A structural optimization analysis of cable-driven soft manipulator

Abstract

Cable-driven soft robots hold significant potential for surgical and industrial applications, yet their performance and maneuverability can be further enhanced through design optimization. By optimizing the design, factors such as bending angles, manipulator deformation, and overall functionality can be directly influenced, leading to improved interaction with the environment and more accurate task performance. This article presents a physics-based design optimization approach for cable-driven soft robotic manipulators, aiming to enhance bending performance through structural design enhancements. Four design criteria, namely, cross-sectional shape, material, gap shape, and gap size, are considered in the optimization process. Given the inherent nonlinearity of soft materials, finite element modeling techniques are employed to analyze the effects of modifying each design parameter on displacement and bending angle. The manipulator’s design is evaluated using ABAQUS/CAE, and an analysis of variance test is conducted to identify significant performance differences among the design parameters. The results reveal that material variation has the most substantial impact, followed by gap shape and gap size. Based on subsequent parameter optimization, Dragon Skin 10 is determined to be the optimal material for bending motion, while a trapezoidal gap shape is preferred. In addition, a genetic algorithm is utilized to select a maximum gap size of 8.87 mm. These findings provide valuable insights into key design principles for cable-driven soft manipulators, aiming to enhance flexibility and reduce actuation forces. By establishing a fundamental understanding of the relationship between morphology and motion capability, this methodology demonstrates an effective simulation-driven optimization approach that incorporates the nonlinear elastic behavior of materials to improve performance. Overall, this work establishes a framework for optimizing cable-driven architectures to suit various applications in the field of soft robotics.

Keywords

Cable-driven soft manipulator FEM ANOVA genetic algorithm

Introduction

Soft robotics is a rapidly evolving field that draws inspiration from flexible biological locomotion. Unlike traditional rigid-bodied robotics, soft robotics utilizes flexible materials in design, control, and construction. This approach offers advantages such as enhanced safety during human interaction and the ability to create intricate movements.^1
–3 Soft robots have contributed significantly to industries such as medicine and food processing. Recent reviews have underscored challenges in modeling and controlling soft robotic systems, given their dynamic characteristics. Further research aims to address these challenges through novel approaches tailored to the flexible nature of soft robots.^4
–6

In soft robotics, actuator performance is crucial to the overall effectiveness of a given system. Unlike traditional electric motors, soft actuators must be designed to be highly compliant and flexible. However, creating an artificial muscle that can match the performance of natural muscle remains one of the key challenges in this field.^7
–9 To tackle this issue, researchers proposed various strategies, the most common like pressure-driven actuation,^10
–12 electrically responsive actuation,¹³ and thermally responsive actuators.¹⁴ Due to its accuracy and ease of position control, the study is focused on cable-driven actuators to regulate the movement.^15

–20 In contrast, pneumatic actuation has some limitations and challenges because it cannot provide feedback for accurate movement, is more difficult to control, and is less portable, making it potentially challenging to directly control robot motion using deformation.¹⁰ Hysteresis effects, restricted strain recovery, and control of shape changes are additional challenges that may arise when using shape memory alloys for soft actuation.¹⁴

Soft robots differ from their stiff counterparts in that they use flexible materials like silicone rubber due to their excellent flexibility and ability to withstand significant deformations during actuation. Such materials can be modeled using the finite element method. The behavior of soft robotic systems is typically described by hyperelastic models, with the most significant models used in soft robotics outlined in earlier studies.^21,22 While silicone rubber is considered isotropic and incompressible, viscoelasticity and stress softening are often disregarded.²³

Prior works have applied optimization approaches to enhance the performance of pneumatic soft robotic actuators. Finite element method (FEM) and analysis of variance (ANOVA) methods have been utilized to optimize structural factors like channel morphology to maximize bending angles of pneumatic network actuators.^24

–27 Separate efforts have focused on developing model-based strategies combining evolutionary algorithms with finite element analysis (FEA) to improve soft manipulation capabilities across various actuator types.^28
–30 Specifically, genetic algorithms (GAs) have been leveraged to optimize inverse kinematics of concentric tube manipulators,³⁰ tune control parameters of flexible joint robots,³¹ and boost the accuracy of motion prediction from electromyography data.³² Swarm intelligence methods have also been explored to optimize the parameters of central pattern generators used in controlling bio-robotic fish.³³ customized GAs with specialized crossover and mutation schemes have demonstrated enhanced convergence for flexible manipulator optimization.³⁴ Multiobjective goals balancing bending angle and contact force have been targeted through integrated FEA and optimization.^35

–38 Overall, these pioneering studies have established the utility of modeling and analysis techniques for improving soft actuator designs.

