SORI: A softness-rendering interface to unravel the nature of softness perception

Significance

The sense of softness is vital for survival, well-being, and complex social interactions among animals and humans. It guides decisions ranging from food selection in animals to the detection of medical anomalies in humans. Yet, our grasp of this sensation, including its neural pathways and underlying cognitive processes, remains incomplete. This study introduces a haptic display, the softness-rendering interface (SORI), which quantitatively replicates softness sensations. By adapting to the individual properties of fingertips and bridging the gap between actual and perceived softness, SORI offers a leap forward in understanding and accurately simulating this pivotal sense. This advancement not only holds promise for enhancing haptic technology but also paves the way for deeper insights into the neuroscience of softness perception.

Abstract

Tactile perception of softness serves a critical role in the survival, well-being, and social interaction among various species, including humans. This perception informs activities from food selection in animals to medical palpation for disease detection in humans. Despite its fundamental importance, a comprehensive understanding of how softness is neurologically and cognitively processed remains elusive. Previous research has demonstrated that the somatosensory system leverages both cutaneous and kinesthetic cues for the sensation of softness. Factors such as contact area, depth, and force play a particularly critical role in sensations experienced at the fingertips. Yet, existing haptic technologies designed to explore this phenomenon are limited, as they often couple force and contact area, failing to provide a real-world experience of softness perception. Our research introduces the softness-rendering interface (SORI), a haptic softness display designed to bridge this knowledge gap. Unlike its predecessors, SORI has the unique ability to decouple contact area and force, thereby allowing for a quantitative representation of softness sensations at the fingertips. Furthermore, SORI incorporates individual physical fingertip properties and model-based softness cue estimation and mapping to provide a highly personalized experience. Utilizing this method, SORI quantitatively replicates the sensation of softness on stationary, dynamic, homogeneous, and heterogeneous surfaces. We demonstrate that SORI accurately renders the surfaces of both virtual and daily objects, thereby presenting opportunities across a range of fields, from teleoperation to medical technology. Finally, our proposed method and SORI will expedite psychological and neuroscience research to unlock the nature of softness perception.

Tactile perception of softness is integral to survival in nature, well-being, and social interaction among animals and humans (1–4). Information about object softness and compliance informs food selection in Drosophila and howler monkeys (5, 6); grasp and squeeze capabilities in rhesus macaque monkeys (7); and disease detection, such as cancer or tumors, in humans through medical examination or palpation (8, 9).

Previous psychological and neuroscience research confirms the complexity of softness perception that incorporates multiple sensory modalities, cognitive processes, and interaction phases (10–12). Prior studies (13–18) assert that softness is cognitively perceived as a blend of kinesthetic and cutaneous cues. While pressure and skin deformation predominantly influence softness sensing, factors such as vision (19–21), temperature (22), and prior experience or memory (23) also contribute. Despite varying perceptual performance among different fingers in softness discrimination (24), factors such as contact area, indentation depth, and force play a particularly critical role in sensations experienced at the fingertips (14, 18, 25), which are abundant in mechanoreceptors in primates (26). However, a full understanding of softness perception, including its neural representation and the cognitive process behind it, remains elusive (27, 28).

Existing fingertip haptic interfaces predominantly generate either pure kinesthetic (29) or cutaneous tactile feedback (30–34). Despite their ability to render stiffness, shear forces, and vibrotactile stimuli, these devices fail to render softness due to their lack of control over both contact area and force. Consequently, researchers have developed fingertip haptic softness displays, with early versions using metallic telescopic cylinder arrays to cover the fingerpad (15). However, these devices’ rigid and discrete interaction cannot adequately conform to fingertips’ compliance and shape. Subsequent displays, equipped with flexible/stretchable membranes driven by electric motors (35, 36) and soft interfaces driven by pneumatic actuators (16, 37) and DEAs (38), offer improved conformability and continuous contact. However, none of the existing softness displays can decouple the force and contact area control and quantitatively mimic softness cues, due to the challenges in estimating complex softness information and mapping it to a physical display.

