Soft Robotic Arm: Design & Control Insights

• Soft robotic arms are compliant continuum manipulators made from elastomeric or fabric materials, actuated via fluidic, cable-driven, or electric mechanisms.
• They require advanced modeling methods such as piecewise constant curvature, Cosserat rod theory, and data-driven techniques to manage nonlinear dynamics and high redundancy.
• Applications include underwater exploration, aerial manipulation, and high payload tasks, leveraging inherent safety, adaptability, and morphological computation.

A soft robotic arm is a compliant, continuum manipulator constructed from elastomeric or fabric materials and actuated via fluidic (pneumatic, hydraulic), cable-driven, or electrically-driven mechanisms. Unlike traditional rigid-link manipulators, soft arms exploit high degrees of passive freedom, distributed elasticity, and morphological computation, which confer inherent safety, adaptability, and robust interaction in unstructured environments. Modeling, control, and sensing in soft arms are distinctively challenging due to hyper-redundancy, nonlinear continuum dynamics, and strong coupling between body, environment, and control.

1. Structural Architectures and Actuation Modalities

Soft arm architectures encompass multicellular pneumatic networks, modular cable-driven segments, metamaterial-based beams, and continuum chambers actuated by antagonistic bellows or artificial muscles. Typical materials are low–Shore–hardness silicone elastomers (Ecoflex 00-10/00-50), thermoplastic polyurethanes (TPU), and textile composites. Actuation methods include:

• Pneumatic/hydraulic: Fiber-reinforced chambers, antagonistic bellows (Hofer et al., 2020), and prismatic artificial muscles (Wand et al., 2022), enabling bidirectional bending, extension, and variable compliance.
• Cable-driven: Multi-section arms with nonlinear cable–body interaction and decoupled kinematics via rigid endcaps and silicone channels (Qi et al., 2024, Ouyang et al., 10 Oct 2025).
• Metamaterial/electric: Stacks of handed shearing auxetic (HSA) units and bendable–extendable torque-resistant (BETR) shafts support high payloads and fully electric actuation (Good et al., 16 Jan 2025).
• Hybrid rigid-soft: Rigid skeletal frames coupled with pneumatic continuum segments for strength–compliance balance (Johnson et al., 2024).

Submersible and aerial variants integrate waterproof electronics and compact morphologies for operation in fluid environments (Null et al., 2022, Jitosho et al., 26 Mar 2025).

2. Modeling Paradigms: Kinematics, Dynamics, and Continuum Mechanics

The basic theoretical tool for soft arm modeling is the piecewise constant curvature (PCC) assumption, which postulates constant curvature within each segment. More advanced formulations include:

• Unified Multisegment Kinematics: Serial universal–joint or augmented rigid–body models allow efficient kinematic and dynamic representation in 3D and are superior to pure PCC when gravity or loads are present (Wang et al., 2021, Szász et al., 2021).
• Cosserat Rod Theory: Full nonlinear continuum models represent distributed strains (shear, extension, bending, torsion) along the backbone, suitable for configuration tracking and control in multi-segment arms (Doroudchi et al., 2022, Warda et al., 20 Oct 2025). The equations of motion in material and spatial frames involve balance laws for internal force/moment and constitutive relations for elasticity and damping.
• Nonlinear Static Cable Models: Analytical mapping from cable lengths to curvature accounts for cable penetration into soft bodies and is essential for accurate trajectory tracking, especially under large bends (Qi et al., 2024).
• Koopman Operator and Dynamic Mode Decomposition (DMD): Data-driven linear predictors (HDMD) enable model reduction and LQR control for highly complex, inertially dominated arms (Haggerty et al., 2020).
• Data-Enabled Predictive Control (DeePC): Input–output Hankel matrix regression directly utilizes persistent excitation data to form high-fidelity, model-free predictive controllers, circumventing explicit identification (Ouyang et al., 10 Oct 2025).

Models must accommodate environmental interactions, gravity, fluid–structure coupling, and hysteresis. In fluid environments, elastohydrodynamic effects produce non-Hermitian dynamics and instabilities, requiring exact Cosserat rod analysis (Warda et al., 20 Oct 2025).

3. Control Strategies: Adaptive, Learning-Based, and Feedback Laws

Soft arms necessitate advanced control algorithms to handle nonlinearities, model uncertainty, and output constraints:

