Physically intelligent soft antennae enhance tactile perception by active touch

Physically intelligent soft antennae enhance tactile perception by active touch | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Physically intelligent soft antennae enhance tactile perception by active touch Lingsheng Meng , Parker McDonnell , View ORCID Profile Kaushik Jayaram , View ORCID Profile Jean-Michel Mongeau doi: https://doi.org/10.1101/2025.10.20.683587 Lingsheng Meng 1 Department of Mechanical Engineering, The Pennsylvania State University , University Park, PA 16802, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Parker McDonnell 2 Department of Mechanical Engineering, University of Colorado Boulder , Boulder, CO 80309, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Kaushik Jayaram 2 Department of Mechanical Engineering, University of Colorado Boulder , Boulder, CO 80309, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Kaushik Jayaram Jean-Michel Mongeau 1 Department of Mechanical Engineering, The Pennsylvania State University , University Park, PA 16802, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Jean-Michel Mongeau Abstract Full Text Info/History Metrics Data/Code Preview PDF Abstract Soft robotic sensors today struggle to interpret complex tactile scenes without incurring significant computational costs. Inspired by insect antennae—soft, distributed sensors that efficiently process tactile information through physical intelligence—we investigated whether mechanical design and active touch sensing strategies could enhance robotic tactile feature perception. We hypothesized that insect-inspired antenna dynamics, specifically stiffness gradients and active touch speed, could simplify tactile classification. Using bioinspired computational and robophysical models of cockroach antennae, we introduce the notion of tactile tensors—spatiotemporal representations of tactile stimuli shaped by contact location, feature type, and active touch speed. Our analyses show that cockroach-inspired antenna mechanics and active touch speeds significantly improve feature classification accuracy compared to conventional sensors by increasing tactile data sparsity and dispersion. Through sim-to-real transfer, these principles were successfully demonstrated on a miniature distributed soft robotic antenna, validating their effectiveness in real-world robotic systems. Unlike robotic vision systems—which also use distributed sensing but cannot leverage mechanical gradients and contact dynamics—our approach achieves efficient sensing through physically intelligent, adaptive mechanics. Our work for the first time demonstrates how active movement of a mechanically tuned soft, distributed tactile sensor enhances robotic perception. Taken together, this work presents a biologically grounded framework for tactile sensor design that reduces computational load and enhances adaptability. One-Sentence Summary Insect-inspired antenna dynamics enable physically intelligent robotic tactile sensing with improved efficiency and classification accuracy. INTRODUCTION A critical challenge in robotics is in efficiently interpreting tactile information from complex environments. Animals, particularly insects, excel at navigating dynamic, cluttered habitats by leveraging physical intelligence—the intrinsic ability of their body mechanics to simplify sensory processing and reduce cognitive load ( 1 , 2 ). While robotic perception through non-contact modalities such as vision has significantly advanced, tactile sensors inspired by biological systems like mammalian whiskers ( 3 ) and insect antennae ( 4 ) remain relatively less developed. Unlike vision, tactile sensing directly interacts with the environment, providing unique insights into object geometry, texture, and mechanical properties. However, these physical interactions pose challenges in terms of sensor design, information processing and perception. Investigating and adopting biological principles of physical intelligence could therefore lead to transformative advancements in robotic sensing, enhancing efficiency, adaptability, and scalability. In this study, we explore two central open questions: (1) How do biological systems efficiently encode complex tactile information with minimal computational resources? and (2) What specific biological principles can be leveraged to create novel distributed tactile sensors for next-generation robotic awareness capable of animal-like performance? Insect antennae exemplify these principles through their distributed mechanosensors and adaptive mechanical properties, such as stiffness gradients, enabling rapid and precise tactile perception and guidance ( 5 , 6 ). Such structural features may facilitate a diverse range of tasks from rapid obstacle avoidance during locomotion to fine- scale tactile exploration ( 7 , 8 ). Previous studies have suggested that nonuniform stiffness gradients in biological structures, including insect wings and rodent whiskers, simplify sensory processing by mechanically mediating sensory input ( 9 , 10 ). Similarly, soft antenna sensors with stiffness gradients are hypothesized to enhance tactile acuity by increasing the spatial resolution of tactile sensing and mitigating mechanical perturbations ( Fig. 1A ) ( 4 , 6 ). However, precisely how these mechanical adaptations influence tactile feature perception—by potentially enhancing data sparsity, feature separability, and reducing cognitive demand remains poorly understood ( Fig 1B ). Specifically, how a stiffness gradient influences tactile feature discrimination, such as distinguishing shapes, sizes, and contact locations, requires systematic exploration. Download figure Open in new tab Fig. 1. An insect-inspired design framework for tactile perception with distributed sensing. ( A ) A high compliance distributed sensor increases the information available by activating more mechanosensors. Δ x : sensor spacing. ( B ) Tactile sensation with distributed sensors is influenced by spatial information, temporal information and mechanics. ( C ) The American cockroach Periplaneta americana has a pair of soft, distributed antennae for touch sensation. ( D ) Framework combining animal experiments, mathematical and physical modeling. ( E ) Contact of the antenna with features generates a spatiotemporal gradient of strain along its length. The relationship between strain, distance and time can be represented as a tactile tensor. Additionally, active sensing behaviors, such as varying contact speeds, in synergy with sensor mechanics likely modulate tactile sensitivity and classification accuracy. For example, animals might adjust their exploration speeds to optimize tactile perception, analogous to the speed- accuracy trade-offs during decision-making tasks extensively studied in vision ( 11 – 13 ). Slower contact speeds potentially allow extended sensory integration times, increasing the quality and resolution of tactile information ( Fig. 1B ). Despite these expected benefits, the relationship between tactile exploration speeds and the fidelity of feature discrimination has yet to be quantified systematically in insect tactile systems. Addressing this gap would reveal how active sensing modulates tactile perception, providing insights into fundamental trade-offs between sensory accuracy and energetic costs in insects, and informing the design of energy-efficient robotic tactile sensors. Cockroach antennae represent ideal biological systems for testing these hypotheses. The American cockroach ( Periplaneta americana ) relies on its antennae, which is approximately 1.5 times the body length, for feature discrimination during tactile exploration, acquiring critical information about feature position, texture, contact angle, and distance ( 8 , 14 – 16 )( Fig. 1C ). It has a distinct mechanical profile characterized by an exponentially decreasing stiffness gradient ( 6 ), a feature shared with other biological tactile sensors ( 17 ), potentially hinting at convergent evolution- led design principle. However, unlike mammalian whiskers, insect antennae feature a large population of mechanosensors distributed throughout their length. For example, each cockroach antenna has roughly 40,000 mechanosensors distributed along its length ( 18 , 19 ). However, it remains unclear how cockroaches precisely integrate and interpret signals from thousands of mechanosensors to discriminate tactile features and guide adaptive behaviors. One possibility is that mechanical properties of the antennae, such as intrinsic stiffness gradients, in synergy with active behavioral strategies, such as preferred contact speeds, may simplify the sensory encoding process, enhance tactile discrimination and reduce cognitive demand. In this manuscript, we combined bioinspired computational modeling and robophysical experiments to test the hypothesis that insect-inspired antenna mechanics and active sensing behaviors enhance tactile feature discrimination ( Fig. 1D ). Using detailed computational simulations grounded in recent morphological and mechanical characterization of cockroach antennae ( 20 ), we systematically examined how antenna stiffness gradients and contact speed shape tactile sensory data. We generated comprehensive datasets of tactile tensors—spatiotemporal representations of mechanical stimuli ( Fig. 1E )—and employed dimensionality reduction and classification analyses. Our results demonstrate that cockroach-inspired antenna mechanics and slower active sensing speeds substantially increase tactile data sparsity and dispersion, significantly enhancing tactile feature classification compared to conventional sensor models. Finally, we validated these biologically inspired principles through a sim-to-real transfer. We developed a miniature, distributed soft robotic antenna