In this study, we introduce a haptic softness-rendering interface (SORI) that renders softness cues at the fingertip by independently controlling contact area and force. SORI’s ability to decouple control of these cues enables the rendering of both homogeneous surfaces of varying softness and non-homogeneous surfaces composed of stacked layers (Fig. 1A). SORI consists of two main parts: the stiffness and contact area rendering parts (Fig. 1B, SI Appendix, Fig. S1 and Design and Fabrication of SORI, and Movie S1). The contact area rendering part at the top includes a toroidal soft pneumatic actuator (SPA), which, when inflated, encompasses the fingertip and controls the contact area without triggering the sensation of curvature change (SI Appendix, Contact Area Rendering Part and Fig. S2). This toroidal SPA applies negligible normal force to the fingertip, a key feature in decoupling contact area and force cues. Its design conforms to the fingertip’s contours, enabling a continuous pressure distribution. The stiffness rendering part, located at the bottom, consists of an origami-inspired prismatic joint driven by a pouch motor. This joint restricts movement to the vertical axis and exhibits negligible deformation under off-axis loading. The device incorporates a force sensor and a position-sensing mechanism used in previous work (39). The SORI prototype, excluding the pneumatic control unit, weighs 8 g, generates forces up to 16.3 N at 200 kPa, and has a 5-mm range of motion (RoM), $\mathrm{\Delta }\delta$.

Fig. 1.

A haptic SORI. (A) SORI replicates tactile cues on fingertips to simulate both soft and hard homogeneous objects, as well as heterogeneous objects composed of layers with varying hardness. Examples of these objects include a marshmallow, an aluminum block, and a “Puskevit,” which is a biscuit layered on top of Turkish delight. (B) SORI consists of a toroidal SPA and a pouch-motor-driven origami prismatic joint. When inflated, the toroidal SPA envelops the fingertip without applying significant normal force. The joint restricts motion to the vertical axis, while the pouch motor generates force. SORI dynamically alters its contact area (A) and force (F) by controlling the pressure within the toroidal SPA ($P_1$) and pouch motor ($P_2$) in real-time, based on the applied force, indentation depth (δ), physical fingertip parameters ($K_F$), target contact area spread rate (p), and stiffness (k).

Furthermore, we propose a general method for regenerating the sensation of softness at the fingertips using SORI. Softness perception varies among individuals due to biomechanical properties of their fingertips such as the shape, size, and elastic modulus. Indeed, different indenters are exposed to different forces and contact areas when pressed onto the same surface with exact indentation depth (SI Appendix, Fig. S3B). Consequently, the sensed stiffness and contact area spread rate (CASR) (14, 35) differ for fingers with varying physical properties. Therefore, as the initial step of softness regeneration, we identify the fingertip physical parameters radius (R) and Young’s modulus ($E_F$) to personalize rendered softness cues.

Before reproducing softness cues, it is necessary to estimate them upon contact with the target surface. Thus, we identify Young’s modulus and stiffness of the contact surface as the second step. We employ standardized Shore Hardness durometers to extract Young’s modulus information, aided by the hardness-to-Young’s modulus conversion model (40). To acquire stiffness information, we employ a universal testing machine outfitted with a rigid spherical indenter.

Subsequently, we propose a comprehensive model to estimate the CASR and stiffness for any fingertip with varying properties by considering the identified fingertip and surface properties. We utilize the extended Hertzian contact model for nonrigid indenters on flat surfaces (41). Moreover, we incorporated a nonlinear fingerpad model from ref. 42 into our contact mechanics model.

After estimating the contact area and force on the fingertip, we map these values to the softness display. We adopt a model-based approach to determine the target control inputs through an inverse model of SORI, which calculates two control pressure inputs to render the desired contact area and force. Regarding the stiffness rendering part, we build an empirical model derived from force–displacement experiments conducted at varying pouch pressures (SI Appendix, Fig. S3a and Stiffness Experiments).

In the final step of our softness regeneration method, we transmit the target pressure inputs to SORI. We drive SORI with a custom pneumatic control unit, achieving a pressure control bandwidth of 10 Hz and a stiffness control bandwidth of 4 Hz (SI Appendix, Pneumatic Control Setup, SORI Stiffness Rendering Characteristics and Bandwidth, and Fig. S4). This actuation bandwidth sufficiently stimulates type SA I Merkel cells, densely distributed in the fingertips and sensitive to low-frequency stimuli, 0.4 to 3 Hz (43–45). These receptors respond to light touch, also referred to as discriminative touch, with optimal stimuli being indentation. However, the roles of other mechanoreceptors in softness perception should be further explored and used as reference specifications for future softness display development.

Our proposed approach, summarized in Fig. 2A, quantitatively maps expected softness cues to SORI by providing a comprehensive model for the display and for the estimation of softness cues on the fingertip. Our method takes into account the physical properties of the fingertip to reconstruct personalized contact area spread rate (CASR) and stiffness.