While prior works have focused predominantly on pneumatic soft robot architectures, this work uniquely targets cable-driven designs exhibiting distinct challenges in achieving substantial bending under minimal actuation loads for delicate tasks. The presented methodology relates design factors to fundamental bending mechanics through physics-based modeling, enabling systematic tuning of morphological features to enhance cable-driven performance. The combined analysis of variance and GA optimization strategy specifically addresses the flexibility of cable-actuated manipulators across applications including medical and food-handling contexts.

The key contribution is to use nonlinear finite element simulations to investigate the implications of design decisions on maximum tip deflection. In contrast to data-driven techniques, directly integrating complex material behaviors yields physical insights that link morphology to bending performance. This enables mechanical design optimization to increase gripping functionality without extensive prototyping, providing advantages over current pneumatic soft robot simulation methodologies.

The approach might be extended to multicriteria optimization, which balances considerations in flexibility, strength, precision, and speed dependent on the intended application. By explaining these physical correlations, specialized solutions for limited space manipulation tasks in fields ranging from surgery to food industry robotics may be created.

This is how the manuscript is structured: The cable-driven soft manipulator’s construction is detailed in the structure of the cable-driven soft manipulator section, followed by the selection of each parameter in the evaluation of design parameters section, which details the optimization tools; furthermore, the bending angle is studied through the section calculation of final joint angle. After that, the validation for the proposed manipulation is implemented in the experimental setup and validation sections. Finally, the summaries of the article’s major contributions and the discussion of potential directions for future study are detailed in the conclusion and future work sections.

The structure of the cable-driven soft manipulator

In industrial applications, the use of a flexible soft manipulator can provide significant assistance. The objective of this proposed manipulator is to optimize the manipulator structure while ensuring simplicity, cost-effectiveness, and lightweight construction. To achieve precise design parameters, this study considers factors such as cross-sectional shape, material selection, gap shape, and gap size, utilizing a cable-driven actuation principle. Therefore, this study presents a cable-driven soft manipulator design, consisting of a row of vertebrates arranged in a linear configuration as depicted in Figure 1. The cable is securely fastened inside the manipulator, and motors are employed to retract it, thereby creating a concentrated load at the end tip. For static structural analysis, the geometry of the cable-driven soft manipulator was created in SOLIDWORKS (Dassault Systemes, Waltham, MA, USA). Key dimensions include a length of 85 mm, and a gap width varied from 5 mm to 10 mm.

Figure 1.

Cable-driven soft manipulator design: (a) front view and (b) side view (all dimensions in mm).

For FEA, this geometry was imported into ABAQUS/CAE, where parts were assigned section properties and material definitions. When the input load is increased, the deformation and bending angle increase significantly. Based on cantilever beam theory, the model assumes a fixed end (boundary condition) by confining all degrees of freedom. A concentrated force imitating the tendon cable force was delivered to the opposite end. Frictionless contact was defined between adjoining manipulator sections to allow gap opening as in Figure 2. In this study, the tendons were not explicitly modeled in the FEA, and the applied loads directly represent the tendon forces. This simplification is commonly employed in initial soft robot FEA studies. Material properties of the silicone rubber parts are considered, and the finite element model incorporates the effects of large deformations using hyperelastic models. Hyperelastic material models were used to simulate the nonlinear stress–strain behavior of the silicone rubber. Specifically, the Yeoh model was utilized, defined as

w_{yeoh} ({\bar{I}}_{1}, J) = \sum_{i = 1}^{n} C_{i 0} ({\bar{I}}_{1} - {3)}^{i} + \sum_{k = 1}^{n} \frac{1}{D_{k 1}} (J - {1)}^{2 k}

where the Cs and Ds are material parameters that are experimentally derived through curve fitting.

Figure 2.

The proposed manipulator with load and boundary conditions.

