Thermoregulatory integration in hand prosthesis and humanoid robots through blood vessel simulation

In this paper, we introduce a new approach to give robotic faces a thermal signature similar to that of humans and equip prosthetic or robotic hands with a lifelike temperature. This enhances their detection by infrared cameras and promotes more natural interactions between humans and robots. This method integrates a temperature regulation system into arti�cial skin, drawing inspiration from the human body's natural temperature control via blood �ow. Central to this technique is a �ber network simulating blood vessels within the arti�cial skin. Water �ows through these �bers under speci�c temperature and �ow conditions, forming a controlled heat release system. The heat emission can be adjusted by changing the dilation of these �bers, primarily by modulating the frequency of circulation. Our �ndings indicate that this approach can replicate the varied thermal characteristics of different human face and hand areas. Consequently, robotic faces appear more human-like in infrared images, aiding their identi�cation by infrared cameras. At the same time, prosthetic hands achieve a more natural temperature, reducing the typical discomfort felt in direct contact with synthetic limbs. This study sought to address the challenges faced by the users of prosthetic hands. It also heralds a promising direction in humanoid robotics, fostering improved tactile interactions and rede�ning human–robot relationships. The innovative technique paves the way for further advancements, blurring the lines between arti�cial aids and natural biological systems.


Introduction
Human skin acts as the primary barrier and interface with the external environment.It shields the body from external disturbances and skillfully modulates internal mechanisms to adapt to external shifts.At its core, it is instrumental in maintaining standard physiological processes.The skin's roles encompass protection, temperature regulation, sensation, secretion, vitamin D production, facial expressions, regeneration, and immune reactions.Additionally, it plays a signi cant part in tactile sensing, allowing individuals to identify objects through touch.Recent advancements have highlighted the creation of synthetic skin sensors.2][3][4][5] Hand prosthetics, a major application area for arti cial skin, have seen remarkable innovations, enabling prosthetic limbs to simulate tactile and nociceptive sensations similar to natural limbs. 6,7Simultaneously, there's a push to integrate stress or pressure sensors into arti cial skin, enhancing tactile and pressure feedbacks. 8,9A notable study has also shed light on a soft human-machine interface, which combines ultra-sensitive multimodal physicochemical sensors, facilitating the detection of trace amounts of harmful compounds. 10 the realm of humanoid robots, the goal of tactile sensors is to perceive and distinguish a variety of tactile stimuli, from pressure and temperature to vibration.While many past studies have delved into skin material (soft vs. hard) and interaction dynamics (robot-focused vs. human-focused), 11,12 tactile sensations have often been overlooked.Recent efforts have successfully replicated the texture and rmness of real skin by simulating its exterior, fatty, and muscle layers. 3,13However, the feeling of temperature remains an essential aspect of tactile experience.5][16][17] As robots become more commonplace in human routines, their inherently cold touch might elicit discomfort, 18,19 especially when robots take on roles in more personal contexts, such as in healthcare or service industries.Therefore, the advancement of humanoid skin technology should aim to incorporate features that replicate the natural warmth of human skin.The human circulatory system enables a vast array of complex and interrelated functions, centered on the circulatory pathways of the bloodstream.Thermoregulation is a primary function of this system, crucial for homeothermic beings such as humans.It allows the maintenance of a constant core body temperature, approximately 37°C, irrespective of external environmental changes.This intricate process involves various physiological responses: modulation of heart rate, vasodilation and vasoconstriction of blood vessels, sweating, non-shivering thermogenesis, and thermogenic activities in brown adipose tissues. 20,21Central to thermoregulation is the heart's role in ensuring homeostasis.3][24] Blood vessels are essential in this process, directing the heat generated by metabolic activities.They use blood as a heat distribution medium and manage heat dissipation by dilating or constricting in response to external temperature changes. 25,26is study entailed the development of a groundbreaking arti cial skin that replicates the thermoregulatory functions inherent to human skin.It draws inspiration from the human vascular system's role in thermoregulation.We employed stretchable and elastic silicone to create bers akin to blood vessels, each having a hollow diameter of approximately 500 µm.These bers were embedded within a silicone-based arti cial skin layer, allowing for exible movements, including wrinkling, stretching, and bending, culminating in a thermoregulatory skin system.Within this design, water, acting as a heat medium, circulated through the vessel-mimicked bers.This circulation is reminiscent of the heart pumping blood throughout the body, regulated at various temperatures, ow rates, and frequencies.