incorporating these mechanical and active sensing strategies. Our robotic implementation confirmed the practical effectiveness of insect-inspired physical intelligence, demonstrating improved tactile discrimination accuracy and efficiency. Collectively, these findings underscore the potential of bioinspired physical intelligence to transform robotic tactile sensing technologies, enabling more efficient and adaptive robotic systems. RESULTS Tactile interactions generate diverse spatiotemporal representations of tactile tensors Animals and robots routinely encounter mechanical features with finite span, such as post-like features from plant or grass stalks, obstacles such as pebbles, features from conspecifics or predators, etc. To systematically investigate how cockroach-inspired antenna mechanics might influence tactile feature perception in these conditions, we examined how distinct mechanical contacts—varying by speed, location, and object geometry—generate sensory information encoded as tactile tensors. Using a computational model inspired by cockroach antenna mechanics ( Fig. 2A– C ; Movie S1 ) which enabled the high-throughput generation of tactile tensors ( Movie S2 ), we explored how antenna mechanics might simplify information processing during contact with a small-field feature or to estimate distance to a wide-field feature, i.e. a wall. To create a comprehensive dataset of tactile tensors that animals and robots may encounter when locomoting, we simulated mechanical loading to a broad set of stimuli. We defined 90 distinct tactile stimuli across three contact speeds, five contact locations, and six contact features ( Fig. 2D ; see Materials and Methods). The contact features included two different sizes and three shapes. The shapes were chosen to approximate a point contact (triangle) and distributed contacts of distinct curvatures (“box” and “ball”), which broadly capture natural statistics of tactile scenes ( 21 ). Contact with these features generated a broad set of tactile tensors sensitive to size, shape and contact speed ( Fig. 2E ). Qualitatively, the resulting tensors demonstrated considerable variability depending on feature type, location of contact, and speed of interaction, suggesting that mechanical properties of the antenna inherently structure sensory data. Thus, the tactile tensor dataset provides a comprehensive basis for quantitatively analyzing how insect-inspired antenna mechanics and behavioral modulation via contact speed may simplify tactile information processing as detailed below. Download figure Open in new tab Fig. 2. A simulation-based framework for designing distributed sensors with mechanical intelligence. ( A ) Simulation tool for distributed sensor design. A modular simulation framework computes mechanical response and sensor configuration using input stimuli and adjustable mechanical parameters. ( B ) Model validation. Tip displacement in both experiments (blue) and simulations (red) from step and impulse tests. Data from n = 5 animals in each scenario. Line: mean. Shaded region: ±1 STD. Adapted from ( 6 ). ( C ) Bioinspired application. A distributed sensor array embedded in a segmented antenna model captures mechanical intelligence through biologically tuned properties. ( D ) Mechanical input variation. Six distinct features (green) impacted the antenna at five locations from middle to tip (red dots), simulating diverse tactile interactions. ( E ) Tactile tensor outputs. Spatiotemporal tactile tensors from feature contacts under slow collision speed demonstrate sensitivity across the antenna with bioinspired sensor mechanics. Antenna mechanics simplify distance estimation to wide-field tactile features For touch sensation, a wall represents a wide-field feature that has infinite span, analogous to a background scene for the visual sense. Cockroaches often exhibit wall-following behavior, where they walk or run along walls with both antennae extended forward to avoid collisions and maintain stable body-to-wall distance by using tactile feedback to adjust their trajectory ( 7 , 22 , 23 ). During this behavior, the point of greatest curvature of the antenna is located close to the point of contact with the wall ( 6 , 7 ). This point of contact appears linearly related to the distance between the cockroach and wall since cockroaches maintain their inter-antennal angle approximately constant (∼30 degrees). Therefore, the position of the greatest curvature is believed to provide a salient mechanical stimulus to rapidly estimate body-to-wall distance for wall-following behavior ( Fig. 3A ). Consequently, it has been hypothesized that the flagellar mechanosensory information constitutes a one-dimensional sensory map to guide wall following ( 7 ) ( Fig. 3A ; see Materials and Methods). Download figure Open in new tab Fig. 3. Antenna mechanics enable simplified wall distance estimation, enhancing accuracy while reducing computational demand. ( A ) Wall-following behavior in experiment and simulation. A tethered cockroach experienced an approaching wall. Points of greatest curvature along the antenna are highlighted as colored dots. ( B ) Curvature-based wall distance encoding. The body-to-wall distance correlates with the location of greatest antenna curvature for different mechanical models (see Movie S3 ). Colored dots show experimental curvature points; dashed lines represent best linear fits with corresponding R 2 values. ( C ) Tactile tensors at fixed wall distances. Simulated tactile tensors show how contact patterns change as the wall moves parallel to the body while maintaining constant distance. ( D ) Tactile tensors from the wall-following behavior simulation using the exponential model. The antenna bent inward as the wall approached the body. To test this hypothesis and clarify how specific mechanical properties influence distance estimation, we simulated the antenna bending response as the wall approached the body ( Fig. 3A ; Movie S3 ). Using this simulation, we tested the influence of mechanics, i.e. different flexural stiffness profiles of the antenna, in simplifying this one-dimensional mapping. The bio-inspired model with an exponentially decreasing stiffness gradient produced a strong linear relationship (R 2 = 0.985) between the position of greatest antenna curvature and body-to-wall distance ( Fig. 3B ). In contrast, models with linear decreasing and constant profiles resulted in weaker, less predictable relationships (R 2 =0.924 and R 2 =0.704, respectively). Notably, simulation and experimental data from each body-to-wall distance scenario corresponded to a unique tactile tensor when using exponentially decreasing profile ( Fig. 3C , D ), suggesting a potential mechanism for insects to gauge wall distance and simplify tactile sensing. Taken together, these results suggest that the bio-inspired model can simplify touch-based distance estimation. Emergent tactile bases encode distinct feature locations and enhance discrimination To uncover how insect-inspired antenna mechanics might influence tactile feature encoding and identify common features across all tactile tensors, we formulated the following efficient encoding of tactile tensors based on convolutive non-negative matrix factorization (cNMF; Fig. 4A ; see Materials and Methods). This encoding decomposed the tactile tensor into a set of spatiotemporal bases and their corresponding activations. To evaluate the influence of the number of bases, w i ( x, t ), on tactile tensor encoding, we varied the number of bases, M , and obtained the optimal bases along with their corresponding activations. To quantify the information captured by the activations, we calculated their Shannon entropy across different numbers of bases. As the number of bases increased, entropy generally increased while the L2 norm residual decreased ( Fig. 4B ), indicating that more information could be preserved with more bases. Download figure Open in new tab Fig. 4. Emergent bases represent a sparse set of tactile features linked to contact location. ( A ) The methods pipeline for determining classification rate. ( B ) As the rank ( M ) increased, the encoding residual decreased, while the entropy of activations generally increased, except at M = 4. ( C ) The optimal bases from convolutive non-negative matrix factorization with different number of bases. Each row corresponds to an encoding of fixed rank from 2 to 5. The y-axis of each basis tensor represents 56 sensors from the base to the tip of the antenna. The x-axis represents the duration of each basis (40 ms). ( D ) Example activation vectors of fixed rank M = 3 for the ball and box collisions. We also found that similar patterns emerged when the number of bases, M , was varied ( Fig. 4C ). In the case of three bases, the first basis exhibited the highest activity in the lower left corner of the tactile tensor, indicating its activation during early time points and in the proximal region of the antenna. The second basis was most active around the middle region of the antenna and spanned the entire time. The third basis was most active around the upper right corner, corresponding to later time points and the distal region of the antenna. Accordingly, contact at different locations along the antenna produced distinct activation patterns across the bases: collisions near the proximal end primarily activated the first basis, while collisions at the tip strongly engaged the third basis ( Fig. 4D ). This suggests that the optimal bases obtained through cNMF encoding preserve mechanical stimulus information; specifically, optimal bases represent distinct contact locations, which could facilitate tactile feature discrimination. Collectively, these results indicate that antenna mechanics inherently structure tactile information into distinct spatiotemporal bases