The hybrid quadratic mesh formulation is suitable for hyperelastic materials with a density of 1070 kg/m³. A mesh convergence study determined that an element size of 1–2 mm provided a balance of accuracy and computational efficiency. Quadratic tetrahedral elements (C3D10H) with hybrid formulation were utilized, consisting of roughly 5000–10,000 elements per model.

This research methodology aims to facilitate the development of optimized cable-driven soft manipulator designs that effectively handle soft materials. In addition, it provides insights into the influence of different design variables on the manipulator’s functionality (manipulator’s cross-section, gap size, gap shape, and material). The bending angle is evaluated for each design, depending on the applied force. For applying the optimizing problem, the manipulator’s cross section is evaluated to three different shapes and then kept constant in the optimization problem, also the length remains constant across all models, while variations in gap size, gap shape, and material selection are considered. Figure 3 illustrates the effect of different loads on the bending angle, where a load of 0.4 N corresponds to a bending angle of 35°.

Figure 3.

The effect of different loads on the bending angle.

Evaluation of design parameters

The use of a finite element method (FEM) in this study allows for the exploration of various parameters of soft manipulators, reducing the need for extensive simulation and experimentation. Designers employ optimization techniques to select the preferred parameters that lead to the desired final design, considering the significant impact of different parameters on performance. The study utilizes DESIGN-EXPERT software (Stat-Ease, Minneapolis, MN, USA) to conduct a full factorial analysis by automatically developing and simulating combinations of the factor levels and to analyze the influence of factors on soft manipulator deformation and essential variables.^25,27 In the simulated setting, a uniform input force of 0.1 N was used for the investigation. The design optimization of the proposed manipulator considers variations in gap shape, size, and material parameters while holding the cross section and manipulator length constant. The optimization process aims to evaluate how geometry affects deformation, with the levels for each optimization parameter detailed in Table 1.

Table 1.

The levels of optimization parameters.

Parameters		Levels
Gap shape	Triangle	Circle	Trapezoidal
Gap size	0.5	0.75	1
Material	Ecoflex 30	Ecoflex 50	Dragon Skin 10

The summary of the ANOVA results can be seen in Table 2, which shows that the model F-value of 102.64 is significant. p-Values <0.0500 demonstrated the significance of model terms A, B, and C as well.

Table 2.

ANOVA results.

Source	F-Value	p-Value
Model	102.64	<0.0001
A-gap shape	60.48	<0.0001
B-gap size	32.60	<0.0001
C-material	398.85	<0.0001

ANOVA: analysis of variance.

In summary, the material plays a critical role in optimizing the cable-driven soft manipulator, with the gap shape and size also proving to be significant factors to consider. The significance level also emphasizes the research’s robustness and strengthens its conclusions to support cable-driven soft manipulator design and development.

Cross-sectional shape selection

Selecting the cross section is the initial step in creating the proposed manipulator design. Investigating the effects of three distinct cross-sectional shapes (circular, triangular, and square) is done using finite element method (FEM). In the cross-sectional shape selection analysis, the material is set as Dragon Skin 10, the gap shape is circular, and the gap size is 0.5 mm. The model is implemented in ABAQUS/ACE to study the deformation with input force 0.1 N – as depicted in Figure 4. The bending angle variation for each cross-sectional model is demonstrated in Figure 5(a), where the increment of each angle is shown in Figure 5(b).

Figure 4.

FEM models of (a) circular cross section, (b) squared cross section, and (c) triangular cross section.

Figure 5.

Variation of different cross-sections on bending angle (a) bending angle under different cross-section shapes and (b) increment in bending angle under different shapes.

The FEA revealed a gradual improvement in bending angle with the cross-sectional geometry variation. Specifically, the circular shape enabled a 22.35° deflection angle. The square cross section led to a minor increase at 22.63°. Finally, the triangular morphology achieved the maximum angle of 22.97°. Compared to the 22.35° for the circular shape, this corresponds to a 2.8% enhancement with the triangular cross section. The underlying reason is that the triangular shape allows greater gap opening and separation between adjoining manipulator sections during bending. This reduced contact area provides less resistance to flexing deformations. By enabling higher flexibility under equivalent loads, the triangular cross section is better suited for delicate material handling tasks requiring substantial yet careful manipulator deflections. In conclusion, the bending angle improvements from the finite element study confirm the triangular geometry as the optimal cross-sectional shape for cable-driven soft robotic manipulators targeting enhanced flexibility.