We conducted a comprehensive analysis of the volume change patterns of these arti cial bers based on water parameters, linking them with heat dissipation properties.Additionally, we studied the thermal infrared temperature and distribution patterns of this arti cial skin concerning variations in skin thickness and ber con gurations.Results from the experiments on parameters including water temperature, ow rate, frequency, skin thickness, and ber arrangement facilitated the mimicking of thermal infrared temperature and distribution patterns observed in human faces and hands.This innovation offers solutions to challenges faced by individuals using prosthetic hands, potentially reducing the discomfort during skin-to-skin interactions.In the future, this technology could nd extensive use in robotic limbs and faces, enhancing the natural feel and comfort of human-robot interactions.

Materials and Methods
Fabrication of blood vessel-mimicked ber and control of heat dissipation characteristics.We produced a ber resembling a blood vessel using a meticulous process.Liquid silicone (Eco ex 00-35, Smooth-On, Inc.) was applied and cured onto a carbon rod with a 0.5 mm diameter, obtained from RC Lab.The silicone compound was a blend of Part A (a prepolymer) and Part B (a curing agent), mixed in a 1:1 mass ratio.A silver foil, laid at on a work surface, acted as the base for the silicone application.The carbon rod, attached to an electric drill (model L514, ES), was set upon this layer.The drill was operated at approximately 35 rpm to ensure the rod received a uniform silicone coating.Before the 5-min curing process, the rod was continuously rotated to prevent silicone displacement due to gravity.This process was repeated four times to achieve the desired rod thickness.After the fth coat, the silicone-coated rod had an external diameter of approximately 2 mm.The silicone was then separated from the carbon rod, resulting in a ber resembling a blood vessel with an internal hollow diameter of approximately 500 µm.For the circulation system's water in ow, set to maintain temperatures between 30-70°C, we used a 2 L beaker lled with 1.8 L of water and placed on a heating plate (model MSH-20D, DAIHAN Scienti c).An external temperature probe (model DH.WMH03021, DAIHAN Scienti c) connected to the plate ensured accurate temperature control.A peristaltic pump (model BT300-2J, Longer), accompanied by a 1,250 mm long and 2.4 mm diameter tube (19# size, Longer), facilitated water ow into the ber.A circulation system was established: water heated in the beaker was pushed into the ber by the pump and then returned to the beaker.The 19# tube connected to the beaker and three 400 mm ber lengths through a 3way connector (model QN659250, NEEDLE STORE).The ber's end was linked back to the beaker using an 800 mm 19# tube.A micro silicone tube (2 mm diameter) served as a bridge for these connections.The water ow rate in the ber, ranging from 1.10-11.0cc/m, was regulated by adjusting the pump's speed between 10 and 120 rpm.An Arduino system integrated with the pump allowed for precise control of water in ow frequency, adjustable between 1 to 8 Hz.The system underwent experimental testing to assess its reliability, speci cally checking for potential leaks at tube junctions under different water ow conditions.
Fabrication of arti cial skin in the shape of plane, face, and hand.The procedures for fabricating arti cial skin in planar, facial, and hand forms are outlined below: Planar Arti cial Skin Fabrication: The silicone rubber used (Mold Max 14 NV, Smooth-On, Inc.) was a combination of Part A (prepolymer) and Part B (curing agent), mixed in a 10:1 mass ratio.For the desired shade of the arti cial skin, 0.6 ml of apricotcolored silicone pigment solution (YOUNGNAM) was added to 300 g of the silicone rubber.Once thoroughly mixed, the concoction was poured into a metal tray measuring 599 × 402 × 30 mm 3 to create four distinct thicknesses: 0.5, 1.0, 2.0, and 3.0 mm.This mixture was then left to cure in ambient conditions for 4 h.Facial Arti cial Skin Fabrication: A facial shape was captured by applying a 1 mm thick plaster bandage onto a mannequin face, followed by air drying for 12 h.For replicating the face, a mold was crafted using silicone mold rubber (Mold Max 60, Smooth-On, Inc.).This involved mixing Part A (prepolymer) and Part B (curing agent) in a 100:3 mass ratio.The mannequin face impression was immersed in this silicone mixture.After curing for 12 h, the impression was removed, providing a mold for facial design.The arti cial skin mixture was poured into this mold and allowed to set for another 4 h, producing a 1 mm thick facial skin.A release agent (ER-200, Mann) was sprayed within the mold to facilitate easy removal of the developed skin.
