Printed helicoids with embedded air channels make sensorized segments for soft continuum robots

Soft continuum robots require embedded sensing for proprioception and contact detection, yet integrating sensors into sparse, highly deformable architected structures remains challenging. We present a model-based strategy that decouples proprioceptive and contact signals from a common set of fluidic pressure sensors embedded in a soft architected segment. Each segment of the Innervated Trimmed Helicoid (ITH) contains six air channels routed in a localized zigzag pattern along the circumference. With only three principal kinematic degrees of freedom (axial compression, bending in x, bending in y), the six pressure readings form an overdetermined system. A piecewise constant curvature model maps pressures to shape, and Huber regression identifies outlier channels whose residuals indicate external contact. On a single ITH segment, this approach achieves proprioceptive shape estimation with a relative bending error of 0.11 +/- 0.02 and a contact detection rate of 97% across 178 trials. We integrate eight ITH segments into Air-Helix, a tendon-driven soft continuum manipulator, and present exploratory whole-arm demonstrations that include tactile teaching by demonstration, admittance-controlled force regulation, and tactile object reconstruction. The results suggest that localized fluidic innervation combined with model-based redundancy resolution is a practical path toward concurrent proprioception and contact sensing in architected soft robots.

Cosserat rod models for soft robots usually construct sectional stiffness by summing material properties over a common cross-section. This assumption becomes inaccurate for trimmed helicoid arms, where load-bearing helix domains are separated and connected only through sparse fused crossings. This paper formulates a separated-section constitutive law that evaluates each helix domain in its local frame and pulls its constitutive response back to the backbone, yielding an effective backbone stiffness. Sparse-fusion mechanics captures the additional compliance caused by relative motion between neighboring domains and determines channel-wise reduction profiles $η_c(s/L)$ for bending, torsion, and extension. The resulting effective sectional stiffness is strongly anisotropic: bending and extension are reduced by about one order of magnitude, whereas torsion remains close to the effective backbone stiffness. The resulting sectional law is embedded in a geometrically exact dynamic Cosserat model with GVS discretization and routed-tendon actuation. Across 103 measured configurations, the three datasets give pooled normalized position errors of $7.7 \ \%$, $6.7 \ \%$, and $7.8 \ \%$, while each full-arm solve requires approximately $0.3 \ \mathrm{s}$ on one CPU core (Intel Xeon, Cascade Lake, $2.8 \mathrm{GHz}$), enabling rapid model-based planning, state and load estimation, and morphology--control co-design for architected soft robots.

This work introduces Ori-Sense, a compliant capacitive sensor inspired by the inverted Kresling origami pattern. The device translates torsional deformation into measurable capacitance changes, enabling proprioceptive feedback for soft robotic systems. Using dissolvable-core molding, we fabricated a monolithic silicone structure with embedded conductive TPU electrodes, forming an integrated soft capacitor. Mechanical characterization revealed low stiffness and minimal impedance, with torque values below 0.01 N mm for axial displacements between -15 mm and 15 mm, and up to 0.03 N mm at 30 degrees twist under compression. Finite-element simulations confirmed localized stresses along fold lines and validated the measured torque-rotation response. Electrical tests showed consistent capacitance modulation up to 30%, directly correlated with the twist angle, and maximal sensitivity of S_theta ~ 0.0067 pF/deg at 5 mm of axial deformation.