aligned with contact locations. This structured encoding potentially simplifies tactile feature discrimination and suggests a mechanism by which mechanical gradients in insect antennae reduce cognitive demands associated with processing complex tactile scenes. Slower active touch speeds enhance tactile feature discrimination Given the potential importance of active behaviors on sensing, we next explored how variations in contact speed could influence tactile feature encoding and classification performance by evaluating tensor data dispersion (see Materials and Methods). Specifically, based on the generated tactile tensor set, we hypothesized that a slower contact speed could facilitate tactile feature classification, analogous to increasing the exposure time or active perception on a camera or eye, respectively. For instance, for the human eye, longer exposure time to a scene allows more light capture (and temporal integration), thus facilitating visual discrimination during perceptual tasks ( 23 ). To assess tactile discrimination under different contact speeds, we divided the tactile tensor dataset and corresponding activation dataset into three groups according to contact speed: slow (0.06 m/s), medium (0.3 m/s), and fast (0.6 m/s) ( Fig. 5E ). The slow contact speed was determined by measuring antenna position during active touch (see Materials and Methods), whereas the fast speed corresponds to rapid running speeds during wall following ( 24 ). We then quantified dataset dispersion within each group using multiple indices: Pearson correlation, structural similarity index measure (SSIM), mean squared error (MSE), and normalized mutual information (NMI). A higher dispersion index indicates a more distinct dataset, which should facilitate classification. We then trained LDA classifiers to predict contact feature types from activation vectors in each speed group ( Fig. 4A , see Materials and Methods), allowing us to evaluate the effect of dataset dispersion on classification performance. Download figure Open in new tab Fig. 5. Slower contact speed and insect-inspired antenna stiffness gradient enhance tactile feature classification. ( A ) Dispersion index (NMI, see Supplement for the other 3 indices) of three subgroups based on contact speed, shown separately for the activation dataset (left) and the tactile tensor dataset (right). ( B ) Dispersion index for the activation dataset (left) and the tactile tensor dataset (right) across three stiffness profile models: exponential, linear, and constant. ( C ) Classification rates under different levels of noise for slow, medium, and high-speed contacts. Line: mean. Shaded region: ±1 STD. ( D ) Classification rates under different levels of noise for slow- speed contacts with exponential decreasing, linear decreasing, and constant stiffness profiles. ( E ) Simulated conditions with distinct speeds and stiffness. ( F ) The optimal bases from cNMFsc with a rank of 3. ( G ) The average entropy of these bases across exponential, linear and constant flexural stiffness. Lower contact speeds produced more dispersed datasets, as Pearson correlation, SSIM, and NMI increased with increasing contact speed in both tactile tensor and activation datasets, while MSE decreased ( Fig. 5A and Fig. S6 ). Lower Pearson correlation, SSIM, and NMI, along with higher MSE, indicate greater variability in the dataset. Thus, slower contact speeds produced more dispersed datasets, which in turn could enhance classification performance. To test this prediction, we trained LDA classifiers for each speed and determined that classification accuracy improved as contact speed decreased, with the highest classification accuracy observed at the slowest contact speed (blue line in Fig. 5C ). Notably, this low speed closely matched the antenna movement speed of active touch during exploration ( Fig. S2 ). To ensure that our results were not specific to the classification method, we also trained a convolutional neural network (CNN) to classify contact features based on the tactile dataset ( Fig. S4 ). The CNN results were consistent with those obtained using LDA classifier. Specifically, the classification rate improved as the contact speed decreased ( Fig. S4 ). Taken together, for a fixed sampling rate, slower contact speeds could provide more contact time and spatial span with features, thereby providing more detailed contact information to facilitate feature discrimination. Collectively, our results support the hypothesis that contact speed is inversely proportional to tactile discriminability, with slower contact speeds, as observed in insects, enhancing the ability to distinguish tactile features by allowing for richer sensory integration, thus informing effective design strategies for robotic tactile sensing. Download figure Open in new tab Fig. S1. Fitted length ratio of each segment along the antenna from n = 4 antennae. Download figure Open in new tab Fig. S2. Determination of slow exploration speed with antennae. ( A ) The planar antennal movement was reconstructed by tracking four landmarks on the cockroach: two at the tips of the antennae, one on the head, and one on the abdomen. ( B ) Boxplot of the average maximum angular speeds of the right and left antennae across six trials (black dots). Red line: median. Cockroach-inspired antenna stiffness gradients enhance tactile classification Building upon the finding that contact speed affects tactile feature discrimination, we investigated how the mechanical properties of the antenna itself affect tensor data dispersion and, consequently, tactile discriminability ( Fig. 5E ). Based on our previous results on the linear mapping to feature distance ( Fig. 3B ), we hypothesized that the exponentially decreasing stiffness gradient observed in cockroach antennae enhances tactile discrimination by promoting a sparser and more dispersed tactile dataset. To test this hypothesis, we compared tactile tensor datasets generated using three distinct stiffness profiles: exponential (cockroach-inspired), linear decreasing, and constant (uniform stiffness) ( Fig. S3 ). To quantify data dispersion across these three models, we computed dispersion indices as done previously (Pearson correlation, SSIM, MSE, and NMI) within each group. The exponentially decreasing stiffness profile produced the lowest Pearson correlation, SSIM values, and NMI values, along with the highest MSE values, indicating greater dataset dispersion ( Fig. 5B and Fig. S6 ). In contrast, the constant stiffness profile exhibited the highest Pearson correlation, SSIM values, NMI values, and the lowest MSE, suggesting lower dataset dispersion. The poor performance of the constant stiffness profile is likely due to its resemblance to a cantilever beam model, where maximum bending is concentrated at the base. It results in highly similar tactile tensors, making it difficult to distinguish between different contact scenarios. The exponentially decreasing stiffness profile, on the other hand, allows for more distributed bending along the antenna, generating a more diverse tactile dataset that enhances classification. We further analyzed the effect of stiffness profiles by applying cNMFsc encoding. The bases derived from the linear decreasing and constant stiffness profile models exhibited considerably higher entropy (average entropies of 2.7 and 2.8, respectively), indicating less structured representation, compared to those from the exponential decreasing stiffness profile model (average entropy of 1.9; Fig. 5F,G ). This suggests that the exponential stiffness gradient can enhance encoding of tactile stimuli. To further evaluate the impact of mechanical properties on tactile classification, we trained LDA classifiers using slow-speed tactile tensor datasets generated under these three different stiffness profiles. The classification accuracy was highest for the exponential decreasing stiffness profile (black line in Fig. 5D ). Taken together, these results demonstrate that cockroach-inspired antenna mechanics substantially enhance tactile discrimination by generating more informative and structured tactile data compared to more conventional touch sensor stiffness profiles. This finding supports the biological hypothesis that mechanical properties such as stiffness gradients inherently simplify tactile information processing, offering key insights for the development of physically intelligent robotic tactile sensors. Download figure Open in new tab Fig. S3. Tactile tensors data set at slow collision speed from exponential decreasing, linear decreasing, and constant stiffness gradient models. Rows represent locations (middle to tip of the antenna from top to bottom). Columns represent contact objects. Download figure Open in new tab Fig. S4. ( A ) CNN architecture schematic diagram. ( B ) Classification rates under different levels of noise for slow, medium, and high-speed contacts. Line: mean. Shaded region: ±1 STD. ( C ) Classification rates under different levels of noise for slow-speed contacts with exponential decreasing, linear decreasing, and constant stiffness profiles. Download figure Open in new tab Fig. S5. Spatiotemporal bases extracted using cNMF from tactile tensors. Each row corresponds to a different basis duration (T = 10 to 60 ms), and each column shows one of the three extracted bases. The x-axis represents time (T ms), and the y-axis corresponds to sensor ID along the antenna length (from base to tip). Download figure Open in new tab Fig. S6. Influence of contact speed and antenna mechanics on dataset dispersion. ( A ) Dispersion indices (Pearson correlation, SSIM, MSE, and NMI) of three subgroups based on contact speed, shown separately for the activation dataset (left) and the tactile tensor dataset (right). ( B ) Dispersion indices for the activation