Material selection

Silicone rubber is the preferred material for its low cost, excellent moldability, low actuation pressure/stress, and desirable actuation properties. Soft robotic applications generally employ hyperelastic models to describe the behavior of such materials. Typically, it is presumed that silicone rubber is isotropic and incompressible in these models, neglecting any inelastic effects like viscoelasticity and stress-softening. A material parameter is the most significant parameter obtained through ANOVA, and it influences the bending angle of the soft robot. The study examines the impact of different material specifications, such as Ecoflex 30, Ecoflex 50, and Dragon Skin 10, on the soft manipulator’s bending angle as shown in Figure 6, where the triangular cross section, trapezoidal gap shape, and 5 mm gap size are kept constant. The study utilized material specifications from literature as in the study by Xavier et al.,²³ which summarizes the soft material specifications used in the research as shown in Table 3.

Figure 6.

Variation of different materials on bending angle (a)bending angle under different materials and (b)increment in bending angle under different materials.

Table 3.

Hyperelastic model parameters.

Material	Shore hardness	Model	Constants
Ecoflex 30	00-30	Yeoh	C1 = 12.7 kPa, C2 = 423 Pa, C3 = −1.46 Pa
Ecoflex 50	00-50	Yeoh	C1 = 0.019, C2 = 0.0009, C3 = −4.75 × 10⁻⁶ MPa
Dragon Skin 10	10A	Neo-Hookean	C1 = 0.0425 MPa

The finite element results revealed notable differences in bending angle performance depending on the hyperelastic material parameters. Specifically, the Ecoflex 30 material enabled a maximum tip deflection of 34.29°. With Ecoflex 50, the angle decreased slightly to 30.87°. Dragon Skin 10 achieved the smallest bending at 23.67°. Compared to Ecoflex 30, Dragon Skin 10’s angle is 31.0% lower, indicating it provides greater stiffness and load-bearing capability. This increased rigidity allows it to withstand gravity and external forces more effectively while being mounted for material handling tasks. At the same time, its flexibility remains high enough to enable the required manipulator deflections for successful grasping motions. This balance of adequate bending range with sufficient blocking strength makes Dragon Skin 10 well suited as the material of choice. In conclusion, the inferior bending performance yet improved sturdiness of the Dragon Skin 10 validates it as the preferred hyperelastic model for the soft robotic manipulator, meeting stability and range of motion requirements.

Gap shape selection

After choosing a triangular cross section, different gap shapes applied like circular, triangular, and trapezoidal gap shapes are modeled to determine which shape would yield the most optimal bending angle. Figure 7 shows the FEM for each gap which is solved by ABAQUS/ACE. The bending angle for each gap shape is illustrated in Figure 8, in which (a) shows the bending angle under different gap shapes, and (b) shows the increment of each bending angle.

Figure 7.

FEM models of (a) circular gap-shape, (b) triangular gap-shape, (c) trapezoidal gap-shape.

Figure 8.

Variation of different gap shapes on bending angle: (a) bending angle under different gap shapes and (b) increment in bending angle under different gap shapes.

The finite element simulations revealed a significant influence of the gap morphology on achievable bending angle. The triangular gap enabled a tip deflection of 19.43°. With a circular shape, the angle increased substantially to 22.98°. The trapezoidal shape achieved a maximum angle of 23.67°. Compared to the triangular geometry, the trapezoidal gap improved bending by 21.8%, indicating its higher flexibility. The circular shape also outperformed the triangular gap. This demonstrates that a tapering, nonuniform gap is preferred over uniform gaps. The underlying mechanism is that the trapezoidal shape concentrates stress at the narrower sections during bending. This leads to localized deformations that promote larger overall deflection. By avoiding evenly distributed stress, the trapezoidal morphology enables greater manipulator flexibility. In conclusion, the superior performance of the trapezoidal gap validates it as the optimal morphology for the soft robotic manipulator, achieving maximum tip deflection.

Gap size selection

After carefully selecting the appropriate cross section and gap shape, finite element modeling with different gap sizes is conducted, as demonstrated in Figure 9. The impact of different gap sizes on the manipulator’s bending angle is analyzed in Figure 10(a), where the increment of each angle is shown in Figure 10(b).

