shape and exerting force are attractive devices. Utilizing great features of shape memory alloys (SMAs), thin continuum modules are developed. SMAs are embedded around an elastic rod and activated through a control algorithm to set a desired shape. However, complex behavior of SMAs in such a multi-input multi-output system, make the control challenging. Additionally, simultaneous control of position and the force applied by the module, as a challenging problem, has not been investigated so far. Handling this problem may increase the application of continuum robots when utilized as manipulators or when pass through narrow and complex canals with sensitive wall. In this research, position and force control of such continuum module is under focus for achieving a more practical tool for better non-invasive medical devices. Further to the position control, the amount of force applied to the environment is adjusted in different locations of the workspace through a novel fuzzy controller. The results indicate the possibility of simultaneous control of the position and force using fuzzy controller with a reasonable accuracy of 0.5° for angle and 0.05 N for the force. The concluded results may be utilized in developing smarter soft robots.

Kinematic analysis and experimental validation of a tripod parallel continuum manipulator

A tripod is a classical lower mobility parallel manipulator with three degrees of freedom. The usual geometrical constraints enforce a type of motion with two rotations on a horizontal plane and a translational motion in a vertical direction. These devices are applicable where a task requires a precise orientational motion. Nevertheless, some parasitic motions occur on the constrained degrees of freedom. Parallel Continuum Manipulators are devices where some elements have been replaced by slender rods whose deformation is source of mobility, allowing the elimination of some of the kinematic joints. This type of closed-loop compliant mechanisms have some features that can be useful in certain applications, e.g., the deformed state introduces a certain preload that avoids backslash, they have an inherent compliance that can be useful in some delicate tasks, and a certain control on wrench applied can be obtained. In this article, the comprehensive kinetostatic analysis of a tripod-type parallel continuum manipulator, 3 P ¯ FS , is explained and compared with that of its rigid counterpart 3 P ¯ RS . Workspace and singularity locus is obtained, positioning accuracy and wrench generation are evaluated experimentally.

Data‐Driven Modeling and High‐Precision Tracking Control of a Soft Continuum Manipulator: Enabling Robotic Sorting of Multiwire Cables

As a new class of robots, soft continuum manipulators have attracted attention due to their flexibility and compliance. However, these characteristics create challenges for precise modeling and control. This study proposes a hybrid offline and online data‐driven scheme to achieve high‐precision tracking control of a soft continuum manipulator. First, a novel multiscale deep neural network learns the manipulator model offline. Specifically, the feature fusion module extracts highly discriminative features and captures long‐term dependencies from the temporal trajectory data. The self‐attention module strengthens the ability to represent fusion features and enhances the model prediction accuracy. Then, the learnt model is updated using multisensor data online, and the proposed controller further compensates for the updated model and enhances the tracking accuracy in the movement stage. Finally, the experimental results demonstrate a significant improvement in motion accuracy under different trajectory‐tracking scenarios (i.e., deviations of <1 mm in position and <0.8° in orientation). The example of the multiwire cable sorting proves the feasibility of the proposed scheme in high‐precision industrial applications.

Soft Robotic System with Continuum Manipulator and Compliant Gripper: Design, Fabrication, and Implementation

This paper presents the design, construction, and implementation of a soft robotic system comprising a continuum manipulator arm equipped with a compliant gripper. Three main objectives were pursued: (1) developing a soft silicone gripper as an alternative to expensive and rigid steel grippers, enabling safe and precise handling of delicate or irregular objects such as fruits, glassware, and irregular shapes; (2) fabricating a continuum manipulator arm with robotic joints inspired by vertebrae, allowing for smooth, non-linear motion and more excellent maneuverability compared to traditional rigid arms, enabling access to hard-to-reach areas; and (3) integrating the compliant gripper with the continuum manipulator and implementing a control system for the soft gripper and remote bending arm using a microcontroller. The soft gripper, manipulator arm vertebrae, and other components were fabricated using 3D printing with PLA material for the molds. The gripper construct used hyperelastic silicone (Ecoflex 00.30). The continuum manipulator achieved a higher degree of freedom and mobility, while simulations and experiments validated the design’s effectiveness. The comparison shows that the close agreements differ by only 2.5%. In practical experiments involving lifting objects, the gripper was able to carry items with a greater mass. The proposed soft, integrated robotic system outperformed traditional rigid approaches, offering safe and flexible handling capabilities in unstructured environments. The nature-inspired design enabled a compliant grip and enhanced maneuverability, making it suitable for various applications requiring dexterous manipulation of delicate or irregularly shaped objects.

Analytical Inverse Kinematics for 2-Segment Extensible Continuum Manipulators

Abstract Fast inverse kinematics (IK) algorithm is significant for real-time precise motion control of continuum and soft manipulator. In this paper, we studied an explicit expression of two-segment continuum manipulator based on the constant curvature assumptions and discussed the existence of the IK solutions. This model used pseudo-rigid-body method, unlike 6-axis rigid industrial robot arm, we found that the two-segment extensible continuum manipulators have limited rotation angle around the direction vector of its tip, i.e., this type manipulator has limited dexterity. Then we pre-constrained five degrees of freedom (DOFs) constrained and discussed the definition of the left DOF. The IK solving process is simplified to realize small calculation cost for most applications. This model will provide a robust and real-time way to control the two-segment extensible continuum manipulators.