Fig. 2.

Softness regeneration method and model. (A) We propose an all-encompassing strategy to numerically replicate the sensation of softness on distinct fingertips. Initially, we determine the physical parameters of a fingertip, such as its radius and modulus, to accurately estimate the softness cues for that specific fingertip. Subsequently, we extract properties of the target surface, such as stiffness and modulus. Using the identified fingertip and surface parameters, we estimate the softness cues, namely the contact area spread rate (CASR) and stiffness. Following this, we map these estimated values to the control inputs of the softness display. Ultimately, we recreate the softness cues on the actual hardware and feedback sensory readings, such as force and indentation depth, back to the estimation step, thus closing the loop. (B) To estimate the CASR and stiffness, we employ an extended Hertzian contact model that accounts for nonlinear fingertips on both soft and hard surfaces. (C) We present an analytical model that computes the required pressure inputs to generate the desired CASR and stiffness (SI Appendix, Contact Area Model).

Modeling

Softness Cues Estimation.

To estimate the personalized CASR and stiffness, we utilize the extended Hertzian contact model for nonrigid indenters on flat surfaces (41). The model claims that indentation with a soft spherical indenter of radius, R, is equivalent to indentation with a rigid spherical indenter with a larger effective radius, $R^{+}$ (Fig. 2B). This equivalence allows us to estimate the geometry of the deformed soft indenter and to calculate the corresponding contact area. We further incorporate the nonlinear fingerpad model (42) into our contact mechanics model, where $E_F^{\ast }=E_{F0}^{\ast }(1+\beta F)$. In this equation, $E_F^{\ast }$, $E_{F0}^{\ast }$, β, and F represent the fingerpad’s secant Young’s modulus, effective Young’s modulus, load coefficient, and force, respectively. We ultimately derive the following contact area equation (SI Appendix, Contact Area Model):

$$\begin{array}{c}\hfill A=\pi {\left(\frac{3FR}{4}\right)}^{2/3}{\left(\frac{1}{E_S^{\ast }}+\frac{1}{E_F^{\ast }}\right)}^{2/3},\end{array}$$ [1]

where A, R, and $E_S^{\ast }$ are the contact area, the radius of the indenter, and the effective Young’s modulus of the surface, respectively. The effective Young’s modulus is defined by the equation $E^{\ast }=E/(1-{\nu }^2)$, where E is Young’s modulus, and ν is Poisson’s ratio. Then, we normalize the fingertip parameters, which gives us the following:

$$\begin{array}{c}\hfill A_{\mathit{norm}}=\pi {\left(\frac{3}{4}\right)}^{2/3}{\left(\frac{1}{E_S^{\ast }}+1\right)}^{2/3}(F^{2/3}).\end{array}$$ [2]

This relationship reveals that the ratio $A_{\mathit{norm}}/F^{2/3}$ depends solely on $E_S^{\ast }$, which we define as the normalized contact area spread rate. Hence, we conclude that normalized CASR is a quantitative term that depends only on surface properties and is valid for any fingertip.

Finally, we estimate the stiffness that the fingertip perceives by transforming the stiffness measurements taken from a universal testing machine that uses a rigid spherical indenter. By employing the extended Hertzian contact model, we compute the force required by the soft fingertip to produce a specific level of deformation. This computation is based on the force that the rigid indenter applies to achieve an equivalent deformation of the surface (SI Appendix, Stiffness Conversion Model).

$$\begin{array}{c}\hfill F_F=F_R\left(\sqrt{\frac{R_F}{R_R}}\right)\left(\sqrt{\frac{E_F^{\ast }+E_S^{\ast }}{E_F^{\ast }}}\right),\end{array}$$ [3]

where $F_F,F_R$ are the force applied by the fingertip and rigid indenter, $R_F,R_R$ are the radius of the fingertip and the rigid indenter, and $E_F,E_S$ are the effective Young’s modulus of the fingertip and the surface.

Softness Cues Mapping.