Figure 9.

FEM models of gap size of (a) 5 mm, (b) 7.5 mm, and (c) 10 mm.

Figure 10.

Variation of different gap sizes on bending angle: (a) bending angle under different gap sizes and (b) increment in bending angle under different gap sizes.

The finite element study analyzed the influence of the gap width between manipulator sections. With a 5 mm spacing, the maximum achieved bending angle was 23.67°. Increasing to a 7.5 mm gap reduced this angle slightly to 22.51°. At a 10 mm gap, the angle measured 22.45°. This demonstrates an inverse correlation between gap size and bending angle as the spacing grows. However, the inclination decreases, with little difference shown between 7.5 mm and 10 mm diameters. This indicates that a performance limit has been reached after exceeding an acceptable gap value. Considering the triangular cross section and trapezoidal gap shape were previously established as optimal, the GA was applied solely to determine the maximum suitable gap size.

GA for gap size selection

The cross-sectional shape (triangular), the gap shape (trapezoidal), and the material (Dragon Skin 10 silicone rubber) were determined to be optimal from the extensive FEA design of experiments and analysis of variance. The gap size does not have discrete options, but rather a continuous range of possible values. Hence, the GA approach applied to optimize this variable only is utilized.

GAs are optimization methods inspired by biological evolution. They operate on a population of candidate solutions encoded into chromosome-like structures. Through iterations involving selection, crossover, and mutation operators, the population evolves toward better solutions measured by a fitness function. An individual population serves as the starting point for a GA. Each individual is initialized at random and represents the possible solution to an optimization issue. Following that, each individual is assessed using a fitness function associated with the optimization issue being resolved. Higher-fitness individuals are more likely to be chosen for reproduction. To create the offspring individuals for the following generation, crossover and mutation procedures are performed on two chosen parent individuals. This evolutionary process repeats for a predetermined number of generations or until convergence criteria are met.²⁸ The fitness function is based on achieving the maximum tip deflection and bending angle through curve fitting for different angles under various gap sizes in the cable-driven soft manipulator. The optimization of the gap size is performed using the fitness function described by equation (2), where $y_{max}$ represents the maximum bending angle, and x is the parameter for the gap size being optimized.

y_{max} = (0.08846 * (x^{2}) - (1.57 * x) + 29.3)

The objective function value is 22.3, and the GA utilizes a population size of 50, a crossover rate of 0.8, a mutation rate of 0.05, and runs for 583 generations. The fitness value of the gap size is depicted in Figure 11. Algorithm 1 presents the pseudocode of the GA.

Figure 11.

The fitness value for gap size.

Algorithm 1.

Genetic algorithm.

By maximizing flexibility, the optimization yielded an ideal spacing of 8.87 mm. In conclusion, the finite element simulations showed that larger gaps make the manipulator more rigid, reducing its ability to bend. The optimized balance is achieved with an 8.87 mm gap, providing sufficient flexibility while maintaining the manipulator’s structural integrity for handling materials.

Optimization outcomes

To concisely convey the key outcomes from the integrated design optimization approach, the optimal parameters and their impact on bending performance are summarized in Table 4.

Table 4.

Effects of key parameters on achievable bending angle.

Parameter tested	Options evaluated	Best option	% Improvement	Bending angle (degrees)
Cross-sectional shape	Circular, square, triangular	Triangular	+2.8%	22.97
Material selection	Ecoflex 30, Ecoflex 50, Dragon Skin 10	Dragon Skin 10	−31.0%	23.67
Gap shape	Triangular, circular, trapezoidal	Trapezoidal	+21.8%	23.67
Gap size (mm)	5, 7.5, 10	8.87 (GA optimized)	–	22.45

The FEA and optimization revealed the triangular cross section, Dragon Skin 10 material, trapezoidal gap shape, and 8.87 mm gap size as optimal for maximizing cable-driven manipulator flexibility and tip bending angle. By summarizing these clear relationships between design factors and performance, this table establishes guidance to inform specialized soft robot development across application contexts.

