EndoFlex: Advanced Compliant Robotics

• EndoFlex is a multidisciplinary robotic hardware paradigm that combines compliant mechanisms, embedded sensing, and adaptive actuation for intricate tasks.
• It features soft endoskeletons, high-resolution tactile imaging, and shape-conforming endoscopic tips optimized for unstructured environments.
• The system employs integrated sensor fusion and actuation strategies, achieving precise manipulation and medical navigation with measurable performance metrics.

EndoFlex is a multidisciplinary robotic hardware paradigm emphasizing compliant mechanisms and continuous high-resolution sensing, designed for advanced manipulation and medical navigation tasks. Its core principles are exemplified in soft endoskeleton robotic hands for tactile object recognition and adaptable tip mechanisms for shape-conforming endoscopic locomotion. EndoFlex integrates structural compliance, embedded sensing, and actuation to achieve robust interactions in unstructured environments and anatomically variable passages.

1. Mechanical Architecture and Materials

EndoFlex systems employ a composite mechanical design that merges soft elastomeric shells with embedded flexible endoskeletons. For robotic manipulation, each finger utilizes a single molded endoskeleton spine fabricated from Markforged Onyx, featuring two rigid segments (length ≈ 30 mm) joined by thin dog-bone flexural beams (thickness 1.5 mm, minimum web width 1.5 mm). This geometry supports substantial compliance while maintaining essential structural rigidity. The external shell is an optically clear silicone (Smooth-On XP-565, 1 : 15 : 5 ratio with phenyl trimethicone plasticizer; cured thickness ≈ 2 mm, modulus $E \approx 200$ kPa, Poisson ratio $\nu \approx 0.49$), providing tactile interface and tear resistance via a sprayed reticulated wrinkle surface (~0.4 mm wavelength) (Liu et al., 2023).

In endoscopic embodiments, expandable tips employ a cylindrical frame with pneumatic bellows actuators (dual-hardness silicone), each controlling a scissor-strut assembly that radially expands toothed track loops. Bellows are Shore-A 30 silicone externally and Shore-00 30 silicone internally, balancing radial constraint with axial compliance (Du et al., 14 Sep 2024).

2. Embedded Sensing and Photometric Reconstruction

EndoFlex integrates multi-view camera modules for continuous tactile imaging. On the robotic hand, two Raspberry Pi Zero Spy cameras (160° FOV, 640×480 px, 30 fps) are embedded in each finger’s rigid segment, yielding six synchronous image streams per grasp. RGB LED arrays spaced 90° apart illuminate the elastomer for photometric-stereo acquisition (Liu et al., 2023). The tactile surface is rendered sensitive by painted aluminum-flaked silicone membranes (4 μm flakes), enabling accurate recovery of surface normal vectors and sub-100 μm geometric features.

The data acquisition pipeline includes per-camera reference image subtraction ($\Delta I(x,y) = I(x,y) - I_0(x,y)$), followed by linear inversion of the lighting matrix $L$ in the Lambertian model ($\Delta I(x,y) \simeq L \cdot n(x,y)$), and reconstruction of the height map $h(x,y)$ by solving the Poisson equation ($$\nabla^2 h(x,y) = \frac{\partial p}{\partial x} + \frac{\partial q}{\partial y}$$, where $(p, q)$ are surface gradients) (Liu et al., 2023). For endoscopic tips, closed-loop sensor integration is a proposed future direction to enable autonomous wall-contact and slip detection for adaptive locomotion (Du et al., 14 Sep 2024).

3. Actuation Principles and Compliance Modeling

EndoFlex leverages cable-driven or pneumatic actuation in conjunction with soft structure kinematics. In the hand, each finger’s actuation DOF (cable-driven spool) bends both flexures in unison, yielding 3 DOF for grasping in a Y-pattern (two 30°-spaced “index” fingers and an opposing “thumb”) (Liu et al., 2023). Compliance of each flexural joint is modeled as a cantilever beam: $$F = \frac{3EI\delta}{L^3}, \quad I = \frac{bt^3}{12}$$ for tip load $F$, length $L$, thickness $t$, width $b$, modulus $E$, and deflection $\delta$. The combined compliance per finger is approximately $C_{pip} \approx 2L^3/(3EI)$.

In expandable endoscope tips, pneumatic bellows operate over a pressure range from –101 mbar to +283 mbar, generating radial force $F_A(P) \approx 0.0137$ N/mbar × $P$ (maximum 3.89 N), and producing up to 53% expansion relative to the undeformed diameter (10 cm → 15.2 cm) (Du et al., 14 Sep 2024). The bellows drive scissor-strut mechanisms, translating axial contraction/extension into radial expansion, with mechanical advantage determined by the linkage’s geometric configuration.

