Soft Continuum Manipulators Research Articles

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.

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.

Variable Stiffness Linear Actuator Based on Differential Drive Fiber Jamming

Variable stiffness technologies have been widely adopted in soft robotics, also combining them with different actuation technologies and demonstrating the potential to increase the range of possible applications of soft systems, such as soft continuum manipulators. However, in most cases, the variable stiffness capabilities of these soft system are far from satisfying the application requirements. With the aim to explore new possibilities to fill this gap, in this work, we present a novel variable stiffness linear actuator (VSLA) based on the combination of composite fiber jamming and the inverse pneumatic artificial muscles working principle. The differential pressure driving approach adopted to control the VSLA decouples the actuator deformation from the variable stiffness capabilities, and this makes the VSLA a suitable candidate for the realization of new kind of continuous arms. Moreover, the VSLA novel architecture introduced in this article was analytically modeled considering the interaction among constituent elements and performances in different loading conditions have been computed. The results obtained from the experimental tests validated the model goodness in terms of assumptions made and showed remarkable variable stiffness capabilities, with a maximum jamming ratio that reaches 21.3.

Reducing Actuators in Soft Continuum Robots and Manipulators

Soft continuum robots and manipulators (SCRaMs) are elongated structures that can be used in many applications, such as exploration, inspection, and minimally invasive surgery. Multi-segment SCRaMs employ numerous actuators to perform their tasks. The large number of actuators increases the cost and complexity of a SCRaM and reduces its reliability. In this paper, a methodology is presented to reduce the number of actuators employed by SCRaMs while maintaining their volumetric workspace. The method presents a new design approach involving one rotary and two linear actuators, providing three degrees of freedom (DOF) and a volumetric workspace. The result of applying the transformation is a 50–86% reduction in the total number of actuators typically employed by multi-segment SCRaMs. The application of this methodology reduces the cost and complexity of conventional multi-segment SCRaMs while improving their efficiency and reliability.

Energy Shaping Control of Hydraulic Soft Continuum Planar Manipulators

This letter investigates the model-based control of a class of soft continuum manipulators with hydraulic actuation that bend on a plane due to pressurization of one or more internal chambers. A port-Hamiltonian formulation is employed to describe the system dynamics, which includes the pressure dynamics of the hydraulic fluid. A new nonlinear control law is constructed with an energy-shaping approach, and it is combined with an adaptive observer to compensate the effect of unknown external forces. Stability conditions are investigated with a Lyapunov approach, and the effect of the tuning parameters and of key model parameters is discussed. The effectiveness of the controller is demonstrated with numerical simulations.

Design, Fabrication, and Performance Analysis of a Vertically Suspended Soft Manipulator

Soft continuum manipulators are comprised of flexible materials in a serpentine shape. Such manipulators can be controlled mechanically through tendons or pneumatic muscles. Continuum manipulators utilizing tendons are traditionally formed in a thick cross section, which presents limitations in achieving a high bending range as well as difficulties for storage and transportation. This study introduces a continuum manipulator comprised of two thin plastic bands and driven by a tendon to provide a bending action. The manipulator’s thin body form enables it to be rolled up for storage and transportation. Experimental results on different section lengths show the possibility of achieving a horizontal displacement of up to 34% of the bending-segment’s length, and a full closed-loop curvature for most segments. However, the results also indicated an elongation of the tip paths owing to gravity. These results, in addition to the manipulator’s flexibility and light weight features, confirm its suitability for applications in space and underwater environments.

Nonlinear energy-based control of soft continuum pneumatic manipulators

This paper investigates the model-based nonlinear control of a class of soft continuum pneumatic manipulators that bend due to pressurization of their internal chambers and that operate in the presence of disturbances. A port-Hamiltonian formulation is employed to describe the closed loop system dynamics, which includes the pressure dynamics of the pneumatic actuation, and new nonlinear control laws are constructed with an energy-based approach. In particular, a multi-step design procedure is outlined for soft continuum manipulators operating on a plane and in 3D space. The resulting nonlinear control laws are combined with adaptive observers to compensate the effect of unknown disturbances and model uncertainties. Stability conditions are investigated with a Lyapunov approach, and the effect of the tuning parameters is discussed. For comparison purposes, a different control law constructed with a backstepping procedure is also presented. The effectiveness of the control strategy is demonstrated with simulations and with experiments on a prototype. To this end, a needle valve operated by a servo motor is employed instead of more sophisticated digital pressure regulators. The proposed controllers effectively regulate the tip rotation of the prototype, while preventing vibrations and compensating the effects of disturbances, and demonstrate improved performance compared to the backstepping alternative and to a PID algorithm.

