Soft Continuum Research Articles

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.

Tailor-Made Reinforcement Learning Approach With Advanced Noise Optimization for Soft Continuum Robots

Tailor-Made Reinforcement Learning Approach With Advanced Noise Optimization for Soft Continuum Robots

A Novel Caterpillar-Inspired Vascular Interventional Robot Navigated by Magnetic Sinusoidal Mechanism

Magnetic soft continuum robots (MSCRs) hold significant potential in fulfilling the requirements of vascular interventional robots, enabling safe access to difficult-to-reach areas with enhanced active maneuverability, shape morphing capabilities, and stiffness variability. Their primary advantage lies in their tether-less actuation mechanism that can safely adapt to complex vessel structures. Existing commercial MSCRs primarily employ a magnetic-pull strategy, which suffers from insufficient driving force and a single actuation strategy, limiting their clinical applicability. Inspired by the inchworm crawling locomotion gait, we herein present a novel MSCR that integrates a magnetic sinusoidal actuation mechanism with adjustable frequency and kirigami structures. The developed MSCRs consist of two permanent magnets connected by a micro-spring, which is coated with a silicone membrane featuring a specific notch array. This design enables bio-inspired crawling with controllable velocity and active maneuverability. An analytical model of the magnetic torque and finite element analysis (FEA) simulations of the MSCRs has been constructed. Additionally, the prototype has been validated through two-dimensional in-vitro tracking experiments with actuation frequencies ranging from 1 to 10 Hz. Its stride efficiency has also been verified in a three-dimensional (3D) coronary artery phantom. Diametrically magnetized spherical chain tip enhances active steerability. Kirigami skin is coated over the novel guidewire and catheter, not only providing proximal anchorage for improved stride efficiency but also serving similar function as a cutting balloon. Under the actuation of an external magnetic field, the proposed MSCRs demonstrate the ability to traverse bifurcations and tortuous paths, indicating their potential for dexterous flexibility in pathological vessels.

Analysis of Robot–Environment Interaction Modes in Anguilliform Locomotion of a New Soft Eel Robot

Bio-inspired robots with elongated anatomy, like eels, are studied to discover anguilliform swimming principles and improve the robots’ locomotion accordingly. Soft continuum robots replicate animal–environment physics better than noncompliant, rigid, multi-body eel robots. In this study, a slender soft robot was designed and tested in an actual swimming experiment in a still-water tank. The robot employs soft pneumatic muscles laterally connected to a flexible backbone and activated with a rhythmic input. The position of seven markers mounted on the robot’s backbone was recorded using QualiSys® Tracking Manager (QTM) 1.6.0.1. The system was modeled as a fully coupled fluid–solid interaction (FSI) system using COMSOL Multiphysics® 6.1. Further data postprocessing and analysis were conducted, proposing a new mode decomposition algorithm using simulation data. Experiments show the success of swimming with a velocity of 28 mm/s and at a frequency of 0.9 Hz. The mode analysis allowed the modeling and explanation of the fluctuation. Results disclose the presence of traveling waves related to anguilliform waves obtained by the superposition of two main modes. The similarities of the results with natural anguilliform locomotion are discussed. It is concluded that soft robot undulation is ruled by dynamic modes induced by robot–environment interaction.

Shape reconstruction of soft continuum robots via the fusion of local strains and global poses

Shape reconstruction of soft continuum robots via the fusion of local strains and global poses

Multifunctional Magnetic Muscles for Soft Robotics

Despite recent advancements, artificial muscles have not yet been able to strike the right balance between exceptional mechanical properties and dexterous actuation abilities that are found in biological systems. Here, we present an artificial magnetic muscle that exhibits multiple remarkable mechanical properties and demonstrates comprehensive actuating performance, surpassing those of biological muscles. This artificial muscle utilizes a composite configuration, integrating a phase-change polymer and ferromagnetic particles, enabling active control over mechanical properties and complex actuating motions through remote laser heating and magnetic field manipulation. Consequently, the magnetic composite muscle can dynamically adjust its stiffness as needed, achieving a switching ratio exceeding 2.7 × 10³. This remarkable adaptability facilitates substantial load-bearing capacity, with specific load capacities of up to 1000 and 3690 for tensile and compressive stresses, respectively. Moreover, it demonstrates reversible extension, contraction, bending, and twisting, with stretchability exceeding 800%. We leverage these distinctive attributes to showcase the versatility of this composite muscle as a soft continuum robotic manipulator. It adeptly executes various programmable responses and performs complex tasks while minimizing mechanical vibrations. Furthermore, we demonstrate that this composite muscle excels across multiple mechanical and actuation aspects compared to existing actuators.

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.