As for the contact area rendering part, we present an analytical contact model of the toroidal SPA. We propose that the contact area on SORI consists of two components (Fig. 2C): The $A_{\mathit{flat}}$ represents the contact area when the finger contacts a rigid flat surface, whereas $A_{\mathit{side}}$ accounts for the bulged up contact area created by the inflated toroidal SPA. We assume that the inflated thin and stretchable membrane conforms to the shape of the fingertip without causing deformation. Consequently, the estimated contact area, $A_{\mathit{contact}}$, is found: $A_{\mathit{contact}}=A_{\mathit{flat}}+A_{\mathit{sides}}$ (SI Appendix, SORI Model). The model computes the required pressure input to the toroidal SPA to achieve the desired side contact area.

Results

Identification of Non-linear Fingertip Parameters.

To identify the physical fingertip parameters R, $E_{F0}$, and β, we conducted a contact area-force experiment (SI Appendix, Contact Area Experiments). In this experiment, participants applied varying levels of force to their fingertips against a flat surface made from hard polylactic acid (PLA), and we recorded the contact area between the fingertip and the surface. Using our contact model (Eq. 1), along with the force–displacement data from the experiment, we calculated the parameters that yielded the best fit. To demonstrate the validity of our approach, we carried out this experiment with two participants (Participants and Protocol in Materials and Methods). The identified fingertip parameters and the comparison of actual and modeled contact area spread rate (CASR) using these parameters are presented in Fig. 3A.

Fig. 3.

Estimation and regeneration of contact area spread rate and stiffness. (A) Identification of physical fingertip parameters: radius R, Young’s modulus $E_{F0}$, and load coefficient β (SI Appendix, Contact Area Experiments). We compare the actual and modeled CASR of two fingers touching a flat PLA surface using the identified parameters. (B) Comparison of actual, estimated, and recreated CASR for two fingertips touching homogeneous and nonhomogeneous objects. (C) Normalized CASR. We compare the model with normalized actual data for different fingers and materials. (D) Stiffness characterization of the materials and the stiffness range of SORI.

Regeneration of Contact Area Spread Rate and Stiffness.

To validate our proposed method and models for softness regeneration, we designed a series of experiments. In the first experiment, we measured the CASR of fingertips pressing against surfaces composed of various materials (SI Appendix, Contact Area Experiments). We then repeated the same experiment with SORI, varying the pressure of the toroidal SPA in discrete increments. We interpolated the results obtained from SORI to select the specific contact area corresponding to the exact target pressure value determined from the previous mapping step, enhancing the precision of our approach. We subsequently compared the actual, model-predicted, and regenerated CASR (Fig. 3B). The results showed successful regeneration of the CASR by the toroidal SPA for three different surfaces on two fingertips. The discrepancies between the actual and recreated CASR can primarily be attributed to our assumption of a spherical shape for the fingertips and to measurement errors. Furthermore, using Eq. 2, we compared the normalized CASR for different fingertips and materials (Fig. 3C). We confirmed that the normalized CASR depends solely on surface properties and is identical for all primate fingertips, concluding that it is an objective softness coefficient.

Next, we measured the stiffness of SORI and the samples used in the preceding experiments. The data indicated that SORI can render stiffness ranging from a minimum of 0.15 N/mm to a maximum of 6.52 N/mm (SI Appendix, Stiffness Experiments). Additionally, we compared the stiffness of the samples with the range of stiffness renderable by SORI (Fig. 3D). SORI accurately replicated the stiffness of the samples, except for that of DS30, which exceeded SORI’s maximum renderable stiffness. Although it is feasible to further enhance SORI’s stiffness capacity by utilizing a more durable pouch material and increasing pouch dimensions, the current results underscore the importance of rendering both CASR and stiffness cues on the fingertip for realistic softness recreation. Moreover, the outcomes demonstrate the efficacy of our proposed methodology and models in faithfully reproducing tactile softness cues on the fingertip (Movie S2).

Finally, we demonstrated that SORI can reproduce realistic tactile softness for both virtual and actual objects (Movie S3). When tasked with reproducing the tactile sensations of two materials, such as salmon and Turkish delight, SORI accurately mirrored their distinct contact behaviors. Specifically, to emulate the sensation of a salmon fillet, SORI produced a broader contact area but exerted less force compared to the sensation of Turkish delight (Fig. 4 A and B). Uniquely, SORI is capable of rendering both static and dynamic contact interactions. As an illustration, it can mimic the dynamic contact of a heart model with a pulse of 30 beats per minute (Fig. 4C and Movie S4). We touched SORI with a rigid indenter, fixed in space and roughly the size of a fingertip, to record changes in force and contact area. As expected, the contact area and force fluctuated in coordination with the heartbeat cycles.