Calculation of final joint angle

The bending angle θ is defined as the angle between the proximal and distal vertebrae segments at their point of connection. It represents the overall angular deflection of the soft manipulator. Figure 12(a) shows the schematic of the blocking angle β which occurs when the proximal and distal points E ₁ and E ₂ overlap.

Figure 12.

(a) Schematic of blocking angle definition and (b) manipulator vertebrae.

To calculate θ, the H_v is defined as the distance from the bending center point to the contact point between vertebrae sections. D_v is the height from the bending center to this contact point. D_v varies based on the vertebrae orientation, following a relationship parameterized by the geometry.

The minimum $D_{v min}$ occurs when the contact point is at the edge of the triangular vertebrae, while the maximum $D_{v max}$ occurs when the contact point is at the center of a vertebrae’s edge.

To determine the key cross-sectional dimensions $D_{v max}$ and $D_{v min}$ , the CAD model was inspected using the SolidWorks measuring tool. $D_{v max}$ was measured as 8.66 mm and $D_{v min}$ as 7.67 mm at the specified locations. Reference planes were created in SolidWorks at the $D_{v max}$ and $D_{v min}$ measurement locations to quantify the angle $ϕ_{v}$ between their orientations. The angle reported between these planes was 50°. The proportionality constant k relating D_v to $ϕ_{v}$ is found as

K = (D_{v max} - D_{v min}) / ϕ_{v}

With H_v and the orientation-dependent D_v known, the angle α is calculated as

α = arctan H_{v} / D_{v}

By relating D_v to the vertebrae orientation, this geometry-based approach allows calculating $θ$ for any configuration without relying on constant curvature assumptions.

To protect against overloading, the joint has a locking mechanism that limits bending at certain orientations. The blocking angle β depends on D_v and the section spacing H_v

β = 2 . α = 2 . arctan H_{v} / D_{v}

The total joint angle $(τ)$ before blocking is reached depends on the number of vertebrae sections N

τ = β . N

Experimental setup

To physically realize the optimized design, SolidWorks first modeled the two-part mold, shown in Figure 13. A 3D printer constructed these casts from polylactic acid plus material Figure 14. A 10:1 ratio by weight of Dragon Skin 10 silicone rubber base to curing agent was mixed thoroughly and then degassed in a vacuum to remove air bubbles. The liquid elastomer was poured into the molds and cured at room temperature for over 24 h before unmolding. An adhesive layer of uncured silicone bonded the molded segments and trimmed to achieve the required geometry. The final prototype shown in Figure 15 closely matched the FEA model dimensions to enable direct performance comparison.

Figure 13.

SolidWorks design for fabrication: (a) upper mold, (b) lower mold, and (c) proposed manipulator.

Figure 14.

3D printed molds: (a) upper mold and (b) lower mold.

Figure 15.

Fabricated manipulator prototype.

Experimental validation

The cable experimental validation utilizes a precision tension rig to characterize the bending response of the fabricated soft manipulator prototype to external loading weighting 20 g. As shown in Figure 16, a low-friction, high-strength nylon tendon line with 0.5 mm diameter and 12 cm length connects to the prototype tip. The tendon routes through a path guide, enabling precise manual attachment of gram-scale weights to induce incremental tensile loads. A 5 N capacity digital scale continuously measures the applied tension at 0.01 N resolution.

Figure 16.

Experimental test setup: (a) precision scale and (b) reading angle.

The force–displacement response curve in Figure 17 plots the average bending angle across runs for each applied load. As seen by comparison to the FEA prediction line, the experimental angles align closely with simulations. The error plot in Figure 18 further examines deviations at each load, finding less than 10% variability. This demonstrates accurate performance and validates the optimized manipulator design. The manipulator materials are modeled as purely hyperelastic in the ABAQUS model, neglecting time-dependent viscoelastic effects that introduce strain rate dependencies or hysteresis. Frictionless contact is defined between manipulator segments in the FEA model when there would be frictional sliding losses. Enhancing the fidelity of the ABAQUS finite element model could enable an even tighter correlation with empirical results.

Figure 17.

Experimental versus simulation results.

Figure 18.

Error curve.

The optimization approach successfully designed an improved manipulator morphology, as validated by bend testing experiments. Comparing the simulation and experimental results also identified ways to enhance the analysis methods further.