Feasibility of Fiber Reinforcement Within Magnetically Actuated Soft Continuum Robots.

Soft continuum manipulators have the potential to replace traditional surgical catheters; offering greater dexterity with access to previously unfeasible locations for a wide range of interventions including neurological and cardiovascular. Magnetically actuated catheters are of particular interest due to their potential for miniaturization and remote control. Challenges around the operation of these catheters exist however, and one of these occurs when the angle between the actuating field and the local magnetization vector of the catheter exceeds 90°. In this arrangement, deformation generated by the resultant magnetic moment acts to increase magnetic torque, leading to potential instability. This phenomenon can cause unpredictable responses to actuation, particularly for soft, flexible materials. When coupled with the inherent challenges of sensing and localization inside living tissue, this behavior represents a barrier to progress. In this feasibility study we propose and investigate the use of helical fiber reinforcement within magnetically actuated soft continuum manipulators. Using numerical simulation to explore the design space, we optimize fiber parameters to enhance the ratio of torsional to bending stiffness. Through bespoke fabrication of an optimized helix design we validate a single, prototypical two-segment, 40 mm × 6 mm continuum manipulator demonstrating a reduction of 67% in unwanted twisting under actuation.

Position regulation in Cartesian space of a class of inextensible soft continuum manipulators with pneumatic actuation

This work investigates the position regulation in Cartesian space of a class of inextensible soft continuum manipulators with pneumatic actuation subject to model uncertainties and to unknown external disturbances that act on the tip. Soft continuum manipulators are characterised by high structural compliance which results in a large number of degrees-of-freedom, only a subset of which can be actuated independently or instrumented with sensors. External disturbances, which are common in many applications, result in uncertain dynamics and in uncertain kinematics thus making the control problem particularly challenging. We have investigated the use of integral action to model the uncertain kinematics of the manipulators, and we have designed a new control law to achieve position regulation in Cartesian space by employing a port-Hamiltonian formulation and a passivity-based approach. In addition, we have compared two adaptive laws that compensate the effects of the external disturbances on the system dynamics. Local stability conditions are discussed with a Lyapunov approach and are related to the controller parameters. The performance of the controller is demonstrated by means of simulations and experiments with two different prototypes.

A Recurrent Neural-Network-Based Real-Time Dynamic Model for Soft Continuum Manipulators.

This paper introduces and validates a real-time dynamic predictive model based on a neural network approach for soft continuum manipulators. The presented model provides a real-time prediction framework using neural-network-based strategies and continuum mechanics principles. A time-space integration scheme is employed to discretize the continuous dynamics and decouple the dynamic equations for translation and rotation for each node of a soft continuum manipulator. Then the resulting architecture is used to develop distributed prediction algorithms using recurrent neural networks. The proposed RNN-based parallel predictive scheme does not rely on computationally intensive algorithms; therefore, it is useful in real-time applications. Furthermore, simulations are shown to illustrate the approach performance on soft continuum elastica, and the approach is also validated through an experiment on a magnetically-actuated soft continuum manipulator. The results demonstrate that the presented model can outperform classical modeling approaches such as the Cosserat rod model while also shows possibilities for being used in practice.

Closed-loop control of soft continuum manipulators under tip follower actuation

Continuum manipulators, inspired by nature, have drawn significant interest within the robotics community. They can facilitate motion within complex environments where traditional rigid robots may be ineffective, while maintaining a reasonable degree of precision. Soft continuum manipulators have emerged as a growing subfield of continuum robotics, with promise for applications requiring high compliance, including certain medical procedures. This has driven demand for new control schemes designed to precisely control these highly flexible manipulators, whose kinematics may be sensitive to external loads, such as gravity. This article presents one such approach, utilizing a rapidly computed kinematic model based on Cosserat rod theory, coupled with sensor feedback to facilitate closed-loop control, for a soft continuum manipulator under tip follower actuation and external loading. This approach is suited to soft manipulators undergoing quasi-static deployment, where actuators apply a follower wrench (i.e., one that is in a constant body frame direction regardless of robot configuration) anywhere along the continuum structure, as can be done in water-jet propulsion. In this article we apply the framework specifically to a tip actuated soft continuum manipulator. The proposed control scheme employs both actuator feedback and pose feedback. The actuator feedback is utilized to both regulate the follower load and to compensate for non-linearities of the actuation system that can introduce kinematic model error. Pose feedback is required to maintain accurate path following. Experimental results demonstrate successful path following with the closed-loop control scheme, with significant performance improvements gained through the use of sensor feedback when compared with the open-loop case.