4. Tactile Sensing, Data Fusion, and Object Recognition

The tactile sensing principle in EndoFlex hands relies on high-resolution map reconstruction from elastomer deformation patterns. The processing pipeline consists of multi-stream camera capture, preprocessing and undistortion (OpenCV), difference image computation, surface normal estimation, Poisson-based depth recovery, and (optionally) force mapping via classical contact mechanics (Hertzian or beam-bending models) (Liu et al., 2023).

For object recognition, sensor images (six per grasp) are montaged (2×3 grid) and input into a ResNet-50 architecture (pretrained on ImageNet, fine-tuned with a learning rate of 1e-3 and step decay), achieving 94.1% validation accuracy and 80% live-test success rate (orange: 90%, cube: 80%, cup: 70%) in distinguishing Rubik’s cubes, stacking cups, and toy oranges from single enveloping grasps (Liu et al., 2023).

5. Adaptive Locomotion and Shape-Conforming Control

In the endoscopic domain, EndoFlex-inspired hardware employs shape-adaptive expandable tips whose diameter can be controlled to maintain propulsion force and stability in variable lumen geometries (Du et al., 14 Sep 2024). The propulsion system utilizes a desktop-mounted stepping motor (NEMA 17) and flexible shaft to drive a worm gear, which actuates four track loops in conjunction with the bellows-driven scissor mechanism. The propelling force is given by

$F_{prop} = n \cdot \mu \cdot N_{tip}$

where $n=4$ tracks, $\mu$ is the wall-track friction coefficient, and $N_{tip}$ is the normal force from tip expansion. Locomotion velocity and propulsion force vary linearly with motor speed up to 150 RPM but decrease above that threshold due to shaft slippage. Maximum linear speeds of approx. 29.3 mm/s at 300 RPM and peak propulsion forces of ≈2.83 N (artificial tissue, $\mu\approx0.20$) have been measured (Du et al., 14 Sep 2024).

Open-loop pneumatic control is implemented via Arduino UNO-operated PWM regulators, with operator selection of motor speed and individual bellow pressures. In diameter-varying environments, bellow pressure is incremented to maintain constant $F_{prop}$ as diameter decreases. A plausible implication is that closed-loop sensing with embedded wall-contact sensors would improve autonomous adaptation and further reduce patient discomfort.

6. Performance, Limitations, and Prospective Enhancements

EndoFlex tactile hands achieve spatial resolution of approx. 0.05 mm per pixel (640×480 px over ≈30 mm), resolving features as small as 3.75 mm ball bearings and 20–50 μm indentations (sub‐0.05 N detectable force) (Liu et al., 2023). Prototype endoscope tips produce 53% expansion, 3.89 N normal force, 8.98 mm axial stroke, and effective propulsion (2.83 N, 29.3 mm/s) in laboratory tissue models (Du et al., 14 Sep 2024).

Limitations include silicone tearing at the hand’s finger base under repeated extension, peripheral image distortion and artifacts, lack of full fingertip coverage, and limited manipulator DOFs (one per finger) (Liu et al., 2023). On the endoscope, frictional drive losses and limited expansion versus colon variability are noted, with miniaturization and sensor integration identified as areas for further research (Du et al., 14 Sep 2024). Proposed solutions encompass higher-elongation silicones, refractive-index matching, marker integration for slip detection, expanded camera coverage, closed-loop quadrant control, and miniaturized low-friction drive components.

7. Context, Comparative Systems, and Future Directions

EndoFlex’s architecture and operational strategies align with recent trends in soft robotic manipulation and shape-adaptive medical instruments, offering continuous tactile sensing and compliance exceeding classical rigid designs. Expansion rates of 53% approach—but do not meet—the colon’s anatomical variability (~73%), with comparative systems such as SoftSCREEN reporting expansions near 70% (Du et al., 14 Sep 2024). Scalable bellows–scissor mechanisms and quadrant-based pneumatic actuation provide advantages in navigating non-circular and bend-rich environments. Low-pressure pneumatic systems (<300 mbar) ensure compatibility with medical standards and patient safety.

Future work involves closed-loop integration of wall-contact and slip sensors, miniaturization for sub-10 mm tips, multi-DOF opposable digit actuation, and autonomous shape-conforming control strategies. This suggests EndoFlex architectures will increasingly enable robust, sensor-rich manipulation and navigation in both industrial unstructured and biomedical settings, with ongoing research in structural optimization and embedded intelligence.