Discussion and conclusion

This work presents a physics-based optimization methodology for enhancing cable-driven soft robotic manipulators. FEA systematically varied cross-sectional shape, gap morphology, sizing, and material parameters to relate design factors to bending performance. The triangular cross section improved flexibility the most out of circular and square options, increasing deflection by 2.8% over the circular shape to 22.97°. Dragon Skin 10 silicone achieved a 31% lower angle than Ecoflex rubbers, improving sturdiness while retaining adequate flexibility. A trapezoidal gap shape enabled 21.8% greater bending versus triangular gaps by concentrating stresses. As gap size grew from 5 to 10 mm, angles declined from 23.67° to 22.45°, but differences attenuated above 7.5 mm. A GA found the optimal balance occurred at an 8.87 mm gap width. Experimental validation using a precision tension test setup aligned simulated and measured manipulation angles within 10.3% variability.

In conclusion, the integrated optimization approach effectively tunes cable-driven morphological features to improve achievable bending for material handling tasks. The methodology could be extended to optimize pneumatic or tendon-driven soft robots for medical and industrial applications. Identifying links between design factors and performance establishes guidance to aid future soft manipulation development.

Future works

Future studies will focus on developing a shape estimation mechanism for the optimized cable-driven manipulator design. Due to the difficulty of operating soft robots, accurately calculating the whole configuration during complicated bending remains an unanswered subject.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Sara G Seadby

Shady A Maged

References

Kolachalama

Lakshmanan

. Continuum robots for manipulation applications: a survey. J Robot 2020; 2020: 1–19.

Schegg

Duriez

. Review on generic methods for mechanical modeling, simulation and control of soft robots. PLoS One 2022; 17(1): e0251059.

El-Atab

Mishra

Al-Modaf

, et al. Soft actuators for soft robotic applications: a review. Adv Intell Syst 2020; 2(10): 2000128.

Della Santina

Duriez

Rus

. Model-based control of soft robots: a survey of the state of the art and open challenges. IEEE Control Syst 2023; 43(3): 30–65.

Russo

Sadati

Dong

, et al. Continuum robots: an overview. Adv Intell Syst 2023; 5(5): 2200367.

Armanini

Boyer

Mathew

, et al. Soft robots modeling: a structured overview. IEEE Trans Robot 2023; 39(3): 1728–1748. doi:10.1109/TRO.2022.3231360.

Zaidi

Maselli

Laschi

, et al. Actuation technologies for soft robot grippers and manipulators: a review. Curr Robot Reports 2021; 2(3): 355–369.

Hao

. Current trends and prospects in compliant continuum robots: a survey. Actuators 2021; 10(7): 145.

Thalman

Artemiadis

. A review of soft wearable robots that provide active assistance: trends, common actuation methods, fabrication, and applications. Wearable Technol 2020; 1: e3.

10.

Hou

Zhang

, et al. Pneumatic soft robots: challenges and benefits. Actuators 2022; 11(3): 92.

11.

Mohamed

Wagdy

Atalla

, et al. A proposed soft pneumatic actuator control based on angle estimation from data-driven model. Proc Inst Mech Eng Part H J Eng Med 2020; 234(6): 612–625.

12.

Walker

Zidek

Harbel

, et al. Soft robotics: a review of recent developments of pneumatic soft actuators. Actuators 2020; 9(1): 3.

13.

Sameoto

. A review of electrically driven soft actuators for soft robotics. Micromachines 2022; 13(11): 1881.

14.

Liu

Hao

Zhang

, et al. A novel design of shape-memory alloy-based soft robotic gripper with variable stiffness. Int J Adv Robot Syst 2020; 17(1): 1729881420907813.

15.

Wang

Zhang

, et al. A light cable-driven manipulator developed for aerial robots: structure design and control research. Int J Adv Robot Syst 2020; 17(3): 1729881420926425.

16.

Huang

Liu

Yin

, et al. Design and validation of a novel cable-driven hyper-redundant robot based on decoupled joints. J Robot 2021; 2021: 1–16.

17.

Nagua

Relaño

Monje

, et al. A new approach of soft joint based on a cable-driven parallel mechanism for robotic applications. Mathematics 2021; 9(13): 1468.

18.

Rao

Peyron

Lilge

, et al. How to model tendon-driven continuum robots and benchmark modelling performance. Front Robot AI 2021; 7: 630245.