dataset (left) and the tactile tensor dataset (right) across three stiffness profile models: exponential, linear, and constant. Simulation-generated tactile tensor principles transfer effectively to novel distributed soft robotics antenna designs To demonstrate the practical applicability of our bioinspired tactile sensing framework and validate its generality, we transferred our computational findings to a physical robotic model. We hypothesized that the tactile encoding principles discovered through simulation—particularly the effectiveness of cockroach-inspired stiffness gradients and active touch behavioral strategies— could be successfully implemented in a physically intelligent, distributed robotic antenna. We built a near-cockroach scale (compact: 7.3x1.6x0.2cm, lightweight: 491mg, low-power: 32mW) robotic antenna equipped with 8 capacitive hinge mechanosensors experiencing natural contact physics and capable of tactile feature discrimination ( Fig. 6A ) ( 25 ). Like the biological antenna, this flexible robotic antenna featured a linearly decreasing flexural stiffness gradient and can resolve hinge angles (<1° resolution) at a maximum sampling rate of 1000 Hz, enabling the generation of high- fidelity tactile tensors ( Fig. 6A ). Due to manufacturing challenges, morphological variations such an exponential gradient or an increased number of mechanosensory units were not tested, but simulation of this eight-segment model yielded results consistent with the higher-degree-of- freedom model. To confirm that the simulation environment effectively captured realistic antenna mechanics, we optimized the physics model to closely match the robotic antenna’s impulse response ( Fig. 6B , Movie S4 ; see Materials and Methods). Taking advantage of the computational efficiency of the simulation environment, we generated a tactile tensor dataset encompassing two contact features, five contact locations, and three contact speeds. We then trained a support vector machine (SVM) classifier to distinguish these features (30 distinct tactile features for training, see Materials and Methods). To evaluate the sim-to-real transferability of our computational results, we applied the trained classifier directly to the robotic antenna in real-world contact experiments ( Fig. 6C ). Real-world contact experiments were conducted by colliding the robotic antenna with ball and box features at its tip under three different speeds (6 distinct tactile features for testing). Using tactile tensors generated from the sensory data of the robotic model and the SVM classifier trained on the simulation dataset, 83% of the experimental conditions were accurately predicted in terms of collision features, speed, and location ( Fig. 6D,E ; Fig. S7 ). In the misclassified class, the model correctly identified speed and location but failed to distinguish the feature, likely due to the limited spatial resolution of the robotic antenna. Overall, these results validate the practical effectiveness and robustness of bioinspired tactile sensing principles—particularly stiffness gradients and active contact speeds—in realistic robotic implementations. Furthermore, this successful sim-to-real transfer underscores the feasibility of using our bioinspired tactile sensing framework to create physically intelligent, distributed soft tactile sensors capable of enhanced perception in complex environments. Download figure Open in new tab Fig. S7. Tactile tensors from simulation model and data collected by the robotic antenna in six different experimental conditions. Download figure Open in new tab Fig. 6. Transfer of classifier from simulation to robophysical antenna for tactile feature discrimination. ( A ) A distributed sensor system with eight embedded strain sensors. ( i ) Layout of the robotic antenna system; colored dots indicate the locations of sensors on the hinges. ( ii ) Raw capacitance readouts from the sensors during a collision scenario (collision at the tip with a speed of 0.027 m/s). ( iii ) Predicted hinge angles based on linear regression from sensor calibration ( 25 ). ( iv ) Tactile tensors corresponding to this collision scenario. ( v ) Ball collision at the tip with a speed of 0.027 m/s. ( B ) The impulse responses from the robophysical antenna and simulation model. ( C ) Transfer of a tactile tensor dataset with rich tactile stimuli from simulation to the distributed sensor system. ( D ) Two examples of tactile tensors under the same condition: one from simulation and the other from sensory data collected by the robotic antenna. ( E ) Confusion matrix of the transferred SVM classifier. “Ball” and “box” indicate the two types of collision features. Black, gray, and white correspond to collision speeds of 0.270 m/s, 0.135 m/s, and 0.027 m/s, respectively. DISCUSSION Our study provides quantitative evidence supporting the hypothesis that physical intelligence— sensory processing embedded within mechanical structures—represents a fundamental adaptive strategy in insect antenna ( 2 , 26 ). By combining experiments, simulation, and physical modeling, our findings demonstrate that insect antennae mechanics, particularly non-linear stiffness gradients, together with active touch speed modulation, substantially simplify tactile feature discrimination by increasing data sparsity, dispersion, and decreasing mutual information contained across a variety of naturalistic mechanical stimuli. Although demonstrated here through insect antennae- inspired sensors, such physical intelligence mechanisms can be broadly applied to other tactile modalities and robotic architectures, opening pathways for enhanced efficient tactile perception beyond simple navigation tasks (e.g., object handling, environmental exploration, and autonomous manipulation) in real-world complex environments. Advancing physically intelligent tactile perception inspired by insects Our results represent significant advances toward a comprehensive design framework for physically intelligent tactile sensing, inspired by insect antennae ( Fig. 1 ). First, analogous to cameras, distributed tactile sensor resolution is limited by the spacing between adjacent mechanosensors. The spacing between mechanosensors is inversely proportional to spatial resolution. Second, the sampling rate defines the temporal resolution to distinguish between different shapes, size, speed of contact, etc. Further, the integration time (sampling window; see below) influences tactile perception. Related to integration time is contact speed, as slower contact of the antenna with a feature will increase contact time and therefore the information available. Third, the flexural stiffness of the sensor must be sufficiently low to conform to tactile features. Specifically, a more compliant sensor increases the information available by activating more sensor elements, thereby sampling information from a larger region of space ( Fig. 1A ). In addition to compliance, a stiffness gradient, as described in the cockroach antenna, can promote sparsity in tactile tensors during feature contact, which can improve feature classification. Here, through detailed computational simulations and robophysical experiments, we provide quantitative support that physically intelligent mechanical designs significantly simplify tactile encoding, thus reducing computational and cognitive demands associated with tactile information processing. Taken together, spatial resolution (sensor spacing), temporal resolution (sampling rate, integration time), and mechanics (compliance, gradient) must be considered to design effective tactile sensors ( Fig. 1B ). Crucially, this work establishes the foundation for a broader tactile sensor design framework applicable to diverse robotic contexts beyond navigation alone. The demonstrated principles of mechanical stiffness gradients and active sensing have potential relevance across multiple robotic tasks, including manipulation of delicate objects, exploration of complex terrains, human-robot interaction, and prosthetic sensing systems. For example, robotic grippers employing similar bioinspired mechanical gradients could achieve improved sensitivity, dexterity, and adaptability, enabling reliable manipulation of diverse objects in uncertain environments ( 27 , 28 ). Similarly, wearable tactile sensors incorporating these principles could significantly enhance feedback quality and intuitive control in prosthetic and assistive technologies. Thus, the broader potential of physically intelligent tactile sensing frameworks extends well beyond the antenna-inspired sensors demonstrated here, offering transformative possibilities across various robotics and human-machine interfaces. Trade-off between speed of contact (energy) and information Temporal integration is a fundamental feature in perceptual decision-making ( 12 ), allowing sensory systems to accumulate information over time. Longer sensing durations enable greater temporal integration, improving sensory estimates. The speed-accuracy tradeoff (SAT) is a well- established principle in psychophysics, describing how animals and humans balance rapid decision- making with the need for precise sensory processing ( 13 , 29 ). In visual perception, acuity varies across the visual field, and humans acquire high-resolution information through brief fixation periods separated by saccades. Studies on rapid serial visual presentation have shown that detection accuracy improves with longer exposure times, highlighting the importance of temporal integration in visual discrimination ( 30 ). Similarly, in tactile perception, temporal cues play a crucial role in spatial-frequency discrimination, such as detecting surface textures ( 31 ). These consistent observations suggest a generalized biological principle of active sensory modulation, offering valuable