Hand-Shaped Arti cial Skin Fabrication: A dense liquid silicone rubber was applied over a bare robotic hand, only revealing its skeletal framework, and then cured in the open air for 4 h.The previously described ber, which resembles blood vessels, was laid over this silicone layer, imitating the heat patterns seen in real human hands.Above this con guration, a 1.0 mm thick planar arti cial skin was positioned.To ensure this, the at skin was cut into six distinct pieces to cover the ve ngers and the back of the hand.
Thermoregulation arti cial skin applied to mannequin's face and robot's hand.The thermoregulation arti cial skin, developed to mirror the thermal infrared features of a human face and hand, utilized two pumps: peristaltic pump A and peristaltic pump B (BT100-2J, Longer).The comprehensive fabrication processes for both face and hand designs are detailed as follows: Face-Shaped Thermoregulation Arti cial Skin Fabrication: Six blood vessel-mimicked bers were linked to both peristaltic pumps A and B using 3-way connectors, with each pump connected to three strands.These bers were then arranged on a mannequin face, following the thermal distribution patterns observed in an actual human face.These ber strands, each 800 mm in length, were deliberately placed 2-5 mm apart from one another.Over these bers, a face-shaped arti cial skin was placed.To facilitate circulation, peristaltic pump A circulated water at 54°C, operating at 5.39 cc/min and 2 Hz for 15 min.Concurrently, peristaltic pump B functioned at 4.47 cc/min and 2 Hz, using water at 52°C for the same duration.
Hand-Shaped Thermoregulation Arti cial Skin Fabrication: Nine bers resembling blood vessels were integrated into the design.Peristaltic pump A was connected to six bers via one 3-way connector and three Y connectors (QN830160, NEEDLE STORE), while pump B connected directly to three bers through one 3-way connector.In accordance with the thermal distribution of a genuine hand, these bers were positioned atop a silicone layer on a robotic hand's skeletal structure.Similar to the face bers, these strands were also 800 mm in length and were spaced between 1 to 5 mm apart.Atop these bers, sections of a plane-shaped arti cial skin were layered.For circulation, over a period of 15 min, pump A operated at 6.26 cc/min and 2 Hz with 52°C water, whereas pump B worked at 5.39 cc/min and 2 Hz, circulating water at 50.5°C.
Measuring the properties of blood vessel-mimicked bers and thermoregulation arti cial skin.In the nal stage of this study, the engineered bers, which mimic blood vessels, were subjected to thorough scrutiny to evaluate their structural and mechanical characteristics.Utilizing a eld effect scanning electron microscope (FE-SEM; JSM-7610F PLUS, JEOL), we delved into a profound examination of the surface and the cross-sectional architecture of these bers.This provided invaluable information regarding their morphological features.Additionally, their mechanical attributes, including the resilience and endurance of the material under various stressors, were determined using a universal testing machine (UTM; TD-U01, T&DORF Inc.).
To deepen our understanding of the capabilities and effectiveness of the thermoregulation arti cial skin, we embarked on a sequence of tests.These were designed to investigate potential disruptions or interferences concerning thermal infrared temperature and distribution.Our experimental framework employed a hot plate, calibrated to speci c temperatures of 30, 50, and 70°C, alongside ice water kept at its freezing threshold.These elements acted as the heating and cooling agents, respectively.Positioned beneath the arti cial skin, they facilitated observations on potential shifts or disruptions in the thermal features.Instrumental to this stage was the use of a thermal infrared imaging camera (T420, FLIR systems).This device captured infrared images of both the ber and the skin.Subsequent analysis of these infrared captures was facilitated through the FLIR Tools software.This analysis illuminated the temperature oscillations, presenting a holistic view of the arti cial skin's thermoregulatory pro ciency.This evaluation was integral in con rming the arti cial skin's capacity to accurately re ect the inherent thermal attributes of human skin.

