Mechanical hysteresis and pneumatic loading complicate contact force estimation from deformation measurements in soft robots. This work presents a 3D-printed polyether block amide (PEBA) Kresling cell with magnetic angular sensing that supports three operating modes: force sensing at zero gauge pressure, force sensing with tunable stiffness under gauge positive pressure, and self-sensing actuation under negative gauge pressure. A multiscale gated recurrent unit (GRU) network estimates contact force from angular histories to account for the the combined effects of geometric deformation and material response. At zero gauge pressure, the model achieves a test RMSE of 0.76N. Positive gauge pressure approximately doubles the average axial loading stiffness at +20kPa over the first 3mm of compression, while pressure-specific models maintain RMSEs below 0.93N. Under negative gauge pressure, an energy-based compensation model enables contact force estimation using the the model trained at zero gauge pressure, achieving RMSEs of 1.66--2.10~N under quasi-static conditions. These results demonstrate a compact approach to combining force feedback, tunable axial stiffness, and self-sensing actuation in soft origami systems.
Figures & tables
Fig. 1: Experimental setup and Kresling geometry. (a) Experimental assembly with magnetic angular sensing. (b) Geometric parameters and unfolded triangular facets.
Fig. 2: Force estimation architectures and temporal input windows. The current angle MLP uses only the instantaneous angle, whereas the short history and multiscale GRU networks additionally incorporate angular histories with validity indicator. The multiscale model combines short (0–3 s, 10 Hz), medium (3–30 s, 2 Hz), and long (30–300 s, 0.2 Hz) histories. The upper panel illustrates these windows relative to the current time (t) on a force trajectory with a piecewise time scale; hatched regions indicate invalid data.
Fig. 3: Force estimation performance at zero gauge pressure. (a) Force–angle responses showing hysteresis and first-cycle effects, with the current angle MLP prediction overlaid. (b) Measured and estimated force trajectories for the three models. (c) Comparison of training RMSE, test MAE, and test RMSE. (d) Detailed view of the first cycle highlighted in (b), with corresponding estimation errors. Gray shaded regions indicate invalid data excluded from analysis.
Fig. 4: Tunable axial stiffness and force estimation performance under positive gauge pressure. (a) Force–compression curves at gauge pressures of 0, +10, and +20 kPa. (b) Measured and predicted force trajectories using pressure-specific multiscale GRU models.
Fig. 5: Contact force estimation during negative pressure actuation at nominal gauge pressures of (a) -10, (b) -20, and (c) -30 kPa. Each panel compares the measured contact force, output from the baseline model, pressure-equivalent force, and compensated contact force estimate. Compensation is applied without retraining the network.
Fig. 6: Finite element analysis of the von Mises stress distribution in the PEBA Kresling cell at an axial compression of 7.24 mm. The left panel shows the exterior view, and the right panel shows a cross-sectional view. Elevated stresses are concentrated around the folding regions.
Fig. 7: Photograph of the experimental platform, showing the Kresling cell mounted in the Instron testing machine with magnetic angular sensing, pneumatic tubing, and data acquisition electronics.
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.
Hugo de Souza Oliveira, Xin Li, Mohsen Jafarpour +1
Grasping deformable objects with varying stiffness remains a significant challenge in robotics. Estimating the local stiffness of a target object is important for determining an optimal grasp pose that enables stable pickup without damaging the object. This paper presents a probe-to-grasp manipulation framework for estimating the relative stiffness of objects using a passive soft-rigid two-finger hybrid gripper equipped with self-sensing pneumatic variable-stiffness joints. Each finger of the gripper consists of two rigid links connected by a soft pneumatic ring placed at the joint, enabling both compliant interaction and controllable joint stiffness via internal pressurization. By measuring the pressure inside the pneumatic ring, we can estimate the interaction force during contact. Building on this, we propose a practical probing strategy to infer relative object stiffness by correlating the estimated normal force with known gripper closing displacement. We validate the self-sensing model through stiffness characterization experiments across bending angles and pressure ranges, and demonstrate stiffness-aware probing-and-grasping in real-life applications: selecting grasp locations on fruits with spatially varying stiffness. The proposed system offers a minimal, low-cost sensing approach for stiffness-aware soft manipulation while retaining probing and grasping capability.
Pneumatic proprioceptive actuators integrate actuation and sensing for soft robots that attract interest due to functional potential. Existing approaches often suffer from assembly errors or stress concentrations caused by heterogeneous materials. In this work, we propose the Monolithic Force-Proprioception Soft (MFPS) design and fabrication method that integrates an Asymmetric Origami Bending (AOB) chamber and a Force-Proprioception Soft (FPS) sensor with single material through one-step Fused Deposition Modeling (FDM) fabrication. Based on the resistance response to strain of conductive thermoplastic polyurethane (TPU), we design and analyze the structure of the FPS sensor, and conduct parametric analysis on the sensing characteristics. The FDM fabrication parameters of the MFPS actuator are analyzed, followed by actuator fabrication and characterization of the actuation and proprioception performance. Experimental results show that the MFPS actuator achieves a bending angle of 40°, an output force of 12.5 N, and a resistance change of 26.9% as the applied external force increased from 0 to 45 N. A two-finger force-proprioception gripper is developed based on the MFPS actuator. The grasping and force-proprioception capabilities are experimentally validated, proving that the MFPS design method provides a new approach for the development of self-sensing actuators.
Nan Huang, Lele Liu, Junfeng Lu +3
Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen, China · Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen, China