insights for adaptive robotic sensing strategies. Moreover, this SAT principle aligns with our findings, where slower contact speeds resulted in greater dataset dispersion, improving the classification of tactile features. Taken together, our findings provide a link between contact speed and tactile dataset dispersion in both simulated and experimental settings. Distributed soft sensor systems, such as the robotic sensor developed here, could optimize tactile information processing by dynamically adjusting contact speed. Future work could explore adaptive speed control strategies in robotic systems, allowing for dynamic modulation of contact speed based on task demands, similar to active touch sensing behaviors in animals. Role of mechanics in tactile discrimination Mechanics and sensing are tightly coupled in biological systems ( 26 ). For instance, insect wings—which act like actuators and sensors—can enhance body rotation detection with their nonuniform stiffness gradient ( 9 ). The tapering of whiskers enhances the reliability of tactile information by facilitating stick-slip motions during surface exploration, which are essential for texture discrimination. In contrast, cylindrical whiskers tend to become stuck or immobilized when sweeping across fine textures, which reduces sensory effectiveness ( 10 ). While these sensors have demonstrated strong performance in spatial mapping and texture discrimination tasks ( 32 , 33 ), their capabilities are often limited by structural rigidity and limited sensor density. In contrast, insect antenna-like sensors offer inherent advantages through their mechanical gradients and high-density sensor distribution. Our findings related to exponential stiffness gradients in cockroach antennae raise the intriguing possibility that these mechanical properties represent convergent evolutionary solutions across tactile sensory systems in diverse taxa. Indeed, mechanical gradients and sensor distributions similar to those we observed have been documented in diverse arthropods including stick insects, crickets and locusts ( 34 , 35 ). Likewise, crayfish antennae exhibit stiffness gradients enabling precise water-flow detection and olfaction ( 36 ). Additionally, the homology between antennae and legs extends to the underlying sensorimotor system ( 37 ) hinting at potential mechanical gradient-based advantages during force encoding and control ( 38 ) during other tactile behaviors such as legged locomotion. Future comparative studies quantifying stiffness gradients, sensor densities, and segmental dimensions across diverse species could provide compelling quantitative support for tactile sensing convergence, offering deeper insights into evolutionary biomechanics and sensing strategies. Our work adds to a growing body of evidence that stiffness gradients play an important role in insect antennae and insect-inspired robotic sensors. Previously, a tunable physical model of a cockroach antenna showed that a decreasing stiffness profile can enhance tactile acuity ( 4 ) while increasing preview distance, which could simplify control of wall following ( 6 ). For artificial tactile systems, our work highlights the critical importance of considering both mechanical structure design and sensor placement for tactile perception. Implications for understanding the sense of touch in biology The tactile dataset generated in this study illustrates the dynamic variations in tactile stimuli encountered during antennal contact. At present, it remains unknown whether cockroaches can actively discriminate between these stimuli. To explore this possibility, we applied cNMFsc and encoding of tactile datasets, to mimic neural signal processing in the antenna. This encoding provides a possible characterization of how tactile signals may be processed within the cockroach’s sensory systems. Notably, the different bases extracted through cNMFsc preserved information about the contact region along the antenna, suggesting the spatial organization of these bases may reflect a form of topographic mapping of tactile feature. This topographic mapping is commonly observed in biological systems, such as somatotopic maps in the somatosensory cortex ( 39 ) and visual feature maps ( 40 ). In cockroaches, adjacent sensory receptors along the antenna could project to adjacent regions in the brain, preserving spatial relationships ( 41 , 42 ). Our spatiotemporal encoding model provides support for this structure. Specifically, the temporal activation patterns reflect a progression from proximal to distal regions of the antenna, mapping contact location into basis space. This topographic-like representation may facilitate efficient neural decoding of contact location, supporting efficient tactile localization. Opportunities for bio-inspired robotics Our work can inform the development of a new class of robotic touch sensors. While whisker- inspired tactile sensors have been widely explored ( 3 ), distributed soft sensors inspired by insect antennae offer unique advantages not afforded by whisker sensors ( 43 ). Many insect antennae are multi-segmented, continuously deformable structures with distributed sensing along their length. This structural complexity could allow for rich information extraction and broad contact-based perception from the environment. Optimizing the structural and mechanical properties of bio- inspired antennae can provide novel opportunities for robotic perception and interaction with complex environments ( 4 , 43 ). One key advantage of our bio-inspired antenna system is its ability to discriminate environmental features while maintaining low energy consumption and minimal weight. While many conventional robotic tactile sensors—such as piezoelectric or resistive tactile sensors—can require supporting electronics with relatively high-power demands, our bio-inspired distributed soft sensors are based on capacitive sensors, which is well known for its low energy requirements ( 44 ). Our robotic antenna operates with a total power consumption below 60 mW and weighs under 500 mg, making it ideal for energy-efficient and lightweight applications ( 25 ). This level of efficiency is particularly beneficial for autonomous insect-scale robotic systems operating in resource-constrained environments. By leveraging key principles from insect antennae, e.g. distributed sensing, low-power encoding, and topographic representation, future artificial systems could improve feature discrimination, reduce energy consumption, and enhance situational awareness when combined with vision-based simultaneous localization and mapping. Thus, our work paves the way for more adaptive and efficient physically intelligent robotic platforms capable of navigating and interpreting complex, dynamic environments. MATERIALS AND METHODS Bio-inspired antenna model to simulate the transmission of tactile stimuli Inspired by the morphology and mechanics of the antenna (flagellum) of P. americana ( 6 , 20 ), our model included a sequence of 140 rigid links connected by hinge joints ( Fig. 1B ). The radius of each link was kept constant, and the mechanical properties of each joint were modeled by modulating the link mass, hinge stiffness and hinge damping. The length of each segment increases from the base to the tip in the antenna of the American cockroach ( 6 , 45 ). This variation was modeled using a sigmoid function fitted from experimental data (squared norm of the residual = 8.7e-5, see Fig. S1 )( 6 ). where y represents the proportion of the length of the segment to the total length, and x is the ratio of the segment number to the total number of segments. The mass of each segment was described by the following equation, where the assumption was that the density is constant along the antenna, resulting in the mass following the same exponential decreasing relationship fitting of the square of the radius ( 6 ). where m i (g) is the mass of the n th segment. The stiffness k and damping c of each joint n were described by exponential functions modeling the mechanics from base to the tip of the antenna ( 6 ). where p 1 and p 2 are the stiffness and damping constants at the first (base) joint, respectively. The rates of exponentially decrease in stiffness and damping of joints along the length are represented by p 3 and p 4 , respectively. To compare the influence of different stiffness and damping profiles, a linear decreasing and constant stiffness and corresponding damping profiles were also implemented in the antenna model. Stiffness and damping parameters for each function were optimized using nonlinear methods to match the damped natural frequency and damping ratio obtained from step deflection data ( Fig. 1D ) ( 6 ). Additionally, the deflection ratios between the middle regions of the antenna (approximately 71% and 86% of its full length) and the tip (100% of full length), obtained from impulse collision experiments ( Fig. 1E ), were used as target quasistatic constraints in the optimization ( 6 ). We used normalized Euclidean distance to quantify the total error of the simulations across the two scenarios, as calculated using with constants defined in Table 1 . View this table: View inline View popup Download powerpoint Table 1. Dynamic and static properties from experiments ( 6 ). To handle non-differentiable target functions, a nonlinear Powell’s method was used to minimize the error ( 46 ). After optimization, the parameter values were determined as follows: p 1 = 37.78, p 2 = 25.24, p 3 = −0.0827, and p 4 = −0.0533, resulting in a local minimum error of 0.067 ( Movie S1 ). It is worth noting that different combinations of p 1 to p 4 can lead to similar errors. As a comparison, the median symmetric accuracy (MSA), as previously used ( 47 ), was 0.0035. The MSA is more robust to outliers as it relies on the