Adaptive Energy Shaping Control of a Class of Nonlinear Soft Continuum Manipulators

Soft continuum manipulators are characterized by low stiffness that allows safe operation in unstructured environments but introduces underactuation. In addition, soft materials such as silicone rubber, which are commonly used for soft manipulators, are characterized by nonlinear stiffness, while pneumatic actuation can result in nonlinear damping. Consequently, achieving accurate control of these systems in the presence of disturbances is a challenging task. This article investigates the model-based adaptive control for soft continuum manipulators that have nonlinear uniform stiffness and nonlinear damping, that bend under the effect of internal pressure, and that are subject to time-varying disturbances. A rigid-link model with virtual elastic joints is employed for control purposes within the port-Hamiltonian framework. The effects of disturbances and model uncertainties are estimated adaptively. A nonlinear controller that regulates the tip orientation of the manipulator and that compensates the effects of disturbances and of model uncertainties is then constructed by using an energy shaping passivity-based approach. Stability conditions are discussed highlighting the beneficial role of nonlinear damping. The effectiveness of the controller is assessed with simulations and with experiments on a soft continuum manipulator prototype.

Energy shaping control with integral action for soft continuum manipulators

This paper investigates the control problem for soft continuum manipulators that operate on a plane and that are subject to unknown disturbances. In general, soft continuum manipulators have more degrees-of-freedom than control inputs and are characterised by nonlinear dynamics. Thus, achieving high position accuracy with these systems in the presence of disturbances is a challenging task. In this paper we present the design of a new partial-state feedback controller by using the port-Hamiltonian formulation and we develop a variation of the Integral Interconnection and Damping Assignment Passivity Based Control methodology for a class of soft continuum manipulators. The system dynamics on the bending plane is described by using a rigid-link underactuated model with n elastic virtual joints. The proposed control law regulates the tip rotation to the desired value while compensating unmodelled disturbances and only depends on the tip rotation, which is measurable, hence it is implementable. The effectiveness of the controller is demonstrated with simulations and with experiments on a soft continuum manipulator prototype that employs pneumatic actuation.

Correction: Dynamic modeling of soft continuum manipulators using lie group variational integration

[This corrects the article DOI: 10.1371/journal.pone.0236121.].

Design and Modeling of Soft Continuum Manipulators Using Parallel Asymmetric Combination of Fiber-Reinforced Elastomers

Abstract Soft continuum arms (SCAs) have a large workspace, dexterity, and adaptability, but at the cost of complex design construction highlighted by concatenating several serial segments. In this paper, we propose a new design architecture for SCAs composed of a parallel combination of pneumatic actuators. The BR2 SCA featured in this work is asymmetric as it combines one soft bending (B) actuator and two soft rotating (R2) actuators as opposed to state of art symmetric architectures that adopt bending segments. Spatial deformation is obtained by combining the bending and rotating feature of the individual actuators. This paper also formulates an approximate forward analysis method based on Kirchhoff rod equations to predict the spatial deformation under external loads with an accuracy less than 9% of the SCAs length. In addition, the model also takes into account the “coupling effect” inherent to the asymmetric parallel combination, where actuating rotating actuator attenuates the bending performance and vice versa. Consequently, this work also refines the design of the SCA that minimizes the coupling effect. A detailed performance study of the refined BR2 manipulator on a swiveling base demonstrates larger workspace and higher dexterity when compared with state of art single section SCAs. The performance of the design is validated through different tasks like obstacle avoidance, pick and place task, and whole arm grasping. These performance attributes surpass any other single segment soft module and is a potential building block for constructing customized SCAs.

Dynamic modeling of soft continuum manipulators using lie group variational integration.

