Fiber-Reinforced Fluidic Elastomer Actuators

• Fiber-reinforced fluidic elastomer actuators are soft actuators made of pressurized elastomer matrices and helically wound fibers, enabling programmable bending, twisting, and extension.
• Design and fabrication focus on precise fiber winding angles, customizable chamber geometries, and tailored hyperelastic materials to control deformation modes effectively.
• Advanced modeling approaches—including 3D analytical, lumped-parameter, and continuum methods—validate actuator behavior with low error margins, guiding robust control strategies.

Fiber-reinforced fluidic elastomer actuators (FRFEAs) are a principal class of soft actuators in which compliant elastomeric bodies are internally pressurized and anisotropically reinforced by helically wound fibers. This architectural paradigm imparts the actuators with nonlinear, programmable deformation profiles, enabling large, reversible bending, twisting, or extension under applied pressure. The coupling between hyperelastic matrix response, constraint by fiber geometry, and internal pressurization yields high compliance, rich kinematic and dynamic behaviors, and suitability for integration in next-generation robotic, medical, and adaptive material systems.

1. Geometric Structure and Fiber Reinforcement

The defining characteristic of fiber-reinforced fluidic elastomer actuators is the encapsulation of one or more fluidic chambers by helically wound fiber bundles or continuous fiber layers embedded within or surrounding an elastomeric matrix. Typical designs involve one-sided or concentric fiber arrangements wound at specific angles (commonly termed the fiber "winding angle" $\gamma$ or $\phi$), which may be spatially varied to tailor actuator behavior.

Key structural configurations include:

• Single-chamber cylindrical actuators with uniform fiber winding, yielding uniaxial elongation or contraction under pressure (e.g., McKibben artificial muscles).
• Asymmetric or bending actuators (e.g., bending fluidic actuators, or BFAs) where fiber reinforcement is placed selectively or paired with inextensible layers, causing preferential expansion and large bending upon pressurization (Cacucciolo et al., 2016).
• Multi-chamber designs (used for continuum arms and complex shape control) composed of parallel or serial pressurizable segments, each with independently configured fiber winding (Toshimitsu et al., 2021).

The fiber winding angle critically governs the dominant actuation mode:

• Angles near $90^\circ$ (longitudinal axis) facilitate maximal extension,
• Angles near $0^\circ$ (circumferential) maximize contraction,
• Angles near the "magic angle" (approximately $54.7^\circ$) in cylindrical contexts maximize enclosed volume and can minimize internal shear under large deformation (Chatterjee et al., 2019).

Combinatorial winding (e.g., adjusting angles segmentally or between opposing chambers) allows for programmable deformation modes such as pure bending, twisting, or combinations thereof.

2. Nonlinear Mechanics and Mathematical Modeling

The mechanics of FRFEAs are governed by a strong interplay between geometric nonlinearities, hyperelastic material response, and anisotropic fiber constraints. Various frameworks have been proposed to model their static and dynamic behaviors, including fully three-dimensional (3D) analytical models, lumped-parameter models, and continuum or Cosserat rod-based approaches.

2.1 Three-dimensional Analytical Models

A comprehensive 3D analytical model for fiber-reinforced bending fluidic actuators (BFAs) (Cacucciolo et al., 2016) employs a toroidal coordinate system for the semicircular domain and a cylindrical system for the rectangular (flat) portion. Kinematics are described by mapping functions $g(\rho, \theta)$ and $f(\rho, \theta)$:

$$g(\rho, \theta) = \sqrt{\rho^2 - \Gamma[\beta^*(1-\rho^2) + \frac{2}{3} \sin\theta (1-\rho^3)]}$$

where $\Gamma = \chi R_2$ is the nondimensional curvature and $\beta^*$ encodes undeformed wall thickness.

Principal stretches $(\lambda_{\rho}, \lambda_\theta, \lambda_\phi)$ and corresponding Cauchy stresses (using a Neo–Hookean hyperelastic model)

$\sigma_i = \lambda_i - \frac{Q}{\lambda_i}$

with $Q$ serving as a Lagrange multiplier for incompressibility, and the incompressibility constraint

$\lambda_\phi \lambda_\rho \lambda_\theta = 1$

together yield a system of nonlinear partial differential equations.