median of the target values, whereas the normalized Euclidean distance gives equal weight to each target. Generation of tactile tensors from contact We implemented the antenna model using the MuJuCo physics engine ( 48 ), chosen for its efficiency and accuracy in simulating multi-rigid body dynamics in contact-rich environments. The default numerical integrator, the implicit-in-velocity Euler method, was employed with pyramidal contact cone in MuJoCo’s soft contact model. This model relaxes the strict complementarity constraint in linear complementarity formulation to increase physical realism for soft contacts ( 49 ). We recorded joint angles as the antenna contacted distinct features at distinct locations and contact speeds. We defined a “tactile tensor” as the full set of segment curvature (or joint angle) across the antenna in time during a tactile event. Thus, each tactile tensor a ( x, t ) has dimension x , the distance to the base of the antenna, and time t ( Fig. 2A ). To generate a comprehensive tactile dataset encompassing a set of mechanical stimuli applied to the antenna, we simulated three different contact speeds: 0.6 m/s (cockroach evasive speed ( 5 )), 0.3 m/s (medium speed), and 0.06 m/s (antenna slow exploration speed ( 50 ), see Supplementary Methods). These speeds were chosen to represent a range of antenna-mediated behaviors. We tested collisions with six different features at five locations along the antenna (indicated by red dots in Fig. 2A ), spanning the middle to the tip region to reflect a broad set of contact points. Joint angles from 56 points, representing the locations of campaniform sensilla (strain sensors) along the antenna length ( 41 ), were recorded every 1 ms, resulting in a dataset of 90 tactile tensors ( Fig. S3 ). Spatiotemporal encoding of tactile tensors To extract features from tactile tensors by dimensionality reduction, we performed spatiotemporal encoding on the tactile tensors based on convolutive non-negative matrix factorization with sparsity constraints (cNMFsc), which has been previously used to encode tactile stimuli to the human hand ( 51 ). cNMFsc decomposed the tactile stimuli, a ( x, t ), into a set of spatiotemporal basis sequences w i ( x, t ), and their corresponding activation vectors h i ( t ) . The algorithm minimizes the L2 norm between a ( x, t ) and the estimated tactile stimuli, , subject to the sparsity constraints ( 52 ) on the activation vectors: where 0 ≤ S h ≤ 1 is the defined sparseness, n is the dimensionality of vector x and M is the number of bases. The sparseness was chosen as 0.8 in this study. We set the duration of the spatiotemporal basis, T , to 40 ms, which approximates the cockroach’s response time to impulse- like perturbations of the antenna ( 7 , 24 , 53 ), although the spatiotemporal profile of the bases exhibited little variation across different durations T ( Fig. S5 ). Dataset dispersion evaluation To assess the similarity between tactile tensors, we computed the Pearson correlation coefficient, structural similarity index (SSIM), mean squared error (MSE), and normalized mutual information (NMI) for each tensor against all other tensors in the dataset. For each tactile tensor, we identified its closest match based on these metrics, selecting the maximum value of Pearson correlation coefficient, SSIM, NMI, and the minimum value of MSE. This process was repeated for all tactile tensors to quantify the most similar counterpart for each tensor in the dataset. Finally, the average Pearson correlation, SSIM, MSE, and NMI across all comparisons were used to evaluate the overall dispersion of the dataset. Feature classification from tactile tensors To further quantify the influence of tactile tensor dispersion on tactile discrimination, we designed a classification task with the objective of using the activation vectors to identify contact locations and features ( Fig. 3A ). First, we performed Principal Component Analysis (PCA) on the flattened activation vector and selected the first 30 features, which could capture ∼90% of the variance for the test sets. To simulate real-world noise and augment the data, we added Gaussian noise ( μ = 0) to the activation vectors and applied dimensionality reduction through the same PCA process. The noise ratio was defined as the deviation of Gaussian noise relative to the maximum value of each activation vector. We initially avoided complex classification methods that would require extensive model tuning, such as convolutional neural networks (CNNs), although classification results using CNNs yielded similar conclusions ( Fig. S4 ). Instead, we chose Linear Discriminant Analysis (LDA) classifiers, which provides a parsimonious method. The data augmentation, dimensionality reduction, and training steps were iterated ten times to derive the average accuracy of the test sets. Collectively, the average accuracy of the test sets provided a measure of tactile discriminability. Animal experiments The methods for quantifying the antenna’s response free response and response to collisions have been described in previous studies ( 6 ). Briefly, cold-anesthetized male P. americana were mounted onto a custom platform. The head–scape and scape–pedicel joints were immobilized with epoxy glue. We fixed the proximal 0.5 cm of the antenna with a pair of fine forceps and recorded the antennae response with a high-speed camera (Phantom v10, Vision Research Inc., Wayne, NJ, USA). We obtained recordings at 1000 frames per second (fps), with a shutter speed of 400 μs and a resolution of 10 pixels per millimeter. A second camera (X-PRI, AOS Technologies AG, Baden Daettwil, Switzerland) directly above the antenna recorded the horizontal motion of the flagellum at 250 fps. We measured the transient response to an initial step deflection. The flagellum was deflected manually and held by a second pair of fine forceps 1 cm distal to its fixation site ( Fig. 1B ). After a brief hold time of a few seconds, the flagellum was abruptly released and snapped back passively to its starting position. To measure responses to an impulse, the flagellum was deflected close to the tip (at ∼95% of its unrestrained length) with a 5 mm LED light mounted to a lever arm ( Fig. 1B ). The lever arm was released manually and rotated in the sagittal plane. To determine the relationship between the point of greatest curvature and body-to-wall distance, we tethered a male P. americana onto a custom stage ( Fig. 2A ). We fixed the body using insect pins and the head as well as the scape and pedicel using dental silicone (Coltene light body, Coltène/Whaledent AG, Altstätten, Switzerland). The antenna was pre-bent in the inverted J-shape characteristic of wall-following behavior ( 7 , 23 , 24 ). The wall was moved toward the cockroach at distinct distances using a linear stage. Robophysical model We built a robotic antenna system with eight integrated capacitance-based hinge angle sensors ( Fig. 5A ). The flexible polyimide hinges of the sensor allow the robotic antenna to respond to tactile stimuli and collect distributed, spatiotemporal tactile information ( 25 ). The bending stiffness of each hinge can be theoretically estimated based on its geometry using the following equation ( 54 ): where E k is the Young’s modulus of Kapton (2.5 GPa), w is the width, t is the thickness, and l is the length of the hinge. Since the sensors were implemented using a multi-layer material system incorporating capacitive elements on Kapton, the actual hinge stiffness is expected to deviate from the theoretical values E k . To account for this difference, we assumed a linear relationship between the actual hinge stiffness and damping and their theoretical estimates. The hinge stiffness and damping can therefore be expressed as: To efficiently generate tactile tensor datasets and facilitate iterative design, we implemented the robotic antenna in the MuJoCo simulation environment. Similar to the parameter optimization process described in the previous section, we used the normalized Euclidean distance to quantify the error between the simulated and robotic antennae in terms of tip damped frequency and damping ratio. After optimization, the parameter values were determined as: p 1 = 1.19, p 2 = 2.06, resulting in a minimum error of 0.0009 ( Movie S1 ). Tactile feature classification from simulation to reality Taking advantage of the computational efficiency of simulation environment, we generated a tactile tensor dataset encompassing two contact features, five contact locations, and three contact speeds (0.270 m/s, 0.135 m/s, and 0.027 m/s). To classify tactile features using tactile tensors generated from both the simulation and the robotic model, we first aligned the tactile tensors based on the first positive peak of the tip trajectory. To mitigate overfitting, we augmented the tactile dataset from simulation by replicating each tactile tensor 10 times and added Gaussian noise ( μ = 0) with a standard deviation equal to 20% of the maximum value of the tactile tensors. For classification, we employed a support vector machine (SVM) classifier with a one-vs-one strategy to distinguish contact features, speeds and contact locations (30 classes for training) within the noise-augmented tactile tensor dataset from simulation. Finally, we applied this trained SVM classifier to categorize tactile tensors generated from the robotic antenna, demonstrating the generalization of the classifier and its application to real-world robotic systems. Supplementary Materials Materials and Methods Figs. S1 to S7 Movies S1 to S4 Funding Army Research Office W911NF- 23-1-0039 (JMM, KJ) Alfred P. Sloan Research Fellowship FG-2021-16388 (JMM) Author contributions Conceptualization: LM, PM, KJ, JMM Methodology: LM, PM, KJ, JMM Investigation: LM, PM Visualization: LM, PM, KJ, JMM Funding acquisition: KJ, JMM Project administration: KJ, JMM Supervision: KJ, JMM Writing: LM, PM, KJ, JMM Competing interests Authors declare that they have no competing interests. Data and materials availability All code and data will be available on Penn State ScholarSphere at the time of publication. Supplementary Materials Movie S1 . Impulse response comparison between the biological antenna and the simulated physical model. Movie S2 . Example of a tactile tensor generated from contact with an object. Movie S3 . Simulation of wall-following behavior with distinct antenna stiffness. Related to Figure 3 . Movie S4 . Impulse response comparison between the robophysical antenna and its simulation. Supplementary Methods Modeling of antenna geometry The length of individual antenna flagellum annulus was previously reported ( 6 ). A sigmoid function was fit to the normalized experimental data, employing the lsqcurvefit function in MATLAB (Mathworks). The fit yielded a squared norm of the residual of 8.7e-5 ( Fig. S1 ). Antenna slow exploration speed Cockroaches actively move their antenna to probe their surroundings. To determine the angular velocity of the antenna as cockroaches move them during exploration, an adult male cockroach was placed in a square acrylic arena in the dark. Five acrylic rods (with diameters of 4, 5, 6, 7, and 10 mm) were affixed in the center of the arena. The exploration behavior of the cockroach was recorded using an indoor security camera equipped with an integrated infrared light. Planar antennal movement was reconstructed using DLTdv8 ( 55 ). The angular movement of the antenna was calculated by measuring the angles between the antenna and body vectors ( Fig. S2A ). The angular data was processed with a second-order Butterworth filter, and the derivative of the filtered angular data was computed to obtain angular speed. Peaks in the filtered angular speed data were detected to determine the fastest angular speeds within each trial. The average maximum angular speed for a trial was calculated by averaging all peak speeds. Six trials were conducted on one adult male cockroach, and the average maximum angular speeds of the right and left antennae were obtained for each trial ( Fig. S2B ). Across all trials, an average maximum angular speed of 86.67 °s -1 was obtained, which is similar to previously reported peak angular speed of exploratory antennal movement (75 °s -1 ) ( 50 ). Based on this, an equivalent lateral exploration speed of 6 cm s -1 was set as the slow exploration speed for the antenna. Tactile tensors from exponential decreasing, linear decreasing, and constant stiffness profile models To evaluate the role of the cockroach-inspired exponentially decreasing stiffness gradient in tactile discrimination, we tested two additional stiffness: linearly decreasing gradient and constant stiffness. Tactile datasets were generated under identical mechanical inputs for this two stiffness. Other classification methods show slower contact speeds and cockroach-inspired antenna mechanics enhance tactile discrimination To ensure the classification rates were not dependent on the cNMF and classification method, we also used a convolutional neural network (CNN) to classify contact objects and locations (30 classes) directly based on the tactile tensors. The structure of our networks is: INPUT(56,380,1) → CONV (15*15,32,Padding[2,2],Stride[1,1]) → batchNormalization → ReLU → MAXPOOL (2,2) → FC(50) → DROPOUT(0.25) → FC(30) → SOFTMAX → CLASSIFICATION Effect of basis duration on the shape of spatiotemporal bases in cNMF encoding To evaluate the influence of basis duration on the shape of spatiotemporal bases, we applied cNMF to the tactile tensors using a fixed number of bases ( M = 3) while varying the basis duration from 10 ms to 60 ms. The resulting spatiotemporal bases exhibited little variation in shape across different durations. Thus, we selected a basis duration of 40 ms in this study. Dataset dispersion evaluation on datasets from different contact speed and model mechanics To assess the similarity between tactile tensors in one dataset (i.e., tensors generated under the same condition—for example, 30 tactile tensors from different collision objects and locations but with the same collision speed; see Methods and Materials), we computed the Pearson correlation coefficient, structural similarity index (SSIM), mean squared error (MSE), and normalized mutual information (NMI) for each tensor against all other tensors in the dataset. For each tactile tensor, we identified its closest match based on these metrics, selecting the maximum value of Pearson correlation coefficient, SSIM, NMI, and the minimum value of MSE as evaluation values. This process was repeated for all tactile tensors to quantify the most similar counterpart for each tensor in the dataset. Finally, the average Pearson correlation, SSIM, MSE, and NMI across all comparisons were used to evaluate the overall dispersion of the dataset. Tactile tensors comparison in simulation model and robotic antenna Real-world contact experiments were conducted by colliding the robotic antenna with ball and box objects at its tip under 3 different speeds (0.270 m/s, 0.135 m/s, and 0.027 m/s). Acknowledgements Funder Information Declared United States Army Research Office, https://ror.org/05epdh915 , W911NF- 23-1-0039 Footnotes ↵ * Email: jmm1175{at}psu.edu http://doi.org/10.26207/tmsg-ad78 References 1. ↵ G. C. H. E. de Croon , J. J. G. Dupeyroux , S. B. Fuller , J. A. R. Marshall , Insect-inspired AI for autonomous robots . Science Robotics 7 ( 2022 ). 2. ↵ R. Pfeifer , C. Scheier , I. Follath , Understanding Intelligence ( MIT Press , Cambridge, MA, USA , 2001 ). 3. ↵ Z. Yu , P. R. N. Childs , Y. Ge , T. Nanayakkara , Whisker Sensor for Robot Environments Perception: A Review . IEEE Sensors Journal 24 , 28504 – 28521 ( 2024 ). OpenUrl 4. ↵ A. Demir , E. Samson , N. J. Cowan , A tunable physical model of arthropod antennae . IEEE International Conference on Robotics and Automation ( 2010 ). 5. ↵ E. Staudacher , M. Gebhardt , V. Durr , Antennal movements and mechanoreception: neurobiology of active tactile sensors . Advances in Insect Physiology 32 ( 2005 ). 6. ↵ J.-M. Mongeau , A. Demir , C. J. Dallmann , K. Jayaram , N. J. Cowan , R. J. Full , Mechanical processing via passive dynamic properties of the cockroach antenna can facilitate control during rapid running . Journal of Experimental Biology , doi: 10.1242/jeb.101501 ( 2014 ). OpenUrl Abstract / FREE Full Text 7. ↵ J. M. Camhi , E. N. Johnson , High-frequency Steering Maneuvers Mediated by Tactile Cues: Antennal Wall-Following in the Cockroach . Journal of Experimental Biology 202 , 631 – 643 ( 1999 ). OpenUrl Abstract / FREE Full Text 8. ↵ J. Okada , Y. Toh , Active tactile sensing for localization of objects by the cockroach antenna . Journal of Comparative Physiology A 192 , 715 – 726 ( 2006 ). OpenUrl CrossRef PubMed 9. ↵ A. I. Weber , M. Babaei , A. Mamo , B. W. Brunton , T. L. Daniel , S. Bergbreiter , Nonuniform structural properties of wings confer sensing advantages . J. R. Soc. Interface . 20 , 20220765 ( 2023 ). OpenUrl PubMed 10. ↵ S. A. Hires , L. Pammer , K. Svoboda , D. Golomb , Tapered whiskers are required for active tactile sensation . eLife 2 , e01350 ( 2013 ). OpenUrl CrossRef PubMed 11. ↵ B. R. Philip , The relationship of exposure time and accuracy in a perceptual task . Journal of Experimental Psychology 37 , 178 – 186 ( 1947 ). OpenUrl CrossRef PubMed 12. ↵ A. Hyafil , J. De La Rocha , C. Pericas , L. N. Katz , A. C. Huk , J. W. Pillow , Temporal integration is a robust feature of perceptual decisions . eLife 12 , e84045 ( 2023 ). OpenUrl PubMed 13. ↵ R. P. Heitz , The speed-accuracy tradeoff: history, physiology, methodology, and behavior . Front. Neurosci . 8 ( 2014 ). 14. ↵ C. M. Comer , L. Parks , M. B. Halvorsen , A. Breese-Terteling , The antennal system and cockroach evasive behavior. II. Stimulus identification and localization are separable antennal functions . Journal of comparative physiology. A, Neuroethology, sensory, neural, and behavioral physiology 189 , 97 – 103 ( 2003 ). OpenUrl CrossRef PubMed Web of Science 15. J. Okada , Y. Toh , The role of antennal hair plates in object-guided tactile orientation of the cockroach (Periplaneta americana) . Journal of Comparative Physiology A 186 , 849 – 857 ( 2000 ). OpenUrl CrossRef PubMed Web of Science 16. ↵ C. M. Harley , B. a English , R. E. Ritzmann , Characterization of obstacle negotiation behaviors in the cockroach, Blaberus discoidalis . The Journal of experimental biology 212 , 1463 – 76 ( 2009 ). OpenUrl Abstract / FREE Full Text 17. ↵ C. M. Williams , E. M. Kramer , The advantages of a tapered whisker . PloS one 5 , e8806 ( 2010 ). OpenUrl CrossRef PubMed 18. ↵ R. Schafer , T. V. Sanchez , The nature and development of sex attractant specificity in cockroaches of the genus Periplaneta. I. Sexual dimorphism in the distribution of antennal sense organs in five species . Journal of Morphology 149 , 139 – 57 ( 1976 ). OpenUrl CrossRef PubMed 19. ↵ R. Schafer , T. V. Sanchez , Antennal sensory system of the cockroach, Periplaneta americana: postembryonic development and morphology of the sense organs . The Journal of comparative neurology 149 , 335 – 54 ( 1973 ). OpenUrl CrossRef PubMed Web of Science 20. ↵ L. Meng , P. McDonnell , K. Jayaram , J.-M. Mongeau , Structure and mechanics of cockroach antennae confer flexibility and shape strain transmission for proprioception . Journal of Experimental Biology, jeb.250651 ( 2025 ). 