This paper presents the derivation and experimental validation of algorithms for modeling and estimation of soft continuum manipulators using Lie group variational integration. Existing approaches are generally limited to static and quasi-static analyses, and are not sufficiently validated for dynamic motion. However, in several applications, models need to consider the dynamical behavior of the continuum manipulators. The proposed modeling and estimation formulation is obtained from a discrete variational principle, and therefore grants outstanding conservation properties to the continuum mechanical model. The main contribution of this article is the experimental validation of the dynamic model of soft continuum manipulators, including external torques and forces (e.g., generated by magnetic fields, friction, and the gravity), by carrying out different experiments with metal rods and polymer-based soft rods. To consider dissipative forces in the validation process, distributed estimation filters are proposed. The experimental and numerical tests also illustrate the algorithm’s performance on a magnetically-actuated soft continuum manipulator. The model demonstrates good agreement with dynamic experiments in estimating the tip position of a Polydimethylsiloxane (PDMS) rod. The experimental results show an average absolute error and maximum error in tip position estimation of 0.13 mm and 0.58 mm, respectively, for a manipulator length of 60.55 mm.

Topology optimization of a cable-driven soft robotic gripper

Improving the functionality of soft continuum manipulators to expand their application space has always been an important development direction for soft robotics. It remains very challenging to calculate the deformations of soft materials and predict the basic structure of soft fingers under complex objective functions and constraints. This work develops a cable-driven soft robotic gripper with multi-input and multi-output using topology optimization considering geometric nonlinearity, which not only performs adaptive grasping but also enables finer manipulations such as rotating or panning the target. A scheme that can describe adaptive grasping behavior is proposed, which converts the contact between the clamping surface and the object into a boundary condition to circumvent complex contact nonlinearities. An additive hyperelasticity technique is used to overcome numerical instabilities, and the finite element analysis is performed in ANSYS. Numerical simulations and experimental results are performed to demonstrate the effectiveness of the optimization algorithm and to illustrate the application potential of the proposed gripper.

A Light Soft Manipulator With Continuously Controllable Stiffness Actuated by a Thin McKibben Pneumatic Artificial Muscle

Soft continuum manipulators based on pneumatic artificial muscles offer the advantages of high compliance, complex environmental adaptability, and safe interaction with humans and work environments. However, most of them cannot continuously change their stiffness under a fixed end position due to the strong coupling of position and stiffness. To overcome this problem, this article develops a light soft continuum manipulator with a continuously controllable stiffness based on thin McKibben pneumatic artificial muscles. By controlling the external 2.0 mm muscles and the internal 1.3 mm muscles, the position and stiffness are decoupled. The math model is established, and the validity is verified by experiments.

High-force soft pneumatic actuators based on novel casting method for robotic applications

Soft pneumatic actuators (SPAs) play an important role in leading the development of soft robotics, and enable diverse and complex hardware design for soft robots. However, due to the limitation of the inherent characteristics of SPAs’ constitutive materials as well as fabrication tools and techniques, they tend to exhibit a lower driving force. In this paper, we propose a class of high-force SPAs that are fabricated by a novel method, embedded core casting. This method is enabled by two main steps: First, a SPA is designed in two parts, an actuating core composed of a fiber-reinforced airbag and an elastic holder made of soft materials, and they are fabricated independently; second, both parts are combined together by assembly and recasting techniques, producing a finished actuator. The bending SPAs fabricated by this method can bear air pressure up to 400 kPa, which provides important hardware for the development of high-load soft robots. Further, we demonstrate the applications of these soft SPAs in soft grippers, continuum manipulators, and soft wearable robots. This study helps improve the fabrication process for fiber-reinforced actuators and propose new high-force SPAs for robotic applications.

Energy-shaping control of soft continuum manipulators with in-plane disturbances

Soft continuum manipulators offer levels of compliance and inherent safety that can render them a superior alternative to conventional rigid robots for a variety of tasks, such as medical interventions or human–robot interaction. However, the ability of soft continuum manipulators to compensate for external disturbances needs to be further enhanced to meet the stringent requirements of many practical applications. In this paper, we investigate the control problem for soft continuum manipulators that consist of one inextensible segment of constant section, which bends under the effect of the internal pressure and is subject to unknown disturbances acting in the plane of bending. A rigid-link model of the manipulator with a single input pressure is employed for control purposes and an energy-shaping approach is proposed to derive the control law. A method for the adaptive estimation of disturbances is detailed and a disturbance compensation strategy is proposed. Finally, the effectiveness of the controller is demonstrated with simulations and with experiments on an inextensible soft continuum manipulator that employs pneumatic actuation.