2.2 Lumped-parameter and Fluid Jacobian Models

For cylindrical and quasi-cylindrical actuators (e.g., FREEs), modeling approaches include lumped-parameter models relying on kinematic constraints imposed by inextensible helical fibers (e.g., McKibben-style models), and state-dependent mappings between internal pressure, elongation, and twist using a fluid Jacobian (Bruder et al., 2018, Sedal et al., 2019):

$\tau(q, p) = J_q^T(q) \cdot p$

where $J_q(q) = \partial V / \partial q$ relates geometric deformation to internal volume change, enabling calculation of generalized force outputs.

A continuum mechanical alternative, suitable in the thick-walled or anisotropic regime, uses strain energy functions with explicit matrix–fiber coupling

$$\Psi_\text{total} = \Psi_\text{isotropic} + \Psi_\text{anisotropic}$$

with

$$\Psi_\text{isotropic} = \frac{C_1}{2} (I_1 - 3),\quad \Psi_\text{anisotropic} = \frac{C_2}{2} (I_4 - 1)^2$$

where $C_1$, $C_2$ are material parameters, $I_1$ is the first invariant of the right Cauchy–Green tensor, and $I_4$ encodes fiber stretch (Sedal et al., 2019).

Cosserat rod theory has been extended to model multi-segment and continuum actuators assembled from FREEs, capturing the full spectrum of bending, stretching, shearing, and twisting (Hanza et al., 2023, Kim et al., 14 Jul 2025).

3. Sources of Nonlinearity and Spatial Effects

Nonlinear behaviors in FRFEAs arise from three principal sources:

1. Material Nonlinearity: The elastomeric matrices are modeled as hyperelastic, typically Neo–Hookean or Ogden-type, with incompressibility enforced by Lagrange multipliers (Cacucciolo et al., 2016, Habibian et al., 2021). Experimental evidence confirms significant deviation from linear response at large strains (Chatterjee et al., 2019).
2. Geometric Nonlinearity: Large deformations, including significant curvature, radial expansion, and longitudinal strain, necessitate full 3D kinematics or multi-segment piecewise constant curvature (PCC) representations (Kelageri et al., 2018, Toshimitsu et al., 2021). Coupled radial–axial effects are especially prominent in pressurized, fiber-constrained geometries (Hanza et al., 2023).
3. Anisotropic Reinforcement: The orientation, density, and extensibility of the fibers strongly dictate permissible deformation directions and the effective transformation of internal pressure into mechanical output. Notably, spatial variation in winding angle or reinforcement asymmetry yields highly tunable, localized actuation.

Unlike prior models that neglected spatial pressure effects or simplified torque–angle relationships, advanced 3D frameworks (Cacucciolo et al., 2016) account for:

• Pressure acting on lateral chamber walls,
• Non-uniform, curvature-dependent tip torque,
• Variable distribution of stresses and strains throughout the actuator cross section.

These refinements are essential for accurate prediction of real actuator behavior, especially in applications requiring precise motion or force output.

4. Design, Fabrication, and Control Implications

4.1 Design and Fabrication Parameters

Key choices in actuator design and fabrication include:

• Elastomer selection for matrix: tradeoffs between modulus, extensibility, and fatigue life (e.g., PDMS, TPE, NR, PUR) (Kelageri et al., 2018).
• Fiber selection: material properties (e.g., aramid, polyester) and winding angle, which determine achievable force, bending angle, and load capacity (Chatterjee et al., 2019).
• Chamber geometry and wall thickness, which interact with fiber layout to define maximum pressure, workspace, and deformation modes.
• Advanced manufacturing, including precision casting, 3D molding (Quick-cast) for single-body, leak-free actuators with <0.2 mm precision in scalable production, and implementations supporting both cylindrical and corrugated chamber designs (Svetozarevic et al., 2018).

4.2 Control Strategies

• Sensorless Model-based Pressure Control: Open-loop strategies predict internal pressure from commanded fluid volume using simplified linear or nonlinear tube models, supporting feedback-free control in cost-sensitive or lightweight systems (Kelageri et al., 2018).
• Feedback Control: Image- or sensor-based position feedback (e.g., vision tracking, embedded flex sensors) can be integrated into closed-loop controllers for accurate tip positioning in the presence of hysteresis and load disturbances. Switching mode (bang-bang) controllers have demonstrated high accuracy in unstructured tasks (Kelageri et al., 2018, Toshimitsu et al., 2021).
• PID and Trajectory Control: Linear and non-linear PID control laws applied to measured rotation or curvature enable trajectory following and step response regulation, as validated in simulation and experiment (Habibian, 2019, Habibian et al., 2021).