21. ↵ N. O. Zweifel , S. A. Solla , M. J. Z. Hartmann , Statistical characterization of tactile scenes in three-dimensional environments reveals filter properties of somatosensory cortical neurons . Neuroscience [Preprint] ( 2022 ). doi: 10.1101/2022.08.03.502632 . OpenUrl Abstract / FREE Full Text 22. ↵ Y. Baba , A. Tsukada , C. M. Comer , Collision avoidance by running insects: antennal guidance in cockroaches . The Journal of experimental biology 213 , 2294 – 302 ( 2010 ). OpenUrl Abstract / FREE Full Text 23. ↵ J.-M. Mongeau , A. Demir , J. Lee , N. J. Cowan , R. J. Full , Locomotion- and mechanics-mediated tactile sensing: antenna reconfiguration simplifies control during high-speed navigation in cockroaches . Journal of Experimental Biology 216 , 4530 – 4541 ( 2013 ). OpenUrl Abstract / FREE Full Text 24. ↵ N. J. Cowan , J. Lee , R. J. Full , Task-level control of rapid wall following in the American cockroach . Journal of Experimental Biology 209 , 1617 – 1629 ( 2006 ). OpenUrl Abstract / FREE Full Text 25. ↵ P. McDonnell , L. Meng , H. K. Hariprasad , A. Hedrick , E. Miscles , S. Gilinsky , J.-M. Mongeau , K. Jayaram , Design of a bioinspired robophysical antenna for insect-scale tactile perception and navigation . arXiv arxiv: 2507.23719 [Preprint] ( 2025 ). doi: 10.48550/arXiv.2507.23719 . OpenUrl CrossRef 26. ↵ H. J. Chiel , L. H. Ting , O. Ekeberg , M. J. Z. Hartmann , The brain in its body: motor control and sensing in a biomechanical context . The Journal of Neuroscience 29 , 12807 – 14 ( 2009 ). OpenUrl Abstract / FREE Full Text 27. ↵ L. Chen , S. Karilanova , S. Chaki , C. Wen , L. Wang , B. Winblad , S.-L. Zhang , A. Özçelikkale , Z.-B. Zhang , Spike timing–based coding in neuromimetic tactile system enables dynamic object classification . Science 384 , 660 – 665 ( 2024 ). OpenUrl PubMed 28. ↵ Y. Massalim , Z. Kappassov , H. A. Varol , V. Hayward , Robust Detection of Absence of Slip in Robot Hands and Feet . IEEE Sensors J . 21 , 27897 – 27904 ( 2021 ). OpenUrl 29. ↵ L. Chittka , P. Skorupski , N. E. Raine , Speed–accuracy tradeoffs in animal decision making . Trends in Ecology & Evolution 24 , 400 – 407 ( 2009 ). OpenUrl PubMed 30. ↵ M. C. Potter , B. Wyble , C. E. Hagmann , E. S. McCourt , Detecting meaning in RSVP at 13 ms per picture . Atten Percept Psychophys 76 , 270 – 279 ( 2014 ). OpenUrl CrossRef PubMed 31. ↵ E. Gamzu , E. Ahissar , Importance of Temporal Cues for Tactile Spatial-Frequency Discrimination . J. Neurosci . 21 , 7416 – 7427 ( 2001 ). OpenUrl Abstract / FREE Full Text 32. ↵ G. Carvell , D. Simons , Biometric analyses of vibrissal tactile discrimination in the rat . J. Neurosci . 10 , 2638 – 2648 ( 1990 ). OpenUrl Abstract / FREE Full Text 33. ↵ J. H. Solomon , M. J. Hartmann , Robotic whiskers used to sense features . Nature 443 , 525 – 525 ( 2006 ). OpenUrl CrossRef PubMed Web of Science 34. ↵ J.-H. Dirks , V. Dürr , Biomechanics of the stick insect antenna: damping properties and structural correlates of the cuticle . Journal of the mechanical behavior of biomedical materials 4 , 2031 – 42 ( 2011 ). OpenUrl PubMed 35. ↵ H. Rajabi , A. Shafiei , A. Darvizeh , S. N. Gorb , V. Dürr , J.-H. Dirks , Both stiff and compliant: morphological and biomechanical adaptations of stick insect antennae for tactile exploration . Journal of The Royal Society Interface 15 , 20180246 ( 2018 ). OpenUrl PubMed 36. ↵ D. C. Sandeman , Physical Properties, Sensory Receptors and Tactile Reflexes of the Antenna of the Australian Freshwater Crayfish Cherax Destructor . Journal of Experimental Biology 141 , 197 – 217 ( 1989 ). OpenUrl Abstract / FREE Full Text 37. ↵ A. Krishnan , S. P. Sane , “ Antennal Mechanosensors and Their Evolutionary Antecedents ” in Advances in Insect Physiology ( Elsevier , 2015 ; https://linkinghub.elsevier.com/retrieve/pii/S0065280615000260 ) vol. 49 , pp. 59 – 99 . OpenUrl 38. ↵ S. N. Zill , J. Schmitz , S. Chaudhry , A. Büschges , Force encoding in stick insect legs delineates a reference frame for motor control . Journal of Neurophysiology 108 , 1453 – 1472 ( 2012 ). OpenUrl CrossRef PubMed Web of Science 39. ↵ J. Ruben , Somatotopic Organization of Human Secondary Somatosensory Cortex . Cerebral Cortex 11 , 463 – 473 ( 2001 ). OpenUrl CrossRef PubMed Web of Science 40. ↵ N. C. Klapoetke , A. Nern , E. M. Rogers , G. M. Rubin , M. B. Reiser , G. M. Card , A functionally ordered visual feature map in the Drosophila brain . Neuron 110 , 1700 - 1711 .e6 ( 2022 ). OpenUrl CrossRef PubMed 41. ↵ H. Watanabe , Y. Koike , K. Tateishi , M. Domae , H. Nishino , F. Yokohari , Two types of sensory proliferation patterns underlie the formation of spatially tuned olfactory receptive fields in the cockroach Periplaneta americana . Journal of Comparative Neurology 526 , 2683 – 2705 ( 2018 ). OpenUrl CrossRef PubMed 42. ↵ H. Watanabe , S. S. Haupt , H. Nishino , M. Nishikawa , F. Yokohari , Sensillum-specific, topographic projection patterns of olfactory receptor neurons in the antennal lobe of the cockroach Periplaneta americana . J of Comparative Neurology 520 , 1687 – 1701 ( 2012 ). OpenUrl 43. ↵ H. Ren , L. Yang , H. Chang , T. Zhang , G. Li , X. Yang , Y. Tang , W. Shang , Y. Shen , A robust and omnidirectional-sensitive electronic antenna for tactile-induced perception . Nat Commun 16 , 3135 ( 2025 ). OpenUrl PubMed 44. ↵ S. Pyo , J. Lee , K. Bae , S. Sim , J. Kim , Recent Progress in Flexible Tactile Sensors for Human-Interactive Systems: From Sensors to Advanced Applications . Advanced Materials 33 , 2005902 ( 2021 ). OpenUrl 45. ↵ S. V. Kapitskii , Morphology of the antenna of the male American cockroach Periplaneta americana . Journal of Evolutionary Biochemistry and Physiology 20 , 59 – 66 ( 1984 ). OpenUrl 46. ↵ M. J. D. Powell , An efficient method for finding the minimum of a function of several variables without calculating derivatives . The Computer Journal 7 , 155 – 162 ( 1964 ). OpenUrl CrossRef 47. ↵ N. O. Zweifel , N. E. Bush , I. Abraham , T. D. Murphey , M. J. Z. Hartmann , A dynamical model for generating synthetic data to quantify active tactile sensing behavior in the rat . Proc. Natl. Acad. Sci. U.S.A . 118 , e2011905118 ( 2021 ). OpenUrl Abstract / FREE Full Text 48. ↵ E. Todorov , T. Erez , Y. Tassa , “ MuJoCo: A physics engine for model-based control ” in 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems ( IEEE , 2012 ), pp. 5026 – 5033 . 49. ↵ E. Todorov , “ Convex and analytically-invertible dynamics with contacts and constraints: Theory and implementation in MuJoCo ” in 2014 IEEE International Conference on Robotics and Automation (ICRA) ( IEEE , Hong Kong, China , 2014 ; http://ieeexplore.ieee.org/document/6907751/ ), pp. 6054 – 6061 . 50. ↵ A. Hoffmann , E. Couzin-Fuchs , Active smelling in the American cockroach . Journal of Experimental Biology 226 , jeb245337 ( 2023 ). OpenUrl CrossRef PubMed 51. ↵ Y. Shao , V. Hayward , Y. Visell , Compression of dynamic tactile information in the human hand . Science Advances 6 , eaaz1158 ( 2020 ). OpenUrl FREE Full Text 52. ↵ P. O. Hoyer , Non-negative Matrix Factorization with Sparseness Constraints . J. Mach. Learn. Res . 5 , 1457 – 1469 ( 2004 ). OpenUrl 53. ↵ J.-M. Mongeau , S. N. Sponberg , J. P. Miller , R. J. Full , Sensory processing within cockroach antenna enables rapid implementation of feedback control for high-speed running maneuvers . Journal of Experimental Biology 218 , 2344 – 54 ( 2015 ). OpenUrl Abstract / FREE Full Text 54. ↵ N. Doshi , B. Goldberg , R. Sahai , N. Jafferis , D. Aukes , R. J. Wood , J. A. Paulson , “ Model driven design for flexure-based Microrobots ” in 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) ( IEEE , Hamburg, Germany , 2015 ; http://ieeexplore.ieee.org/document/7353959/ ), pp. 4119 – 4126 . 55. ↵ T. L. Hedrick , Software techniques for two- and three-dimensional kinematic measurements of biological and biomimetic systems . Bioinspiration & biomimetics 3 , 034001 ( 2008 ). OpenUrl PubMed View the discussion thread. Back to top Previous Next Posted October 21, 2025. Download PDF Data/Code Email Thank you for your interest in spreading the word about bioRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. Your Email * Your Name * Send To * Enter multiple addresses on separate lines or separate them with commas. You are going to email the following Physically intelligent soft antennae enhance tactile perception by active touch Message Subject (Your Name) has forwarded a page to you from bioRxiv Message Body (Your Name) thought you would like to see this page from the bioRxiv website. Your Personal Message CAPTCHA This question is for testing whether or not you are a human visitor and to prevent automated spam submissions. Share Physically intelligent soft antennae enhance tactile perception by active touch Lingsheng Meng , Parker McDonnell , Kaushik Jayaram , Jean-Michel Mongeau bioRxiv 2025.10.20.683587; doi: https://doi.org/10.1101/2025.10.20.683587 Share This Article: Copy Citation Tools Physically intelligent soft antennae enhance tactile perception by active touch Lingsheng Meng , Parker McDonnell , Kaushik Jayaram , Jean-Michel Mongeau bioRxiv 2025.10.20.683587; doi: https://doi.org/10.1101/2025.10.20.683587 Citation Manager Formats BibTeX Bookends EasyBib EndNote (tagged) EndNote 8 (xml) Medlars Mendeley Papers RefWorks Tagged Ref Manager RIS Zotero Tweet Widget Facebook Like Google Plus One Subject Area Bioengineering Subject Areas All Articles Animal Behavior and Cognition (7633) Biochemistry (17681) Bioengineering (13890) Bioinformatics (41929) Biophysics (21446) Cancer Biology (18586) Cell Biology (25492) Clinical Trials (138) Developmental Biology (13374) Ecology (19897) Epidemiology (2067) Evolutionary Biology (24308) Genetics (15606) Genomics (22497) Immunology (17736) Microbiology (40385) Molecular Biology (17175) Neuroscience (88584) Paleontology (666) Pathology (2831) Pharmacology and Toxicology (4822) Physiology (7641) Plant Biology (15149) Scientific Communication and Education (2045) Synthetic Biology (4293) Systems Biology (9822) Zoology (2271)