Digital twins for the design, interactive control, and deployment of modular, fiber-reinforced soft continuum arms

TL;DR

This work tackles the design and deployment bottlenecks of soft continuum arms by introducing Cosserat-rod–based digital twins for modular FREE assemblies, preserving internal modularity while enabling accurate 3D simulations. It provides a complete pipeline: modular FREE fabrication, Cosserat-rod modeling with connectivity, a Vicon-enhanced 3D reconstruction for experimental validation, and an interactive virtual-environment framework for design and sim-to-real deployment. Experimental results show close agreement between simulations and measurements (typical errors <10%), supporting reliable co-design and control development for modular soft manipulators. The demonstrated sim-to-real workflow, including joystick-driven control and Hertzian contact modeling, underscores the potential for remote operation, human-in-the-loop testing, and rapid prototyping in unstructured environments.

Abstract

Soft continuum arms (SCAs) promise versatile manipulation through mechanical compliance, for assistive devices, agriculture, search applications, or surgery. However, the strong nonlinear coupling between materials, morphology, and actuation renders design and control challenging, hindering real-world deployment. In this context, a modular fabrication strategy paired with reliable, interactive simulations would be highly beneficial, streamlining prototyping and control design. Here, we present a digital twin framework for modular SCAs realized using pneumatic Fiber-Reinforced Elastomeric Enclosures (FREEs). The approach models assemblies of FREE actuators through networks of Cosserat rods, favoring the accurate simulation of three-dimensional arm reconfigurations, while explicitly preserving internal modular architecture. This enables the quantitative analysis and scalable development of composite soft robot arms, overcoming limitations of current monolithic continuum models. To validate the framework, we introduce a three-dimensional reconstruction pipeline tailored to soft, slender, small-volume, and highly deformable structures, allowing reliable recovery of arm kinematics and strain distributions. Experimental results across multiple configurations and actuation regimes demonstrate close agreement with simulations. Finally, we embed the digital twins in a virtual environment to allow interactive control design and sim-to-real deployment, establishing a foundation for principled co-design and remote operation of modular soft continuum manipulators.

Figures (4)

• Figure 1: Setup overview. (a) A soft manipulator Uppalapati2021BR2 is integrated with the Vicon vision-tracking system Kim2022Reconstruction. (b) The arm is assembled with modular FREE actuators in various serial and parallel configurations, and specifically designed cross-section markers are applied for tracking. (c) Digital twins assist design and actuation control. Controls are interactively designed using real-time simulations, before deployment to physical hardware. (d) Computationally identified actuation parameters are relayed to SMC valves (ITV0031-2UBL) for FREE pressure regulation via Raspberry-Pi and ROS.
• Figure 2: SCA's modular modeling and reconstruction pipeline. (a) Schematic of FREE fiber angles ($\alpha$, $\beta$) and their change upon pressurization. (b) Individual Cosserat rod model in 3D space. (c) Modeling of a BR2-B3 soft arm, composed of six distinct FREEs, using six Cosserat rods assembled via appropriate boundary conditions. One end of the SCA is fixed (inset shows the base of the arm that connects to pressure regulator). The two segments (BR2 and B3, each made of three rods/FREEs) are serially connected (inset shows the 3D resin-printed serial connector). On the right, the schematic illustrates the connection model used in simulations for both parallel and serial connections. (d) Individual Cosserat rod model replicates primitive deformations of individual FREE modules---bending FREE ($\alpha_{0}=85^\circ$, $\beta_{0}=-85^\circ$) and twisting FREE ($\alpha_{0}=60^\circ$, $\beta_{0}=0^\circ$) of $18~\text{cm}$ lengths. (e) The reconstruction pipeline for the posture of a SCA in the Vicon system includes the following steps: (1) Iterative Closest Point (ICP) algorithm to track the reflective markers representing cross-sectional planes; (2) SO3-filter Mahony2005SO3Filter to denoise both position and directors sequence; (3) reconstruction Kim2022Reconstruction to obtain continuous representation of the arm's posture.
• Figure 3: Experimental validation. For all simulations, we use the Young’s modulus of the elastomer FREEs are made of, and match the area $(A)$ and moment of inertia $(I)$ of each individual rod with the corresponding hollow FREE. Rod modules are then connected together to form various configurations, which are subsequently fabricated for experimental verification. (a) Twist-twist and (b) bend-bend validations are conducted for serially connected FREEs. The validation includes a comparison of the centerline position and orientation (normal and binormal directions) between experiments and simulations, together with the curvature profile (twist: $\kappa_3$, bend: $\|\kappa_{1,2}\|=|(\kappa_1,\,\kappa_2)|$) along the arm’s length. The connection region is shaded in grey in the plots. (c) Three different actuation combinations of the BR2-B3 SCA are tested for validation. These include: (posture-1) actuation of two serially connected bending FREEs at 25 psi, (posture-2) actuation of serially connected bending and twisting FREEs at 20 psi, and (posture-3) a combined actuation of (posture-1) and (posture-2). For the BR2-B3 validation, we compare the posture between the experimental results and simulations. Errors between simulated and experimental postures and strains are listed in Table I, together with the corresponding used metrics. In all cases, deviations are found to be less than 10%.
• Figure 4: Control strategies designed using interactive digital twins are subsequently transferred to physical hardware. (a) Control sequences are interactively (human in-the-loop) identified using a B3-BR2 digital twin immersed in a virtual environment. (b) Digital twin in its operating environment, visualized in Blender. (c) Pressure inputs that allow target retrieval are identified by user in simulations. (d) The real-world experimental setup mirroring the virtual setup. The blue area in the top view indicates the region within which the target payload (AA battery) was randomly placed and from which it was consistently retrieved. (e) Simulated deformation sequence executing the approach-rotate-retrieve task. (f) Physical actuation sequence of the B3-BR2 retrieving the battery. Videos in SI.