Design and performance analysis of continuum manipulator with twisting rotation

The continuum manipulator exhibits excellent flexibility, enabling it to navigate through unstructured and narrow spaces. However, the current motion capabilities of the continuum arm are limited to expansion, bending, or their combination, which restricts its application range and potential uses. Designing a continuum manipulator capable of twisting motion around its axis poses a significant challenge. In this study, we propose a torsion module for the continuum manipulator that enables twisting motions. This module comprises a central trunk made of a torsion spring and a driving mechanism consisting of two tendons arranged in cylindrical helix symmetry. By stretching these driving cables, the module can achieve twisting motion. We describe the principle behind torsional motion, establish a kinematic model for the continuum torsional module, and analyze how structural parameters affect its performance in terms of twisting motion. Furthermore, we construct a continuum arm incorporating this torsion module to enable both twisting and bending motions. We present examples showcasing the versatile capabilities of this continuum manipulator in various specialized scenarios. Experimental results demonstrate that the addition of torsional functionality enhances dexterity and expands design possibilities for continuum manipulators.

Wire-arc directed energy deposition of metal using a tendon-driven soft robotic gun: prototyping and conceptual validation

ABSTRACT Most directed energy deposition (DED) implementations employ a rigid end effector to deposit material layer-by-layer, which is insufficient in cases with space constraints. To enhance the flexibility, this paper proposes a novel soft-robotic gun (SRG) based DED technology. The ideology is to replace the rigid weld gun with a tendon-driven omnidirectional-steering continuum manipulator, which a computer can numerically control. To this end, both requirements and concepts of the SRG-DED are introduced. A prototype system is designed and implemented before dedicated kinematic modelling and trajectory planning mechanisms are presented. As demonstrated by the experimental results, the developed trajectory planning algorithm improves the computational efficiency of tendon variables and enhances the consistency of trajectory tracking. The prototype system can deposit a complex path on an inclined substrate and fabricate a thin-wall component within a pipeline. The validation work confirms the feasibility and applicability of the prototype system for metal additive manufacturing applications.

A Moving Horizon Estimation for a Class of Soft Continuum Manipulators

Abstract This work proposes a formulation for the moving horizon estimation technique considering both states and parameters obtained simultaneously with reduced estimation issues. The parameters can be either constant or time-varying, while states are related to complex output trajectories related to underactuated systems. Particularly, the proposed formulation considers additional equality constraints as a counterpart of the dynamics tube-model predictive control. Thus, it becomes less dependent on probabilistic information, such as probability density function and covariance of the process noise. In addition, the calibration of the method parameters has less sensitivity and driven by the tube constraints. The proposed approach can be applied in different systems; however, here it is detailed for a class of soft continuum manipulators with fluidic actuation through a variable flowrate and demonstrated with numerical simulations in planar motion. Results indicate robustness of the algorithm estimation in a challenging scenario arising from underactuation as well as in the presence of uncertainty and external disturbance, while simultaneously states and a vector of structural parameters are coherently estimated.

Kinetostatics Modeling and Analysis of a Spherical Parallel Continuum Manipulator

Abstract In this paper, a spherical parallel continuum manipulator (SPCM) which is the flexible version of the 3-RRR“Agile Eye” mechanism is proposed and analyzed. The SPCM consists of three parallel flexible limbs, each limb is formed by compliant truncated cone elements, and the moving platform connects each limb with a passive revolute joint. Three servo motors are used to control the manipulator actively, and the spherical motion is realized by the coupled large deflections of the flexible links. An equivalent compliance analysis method of the element is developed based on finite element analysis and principal axis decomposition. By combining all three limbs, the kinetostatics model of the whole manipulator is derived, and a gradient iteration algorithm is developed to solve the forward and inverse kinetostatics. Finally, a prototype of the manipulator is constructed using 3D-printing technology, and the accuracy for element equivalence and end-effector characteristics is validated by experiments. The results show that the derived kinetostatics model can accurately describe the force–deflection behavior of the SPCM.

Tendon-Driven Continuum Robots for Aerial Manipulation—A Survey of Fabrication Methods

Aerial manipulators have seen a rapid uptake for multiple applications, including inspection tasks and aerial robot–human interaction in building and construction. Whilst single degree of freedom (DoF) and multiple DoF rigid link manipulators (RLMs) have been extensively discussed in the aerial manipulation literature, continuum manipulators (CMs), often referred to as continuum robots (CRs), have not received the same attention. This survey seeks to summarise the existing works on continuum manipulator-based aerial manipulation research and the most prevalent designs of continuous backbone tendon-driven continuum robots (TDCRs) and multi-link backbone TDCRs, thereby providing a structured set of guidelines for fabricating continuum robots for aerial manipulation. With a history spanning over three decades, dominated by medical applications, CRs are now increasingly being used in other domains like industrial machinery and system inspection, also gaining popularity in aerial manipulation. Fuelled by diverse applications and their associated challenges, researchers have proposed a plethora of design solutions, primarily falling within the realms of concentric tube (CT) designs or tendon-driven designs. Leveraging research works published in the past decade, we place emphasis on the preparation of backbones, support structures, tendons, stiffness control, test procedures, and error considerations. We also present our perspectives and recommendations addressing essential design and fabrication aspects of TDCRs in the context of aerial manipulation, and provide valuable guidance for future research and development endeavours in this dynamic field.

Recurrent neural network robust curvature tracking control of tendon-driven continuum manipulators with simultaneous joint stiffness regulation

Recurrent neural network robust curvature tracking control of tendon-driven continuum manipulators with simultaneous joint stiffness regulation