• Adaptive Passivity Control: Lyapunov-stable controllers compensate unknown stiffness, damping, system identification errors, hysteresis, and sensor noise using online parameter adaptation, gradient update laws, and robustification via sigma-modification (Azizkhani et al., 2021, Azizkhani et al., 2022).
• Feedforward–PD–Feedforward Cosserat Rod Control: Simulated rod models provide distributed force/moment feedback for configuration tracking of bending and extension in continuum arms (Doroudchi et al., 2022).
• Iterative Learning Control (ILC): Norm-optimal ILC, integrated with feedback, enables fast accurate tracking for fixed trajectories, adapting for valve limitations and unmodeled viscoelasticity (Hofer et al., 2019, Zughaibi et al., 2020).
• Gain-Scheduled Feedback Linearization: Linear parameter-varying (LPV) controllers coupled to identified gray-box models achieve aggressive, large-range pick-and-place with sub-degree accuracy (Zughaibi et al., 2020).
• Data-driven Predictive Control: DeePC solves an online QP to minimize trajectory error over a predictive horizon, leveraging model-free input–output data and SVD-based compression for real-time feasibility; surpasses geometric baselines in accuracy and disturbance rejection (Ouyang et al., 10 Oct 2025).
• Reinforcement Learning (RL): Model-free Q-learning and policy-gradient methods address severe uncertainties or system reconfigurations (Jiang et al., 2020).

Practical implementation is facilitated by proprioceptive sensing methods, including high-resolution string encoders, embedded vision networks, and strain sensors (Hofer et al., 2020, Azizkhani et al., 2022).

4. Sensing, Information Transfer, and Morphological Computation

High-dimensional body sensing is essential for closed-loop control of soft arms. Protocols include:

• Vision-Based Proprioception: Embedded cameras inside fabric or pneumatic actuators provide orientation feedback with ~1° accuracy, preserving full compliance and enabling robust control (Hofer et al., 2020).
• String-Encoder Measurements: Direct measurement of actuator elongation enables calibration-free estimation of configuration variables and curvature parameters (Azizkhani et al., 2022).
• Information-Theoretic Measurement: Momentary Information Transfer (MIT), permutation sorting (MSIT), and local information dynamics quantify delayed spatiotemporal propagation of actuation, shock, or perturbation along the arm (Nakajima et al., 2014). Mapping MIT reveals wave dynamics, morphological computation, and distributed compliance.

These techniques underpin modularity, redundancy, and inherent robustness, permitting fine-grained control and adaptation.

5. Workspace, Manipulation, and Application Domains

Soft robotic arms have demonstrated substantial expansion of workspace and practical manipulation capabilities:

• Workspace Augmentation: Addition of prismatic actuators at the base increases task-space volume by over 116%, enabling pick-and-place, bin retrieval, and reaching beyond hemispherical caps (Wand et al., 2022).
• High Payload and Grasping: Metamaterial–HSA arms exhibit vertical lifting of 2.3 kg, horizontal reach up to 600 g, and robust grasping up to 20 N (Good et al., 16 Jan 2025). Hybrid designs (Baloo) lift end-effector payloads of 19 kg (Johnson et al., 2024).
• Underwater/Submersible Tasks: Modular hydraulic soft arms perform biological sampling, minimally invasive surgery, or nuclear inspection; neural networks outperform analytical models in underwater kinematic prediction (Null et al., 2022).
• Aerial Manipulation: "Flying vine" manipulators utilize quadrotor–soft arm coupling and trajectory optimization for fast tracking (<15 cm error) in aerial environments (Jitosho et al., 26 Mar 2025).
• Whole-Arm, Contact-Rich Manipulation: Hybrid soft–rigid torsos, modular continuum arms, and soft grippers generalize to diverse lifting, grasping, sorting, and in-pipe inspection (Johnson et al., 2024, Good et al., 16 Jan 2025).

Passive compliance simplifies path planning and interaction tasks, shifting much of perception–planning–control to the morphology (Jiang et al., 2020).

6. Elastohydrodynamic Instabilities and Environmental Interaction

Cosserat rod analysis in viscous fluids reveals non-Hermitian, circulatory linear operators and the emergence of Hopf bifurcation–induced oscillatory regimes. In soft arms:

• Stability is lost at a critical pressure $p_1$, with return to stability at a higher threshold $p_2$; between these, stable self-oscillations arise (Warda et al., 20 Oct 2025).
• The slender-beam (Euler–Bernoulli) asymptotics provide analytic thresholds: $p_1L^2/k_3A\approx 20$, $p_2L^2/k_3A\approx 37.7$.
• Feedback damping and material parameters (shear/stretch modulus, length) determine the instability window and control efficacy.

Design implications include pressure modulation about bifurcation points for regime switching or oscillation suppression.

7. Ongoing Challenges and Future Directions

Key research directions for soft robotic arms include:

• Integration of embedded multimodal sensing for real-time estimation and adaptive control.
• Generalization of data-driven control to multi-segment and highly coupled systems.
• Scalable modeling approaches for long arms and aerial manipulation platforms (Szász et al., 2021).
• Characterization and exploitation of morphology-induced computation and information propagation for intrinsic control.
• Extension of metamaterial architectures and hybrid actuation for industrial payloads without sacrificing compliance.
• Theoretical analysis and practical stabilization against fluid-induced instabilities for underwater and active-pumping applications.

Soft robotic arms represent a complex intersection of continuum mechanics, adaptive control, nonlinear system identification, and morphological computation, with technological impact ranging from medical devices and underwater exploration to human–robot interaction and collaborative manufacturing.