Modeling magnetic soft continuum robot in nonuniform magnetic fields via energy minimization

The emerging magnetic soft continuum robots (MSCRs) – a type of slender and soft rods with embedded hard-magnetic particles – hold great promise in endovascular intervention via remote magnetic actuation. Although numerous advantages of using permanent magnets have been demonstrated for manipulating MSCRs (e.g., simple systems with high actuation force, large operating workspace), the magneto-mechanical behavior of MSCRs in nonuniform magnetic fields, particularly those generated by permanent magnets, remains largely unexplored. In this work, a systematic study of MSCRs in the nonuniform field is presented, which includes theoretical modeling using hard-magnetic elastica theory, numerical analyses by energy minimization method, finite element simulations using ABAQUS user element (UEL), and experimental validation. Without solving governing differential equations, the large deflection of MSCRs is efficiently obtained via the minimization of the total potential energy using sequential quadratic programming (SQP). This efficient modeling method offers insights into the control of MSCRs using nonuniform magnetic fields. Two practical strategies are provided for precisely controlling MSCRs by manipulating a cubic magnet through the adjustment of the actuation distance, rotation angle, and spin angle, laying the foundation for applications of magnetically-assisted endovascular intervention.

Hybrid trajectory planning of two permanent magnets for medical robotic applications

Independent robotic manipulation of two large permanent magnets, in the form of the dual External Permanent Magnet (dEPM) system has demonstrated the possibility for enhanced magnetic control by allowing for actuation up to eight magnetic degrees of freedom (DOFs) at clinically relevant scales. This precise off-board control has facilitated the use of magnetic agents as medical devices, including catheter-like soft continuum robots (SCRs). The use of multiple robotically actuated permanent magnets poses the risk of collision between the robotic arms, the environment, and the patient. Furthermore, unconstrained transitions between actuation inputs can lead to undesired spikes in magnetic fields potentially resulting in unsafe manipulator deformation. This paper presents a hybrid approach to trajectory planning for the dEPM platform. This is performed by splitting the planning problem in two: first finding a collision-free physical path for the two robotically actuated permanent magnets before combining this with a path in magnetic space, which permits for a smooth change in magnetic fields and gradients. This algorithm was characterized by actuating each of the eight magnetic DOFs sequentially, eliminating any potential collisions and reducing the maximum undesired actuation value by 203.7 mT for fields and by 418.7 mT/m for gradients. The effect of this planned magnetic field actuation on a SCR was then examined through two case studies. First, a tip-driven SCR was moved to set points within a confined area. Actuation using the proposed planner reduced movement outside the restricted area by an average of 41.3%. Lastly, the use of the proposed magnetic planner was shown to be essential in navigating a multi-segment magnetic SCR to the site of an aneurysm within a silicone brain phantom.

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.

Classification and Evaluation of Octopus-Inspired Suction Cups for Soft Continuum Robots.

The emergence of the field of soft robotics has led to an interest in suction cups as auxiliary structures on soft continuum arms to support the execution of manipulation tasks. This application poses demanding requirements on suction cups with respect to sensorization, adhesion under non-ideal contact conditions, and integration into fully soft systems. The octopus can serve as an important source of inspiration for addressing these challenges. This review aims to accelerate research in octopus-inspired suction cups by providing a detailed analysis of the octopus sucker, determining meaningful performance metrics for suction cups on the basis of this analysis, and evaluating the state-of-the-art in suction cups according to these performance metrics. In total, 47 records describing suction cups are found, classified according to the deployed actuation method, and evaluated on performance metrics reflecting the level of sensorization, adhesion, and integration. Despite significant advances in recent years, the octopus sucker outperforms all suction cups on all performance metrics. The realization of high resolution tactile sensing in suction cups and the integration of such sensorized suction cups in soft continuum structures are identified as two major hurdles toward the realization of octopus-inspired manipulation strategies in soft continuum robot arms.

A Naturally Inspired Extrusion-Based Microfluidic Approach for Manufacturing Tailorable Magnetic Soft Continuum Microrobotic Devices.

Soft materials play a crucial role in small-scale robotic applications by closely mimicking the complex motion and morphing behavior of organisms. However, conventional fabrication methods face challenges in creating highly integrated small-scale soft devices. In this study, microfluidics is leveraged to precisely control reaction-diffusion (RD) processes to generate multifunctional and compartmentalized calcium-cross-linkable alginate-based microfibers. Under RD conditions, sophisticated alginate-based fibers are produced for magnetic soft continuum robotics applications with customizable features, such as geometry (compact or hollow), degree of cross-linking, and the precise localization of magnetic nanoparticles (inside the core, surrounding the fiber, or on one side). This fine control allows for tuning the stiffness and magnetic responsiveness of the microfibers. Additionally, chemically cleavable regions within the fibers enable disassembly into smaller robotic units or roll-up structures under a rotating magnetic field. These findings demonstrate the versatility of microfluidics in processing highly integrated small-scale devices.

Thermally Drawn-Based Microtubule Soft Continuum Robot for Cardiovascular Intervention.

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.