Fig. 4.

Characterization of SORI performance. (A–C) Real-time regeneration of both static and dynamic surfaces. SORI successfully emulates the tactile sensation of a softer salmon fillet (A), a harder Turkish delight (B), and a heart model (C). In (B), SORI generates a smaller contact area while exerting a significantly higher force compared to (A). In (C), the position of the indenter remains stationary while the contact area and force change dynamically, aligning with the simulated heartbeat. (D) Comparison of SORI with other softness displays. An ideal softness display would possess almost zero volume and an infinite stiffness range, with independent control over the softness cues. SORI surpasses the capabilities of current state-of-the-art softness displays (15–17, 35, 37, 38, 46–50).

Discussion

The presented work demonstrates that a haptic platform quantitatively recreates cutaneous and kinesthetic cues simultaneously on any arbitrary fingertip with high fidelity. SORI with decoupled control over softness cues and embedded multimodal sensing recreates homogeneous, nonhomogeneous, stationary, and dynamic surfaces. Crucially, it generates personalized realistic softness cues on various fingertips by accounting for their physical properties, thus, accounting for the subjectivity in softness sensation. To the best of our knowledge, there is no other platform, method, or model to achieve softness rendering at this level (Fig. 4D and SI Appendix, Table S1).

This comprehensive softness-rendering technology has the potential to catalyze psychophysical and neuroscience studies, helping to unlock the nature of softness perception and the somatotopic representation in the brain. It will enhance our understanding of cognitive processes in both humans and nonhuman primates by enabling controllable and repeatable experiments across different subjects. The insights gained from these findings could inform therapeutic interventions to restore lost softness sensation and stimulate technological developments in fields such as haptics, teleoperation, and telepresence. These technologies hold promise for applications ranging from robot-assisted surgery to remote social interactions. When integrated with virtual and augmented reality technologies, they could train physicians in palpation and cancer detection. Moreover, our work presents exciting challenges and research opportunities in areas like modeling, sensing, actuation, and control for the robotics community, ultimately advancing our understanding of our nature and pushing the boundaries of technological innovation.

Materials and Methods

Design and Fabrication of SORI.

SORI comprises two key components: the contact area rendering and stiffness rendering parts. The contact area rendering section utilizes a toroidal SPA, which includes four layers: a top silicone membrane, a mask, a bottom silicone membrane, and a rigid mesh. The fabrication process involves silicone molding and paper masking techniques, using Dragon Skin 30 (Smooth-On) silicone material and a surface tension diffuser SLIDE-STD (Smooth-On) to minimize stiction. To prevent stiction between the silicone and the mask layer, laser-cut copy paper is chosen as the mask material. The inner radius of the mask is designed based on the minimum detectable force threshold for humans, leading to an inner diameter of 4 mm, which includes a safety margin. The mask’s outer diameter is set at 22 mm to ensure comprehensive contact coverage while maintaining an ergonomic design. The top membrane, with a thickness of 0.75 mm, withstands pressures up to 30 kPa without breaking. This design is strategically aimed at minimizing the thickness of the membrane to reduce the normal force exerted on the fingertip, thereby enhancing conformability and enabling high renderable hardness.

The stiffness rendering component of SORI includes an origami prismatic joint and a pouch motor. This origami structure is crafted using a laminate manufacturing method. It consists of 0.5-mm glass-reinforced epoxy laminate (FR4) for the rigid layers, 50 μm Kapton polyimide film for the flexible hinges, and a Poli-Melt 701 film as the adhesive layer to bond the flexible and rigid layers. The pouch actuator, made from thermoplastic polyurethane (TPU) coated fabric and a Teflon sheet, is precisely laser-cut and positioned between the TPU layers. These layers are then heat-pressed at 180°C for 30 s under a pressure of 200 N.

The toroidal SPA is strategically placed on the origami structure, incorporating a force-resistive sensor (Interlink FSR 402) between them. In alignment with methodologies from previous research (39), a position-sensing mechanism based on a linear potentiometer (Alps Alpine RS08U111Z001) is utilized. To ensure precise positioning of the origami structure and the potentiometer, a custom-designed PCB and a 3D-printed holder are employed. This origami assembly achieves a maximum range of motion of 5 mm. (SI Appendix, Fig. S1 and Design and Fabrication of SORI).

Experiments.