19.

Francu

. Modeling and actuation of cable-driven silicone soft robots. Eurographics 2021 – Short Pap 2021; 9–12. doi:10.2312/egs.20211011.

20.

Wockenfuß

Brandt

Weisheit

, et al. Design, modeling and validation of a tendon-driven soft continuum robot for planar motion based on variable stiffness structures. IEEE Robot Autom Lett 2022; 7(2): 3985–3991.

21.

Tawk

Alici

. Finite element modeling in the design process of 3D printed pneumatic soft actuators and sensors. Robotics 2020; 9(3): 52.

22.

Shit

Shah

. A review on silicone rubber. Natl Acad Sci Lett 2013; 36(4): 355–365.

23.

Xavier

Tawk

Zolfagharian

, et al. Soft pneumatic actuators: a review of design, fabrication, modeling, sensing, control and applications. IEEE Access 2022; 10: 59442–59485.

24.

Chen

Wang

. Design optimization of soft robots: a review of the state of the art. IEEE Robot Autom Mag 2020; 27(4): 27–43.

25.

Mutlu

, et al. A structural optimisation method for a soft pneumatic actuator. Robotics 2018; 7(2): 24.

26.

Venkatesan

Shanmugam

Veerappan

. Structural analysis of bending soft pneumatic network actuators for various designs using the finite element method. World J Eng 2022. doi:10.1108/WJE-08-2021-0478.

27.

Venkatesan

Shanmugam

Veerappan

. Optimization of elephant trunk soft pneumatic actuator using finite element method. World J Eng 2021; 19(6): 832–842. doi:10.1108/WJE-05-2021-0272.

28.

Runge

Peters

Raatz

. Design optimization of soft pneumatic actuators using genetic algorithms. In: 2017 IEEE international conference on robotics and biomimetics (ROBIO), Macau, Macao, 05-08 December 2017, pp. 393–400. IEEE, Piscataway, NJ, USA.

29.

Sun

Zhang

Chen

, et al. An optimum design method of Pneu-Net actuators for trajectory matching utilizing a bending model and GA. Math Probl Eng 2019; 2019: 1–2.

30.

Atoosa

Mostafa

Amin

, et al. Optimization of concentric tube continuum robot based on accuracy and overall length of the robot via genetic algorithm. Ann Robot Autom 2020; 4(1): 007–012. doi:10.17352/ara.000003.

31.

Nikdel

Hosseinpour

Badamchizadeh

, et al. Improved Takagi-Sugeno fuzzy model-based control of flexible joint robot via hybrid-Taguchi genetic algorithm. Eng Appl Artif Intell 2014; 33: 12–20.

32.

Pandey

Windridge

. A genetic deep learning model for electrophysiological soft robotics: Balas

Jain

Balas

Shahbazova

(eds) Soft computing applications. SOFA 2018. Advances in intelligent systems and computing, Vol 1221. Springer, Cham.

33.

Wang

Dong

, et al. Control and optimization of a bionic robotic fish through a combination of CPG model and PSO. Neurocomputing 2019; 337: 144–152.

34.

Rizal

Mohammad

Abd Razak

, et al. Hybrid sine-spiral dynamic algorithm for dynamic modelling of a flexible manipulator. In 2019 19th international conference on control, automation and systems (ICCAS), Jeju, Korea (South), 15–18 October 2019, pp. 120–125. IEEE, Piscataway, NJ, USA.

35.

El-Agroudy

Awad

Maged

. Soft finger modelling and co-simulation control towards assistive exoskeleton hand glove. Micromachines 2021; 12(2): 181.

36.

Pranav

Prakash

Rajendran

, et al. Design optimization and analysis of external corrugation and geometry of asymmetrical bellow flexible pneumatic actuator. IOP Conf Ser Mater Sci Eng 2021; 1132(1): 012011.

37.

Ghazaly

Izzat

Jahid

. Characterization of soft bending actuator for high bending angle. Int J Sci Technol Res 2020; 9.

38.

Raeisinezhad

Pagliocca

Koohbor

, et al. Design optimization of a pneumatic soft robotic actuator using model-based optimization and deep reinforcement learning. Front Robot AI 2021; 8: 639102.