Magnetic steering continuum robot for transluminal procedures with programmable shape and functionalities

Millimeter-scale soft continuum robots offer safety and adaptability in transluminal procedures due to their passive compliance, but this feature necessitates interactions with surrounding lumina, leading to potential medical risks and restricted mobility. Here, we introduce a millimeter-scale continuum robot, enabling apical extension while maintaining structural stability. Utilizing phase transition components, the robot executes cycles of tip-based elongation, steered accurately through programmable magnetic fields. Each motion cycle features a solid-like backbone for stability, and a liquid-like component for advancement, thereby enabling autonomous shaping without reliance on environmental interactions. Together with clinical imaging technologies, we demonstrate the capability of navigating through tortuous and fragile lumina to transport microsurgical tools. Once it reaches larger anatomical spaces such as stomach, it can morph into functional 3D structures that serve as surgical tools or sensing units, overcoming the constraints of initially narrow pathways. By leveraging this design paradigm, we anticipate enhanced safety, multi-functionality, and cooperative capabilities among millimeter-scale continuum robots, opening new avenues for transluminal robotic surgery.

A Soft Continuum Robotic Arm with a Climbing Plant‐Inspired Adaptive Behavior for Minimal Sensing, Actuation, and Control Effort

A Soft Continuum Robotic Arm with a Climbing Plant‐Inspired Adaptive Behavior for Minimal Sensing, Actuation, and Control Effort

Chorda Dorsalis System as a Paragon for Soft Medical Robots to Design Echocardiography Probes with a New SOM-Based Steering Control.

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.

Development of a novel nonlinear model and control strategy for soft continuum robots featuring hard magnetoactive elastomers

Magnetoactive soft continuum robots (MSCRs), capable of controllable steering and navigation, hold substantial promise for healthcare applications. However, advancements in MSCRs have been hindered by a limited understanding of MSCR dynamics and a lack of effective control methods. Addressing these gaps, this study presents a novel, time-dependent, and computationally efficient analytical model of MSCR, alongside a new optimal closed-loop control strategy for precise high-frequency trajectory tracking. A finite element (FE) model of the MSCR is initially developed, with its validity confirmed through rigorous laboratory measurements. Using the formulated FE model, a new and computationally efficient analytical model is subsequently developed to accurately predict the highly nonlinear response of MSCR. This model operates as a system of switched linear models, each of which is a reduced-order version of its corresponding high-order linear model extracted from the FE analysis. This innovative approach not only maintains the predictive accuracy of the FE model but also significantly reduces computational demands, operating in just a few seconds. The results highlight that the developed model can accurately predict the dynamic responses of the MSCR while significantly reducing the computational load by almost 80 orders of magnitude compared with the FE model on the same simulation platform. The proposed model has been effectively utilized to develop a novel optimal control strategy using the feedforward interval type-2 fractional-order fuzzy-PID method. A hardware-in-the-loop experimental test has been finally designed to demonstrate the superior performance of the MSCR under the proposed controller.

Driving torque model of the bionic soft arm’s hyperelastic bellows

ABSTRACT The technology of soft continuum robots represents an advance in the field of robotics to benefit a wide range of industries such as healthcare, manufacturing or environmental exploration. Soft continuum robots can be driven pneumatically by bellows as the soft continuum manipulator presented in this article. A driving torque model of the bellows considering hyperelastic material properties, friction and restoring torques is derived, whose purpose is suitability for model-based control design and subsequent trajectory generation. Hence, the driving torque model must be real-time capable. This is realized by an iterative algorithm calculating the bellows’ torque transmission by assuming a two-dimensional no-slip membrane contact. Nonlinear strain behaviours and hysteresis effects of the bellows are considered by the Ogden material model. The driving torque model’s performance is validated experimentally by measuring the external torques of the bellows.

Tissue palpation in endoscopy using EIT and soft actuators.

The integration of soft robots in medical procedures has significantly improved diagnostic and therapeutic interventions, addressing safety concerns and enhancing surgeon dexterity. In conjunction with artificial intelligence, these soft robots hold the potential to expedite autonomous interventions, such as tissue palpation for cancer detection. While cameras are prevalent in surgical instruments, situations with obscured views necessitate palpation. This proof-of-concept study investigates the effectiveness of using a soft robot integrated with Electrical Impedance Tomography (EIT) capabilities for tissue palpation in simulated in vivo inspection of the large intestine. The approach involves classifying tissue samples of varying thickness into healthy and cancerous tissues using the shape changes induced on a hydraulically-driven soft continuum robot during palpation. Shape changes of the robot are mapped using EIT, providing arrays of impedance measurements. Following the fabrication of an in-plane bending soft manipulator, the preliminary tissue phantom design is detailed. The phantom, representing the descending colon wall, considers induced stiffness by surrounding tissues based on a mass-spring model. The shape changes of the manipulator, resulting from interactions with tissues of different stiffness, are measured, and EIT measurements are fed into a Long Short-Term Memory (LSTM) classifier. Train and test datasets are collected as temporal sequences of data from a single training phantom and two test phantoms, namely, A and B, possessing distinctive thickness patterns. The collected dataset from phantom B, which differs in stiffness distribution, remains unseen to the network, thus posing challenges to the classifier. The classifier and proposed method achieve an accuracy of and on phantom A and B, respectively. Classification results are presented through confusion matrices and heat maps, visualising the accuracy of the algorithm and corresponding classified tissues.

Controller Design for a Soft Continuum Robot With Concurrent Continuous Rotation

Controller Design for a Soft Continuum Robot With Concurrent Continuous Rotation