We designed comprehensive experiments to evaluate SORI’s performance and to validate our models. For characterizing the stiffness range of SORI, we performed tests using a universal testing machine (Instron 5965), equipped with a rigid spherical indenter with a radius of 9 mm. The pressure of SORI was varied from 0 to 200 kPa in increments of 40 kPa (SI Appendix, Fig. S3A and Stiffness Experiments). Furthermore, we quantified the normal force exerted by the toroidal SPA on the fingertip. For this, we utilized a soft spherical indenter with a diameter of 18 mm made of Dragon Skin 10, designed to mimic a soft fingertip. It was mounted on the universal testing machine and positioned to tangentially touch the toroidal SPA. The pressure was incrementally increased in steps of 4 kPa up to a maximum of 24 kPa. The force at each pressure level was recorded. This procedure was replicated three times (SI Appendix, Fig. S2 and Contact Area Rendering Part).

To show the validity of our models, contact area experiments were performed. The experimental setup comprised a finger stand with a linear guide, a 3D-printed finger bed set at a 30-degree angle, and a spring to reset the bed. Participants applied forces of varying magnitudes ($F=[0.5,1,2,3,4]$N) onto surfaces with different softness levels. The fingerprints left on ink-covered surfaces were transferred to copy paper, scanned at high resolution, and analyzed using ImageJ software to determine contact areas. Each material and subject underwent this process three times. The same procedure was applied to SORI, adjusting the toroidal SPA’s pressure from 0 to 24 kPa in 4 kPa increments (SI Appendix, Contact Area Experiments). Additionally, the toroidal SPA inflation-pressure model was validated by measuring the height of its top membrane under varying pressure and force inputs. This was done by mounting the toroidal SPA on a Nano 17 ATI force sensor and employing a OMRON ZW-CE10T high-resolution fiber displacement sensor, which was positioned using an XYZ system with an INNO6 Automatic Precision Stage capable of < ± 1 μm accuracy (SI Appendix, Fig. S3C and Toroidal SPA Characterization).

Participants and Protocol.

Two volunteers, both without any impairments in finger motor skills, participated in the contact area study. The study was approved by the Human Research Ethics Committee at EPFL (No. 081-2023), and participants provided informed consent prior to the procedures.

During the experiments, the participants were seated comfortably in a chair. They placed their index finger on a custom-designed finger stand equipped with a linear guide, a 3D-printed finger bed, and a spring mechanism to reset the bed to its starting position. The finger angle was consistently maintained at 30^° to ensure uniformity across trials.

We conducted all contact area experiments using the subjects’ index fingers to ensure reliable data comparison. The participants were instructed to press samples coated with red ink to capture their fingerprints and then transfer their inked fingerprints onto paper. Each subject repeated the process three times for each force level and material tested. In the case of SORI, we performed analogous tests, adjusting the toroidal SPA’s pressure in increments of 4 kPa, ranging from 0 to 24 kPa. After scanning, the contact areas were quantified using the open-source ImageJ software. For data protection, all scanned fingerprints were deleted from our digital media following analysis.

Supplementary Material

Appendix 01 (PDF)

Movie S1.

Softness Rendering Interface, SORI. The SORI is composed of two independent parts: the contact area and stiffness rendering parts. The contact area rendering part, constructed from a toroidal soft pneumatic actuator (SPA), manages the contact area with the fingertip upon inflation. Conversely, the stiffness rendering part, designed using an origami prismatic joint combined with a pouch motor, regulates the force applied to the fingertip.

Movie S2.

Softness regeneration. SORI replicates tactile cues on the fingertips, simulating both soft and hard homogeneous objects. It also emulates heterogeneous objects composed of layers with varying degrees of hardness.

Movie S3.

Softness regeneration of everyday objects. We measured the shore hardness and stiffness of everyday items, such as marshmallows, bread, salmon, and beef. Subsequently, SORI replicated the tactile sensation of softness associated with these objects.

Movie S4.

Softness replication of dynamic surfaces. SORI simulates the dynamic contact of a heart model pulsating at 30 beats-per-minute.

Movie S5.

SORI non-vertical motion reduction. The movie showcases two SORI prototypes, one with rectangular and the other with castellated folding hinges. The prototype with castellated hinges demonstrates a significant reduction in non-vertical movements during interaction.

Data, Materials, and Software Availability

Models, control codes, and experimental results are available on GitHub (https://github.com/MeTech/rrl-sori-public and https://doi.org/10.5281/zenodo.10246508) (51, 52).