The presence of material and geometric hysteresis, as well as pressure–position path dependence, necessitates combined estimation approaches (e.g., Kalman/Bayesian fusion of pressure and position signals) for robust in situ control.

5. Experimental Validation and Performance Metrics

Experimental studies across both single-segment and multi-FREE assemblies provide extensive validation for the proposed models and control schemes:

• Force, Bending, and Workspace: Force output and maximum bending angle are sensitive to both material (PDMS, TPE) and reinforcement (number of fiber turns, winding angle) parameters. For example, 240 fiber turns over a 170 mm actuator provided optimal performance in both pressure capacity and bending range (Kelageri et al., 2018).
• Tracking Performance: In feedback-controlled scenarios, tip positioning errors as low as 0.3–0.36 mm have been achieved using vision-based control, even in payload-carrying tasks (Kelageri et al., 2018). Dynamic simulation and experimental results for rotational output verify errors of <4% in lumped-parameter models (Habibian et al., 2021), and <10% in lumped + FEA integrated platforms (Habibian, 2019). Multi-segment Cosserat rod simulations closely match experimental reconstructions with errors typically in the 2–8% range (Kim et al., 14 Jul 2025).
• Control Readiness and Real-Time Simulation: Closed-form or semi-analytical 3D models—when computationally tractable—enable real-time simulation and online control in industrial applications (Cacucciolo et al., 2016, Kelageri et al., 2018).

6. Comparative Analysis and Generalization

Comprehensive comparative assessments of modeling frameworks have shown that:

• First-principles continuum models (with few, physically meaningful parameters) generalize more robustly across actuator designs than black-box (e.g., neural network) approaches, though the latter can achieve lower error when trained on a fixed sample (Sedal et al., 2019).
• Lumped-parameter models are highly efficient for fast controller synthesis and low-pressure operation, but their underlying linearization assumptions may break down under large deformation or pressure (Habibian et al., 2021).
• Finite element and continuum Cosserat modeling (Hanza et al., 2023, Kim et al., 14 Jul 2025) provide detailed predictive capacity, especially for complex multi-actuator modules or assemblies, at the cost of increased computational complexity.

Table: Comparative Features of FRFEA Modeling Frameworks

Modeling Approach	Typical Accuracy (Error)	Generalizability
3D Analytical (Toroidal)	<10%	High for geometry changes
Lumped-Parameter	~4%	Limited by assumptions
Continuum/FEA	2–8%	Excellent (with calibration)
Machine Learning (NN)	<2% (trained-only case)	Poor (unless retrained)

Table summarizes aggregate findings across referenced studies.

7. Applications and Future Directions

Fiber-reinforced fluidic elastomer actuators underpin advances in:

• Soft robotic manipulators and arms—enabling safe interaction, high compliance, and versatile shape morphing in assistive, medical, and exploratory scenarios (Kim et al., 14 Jul 2025, Toshimitsu et al., 2021).
• Adaptive grippers and hands—where spatially programmable deformation is critical for robust grasping of delicate or irregular objects (Bruder et al., 2018).
• Wearable and biomedical devices—including compliant exosuits and devices for motion assistance and rehabilitation (Kelageri et al., 2018).
• Architectural and adaptive material systems—leveraging scalable manufacturing for integration in kinetic facades and adaptive building envelopes (Svetozarevic et al., 2018).

Emerging research highlights the necessity for robust modeling under nonlinearity, efficient computational schemes for hardware-in-the-loop control, and physicochemically adaptive architectures (e.g., integrating electroactive polymer actuation or 3D printed graded porosity (Ghosh et al., 2022, Willemstein et al., 2022)) to further expand capability. Integration of advanced proprioceptive sensing, compliant electronics, and embodied fluidic intelligence remains an active area, aiming to provide fully autonomous, adaptive, and efficient soft robots for complex environments.