Results
The human body's thermoregulatory mechanism is crucial in maintaining a relatively consistent body temperature, around 36.5°C, despite external environmental shifts.As depicted in Fig. 1a, a thermal infrared imaging camera illustrates the diverse temperature spread across the skin's various regions.The core organs of the body contribute to approximately 70% of total body heat, with the residual heat being sourced from the skin and peripheral tissues.Given the modest heat generation of skin tissues, temperature disparities manifest across different skin regions.These disparities are majorly dictated by the warmth of arterial pathways, in uenced by central organs, juxtaposed with the cooling veins at the surface.
Additionally, the blood vessels located beneath the skin surface play a pivotal role in determining the core body temperature across varying environmental conditions by adjusting constriction/dilation rates and the velocity of circulation.Within this framework, simulating such a system in a humanoid cover, fabricated from metal as illustrated in Fig. 1b, can enable the portrayal of a thermal infrared image similar to that of human skin, as presented in Fig. 1c.Notably, humans possess the sensitivity to discern subtle temperature variations, approximately 0.5°C. 27,28Thus, ensuring a prosthetic or robotic hand aligns with human body temperature could potentially eliminate discomfort and reluctance during tactile encounters, such as handshakes.
In this study, we developed a exible, elastic ber, which imitates blood vessels, using water to regulate heat transfer and dispersion processes.The choice of water stemmed from its appreciable thermal conductivity of 0.604 W/m•K at 21.11°C, surpassing other common temperature regulating uids such as glycerin, ethylene glycol, and engine oil, which have conductivities of 0.289, 0.249, and 0.145 W/m•K, respectively.The arti cial skin was created using silicone rubber, re ecting the thermal conductivity attributes of human skin.This provided an essential base layer over the organized blood vessel-mimicked bers for our experiments.A central component of this undertaking was the precise control of heat originating from the bers positioned beneath the silicone rubber layer.This was achieved by meticulously managing the water's temperature and ow rate.As a result, we successfully recreated and maintained a thermal ambiance similar to the human body on the thermoregulation arti cial skin, marking a landmark development in biomechanical engineering.
We designed a circulatory system, simulating the thermoregulatory processes of the human heart and blood vessels.This system includes a peristaltic pump, heated water, and bers resembling blood vessels, as depicted in Fig. 2a.The peristaltic pump operates in a manner similar to the human heart, directing the ow of water, with the heated water serving as a heat transfer medium, analogous to blood in humans.This pump facilitates control of both the ow rate and the pulse frequency of the heated water directed to the blood vessel-mimicked ber.The ber, with an estimated diameter of 2 mm, is designed to mimic a blood vessel and contains a hollow core with a diameter of approximately 500 µm, as highlighted in Fig. 2b.Given that human blood vessels frequently constrict and dilate for optimal heat regulation, the ber designed to simulate this was crafted from a exible silicone material, ensuring it could accommodate these dynamic changes.The resulting ber exhibited mechanical properties with approximately 700% strain and a stress of 1.2 MPa upon reaching its rupture point, as illustrated in Supplementary Fig. 1.
We meticulously regulated the temperature, ow rate, and frequency of water owing through the ber imitating blood vessels to control its heat dissipation intensity.The most direct approach to regulate the ber's temperature is by adjusting the internal water temperature.Figure 2c illustrates the temperature uctuations in the ber in relation to variations in the internal water temperature, maintaining consistent ow rates and frequencies at 4.47 cc/min and 2 Hz, respectively.As the water temperature rose from 30 to 70°C, the temperature of the ber increased from 25.4 to 43.1°C.Figure 2d illustrates that, maintaining a water temperature of 60°C and a frequency of 2 Hz, the ber's temperature climbed from 23.8 to 43.3°C as the ow rate varied between 1.10 and 5.39 cc/min.Figure 2e graphically depicts the ber's temperature reactions under varying water temperatures (30-70°C) and ow rates (1.10-11.0cc/min).These ndings suggest that the ber's temperature is directly proportional to increases in both the water's temperature and ow rate.However, a signi cant water temperature increase (a 40°C jump from 30 to 70°C) resulted in a more moderate temperature rise in the ber (an approximately 24°C increment from 27.3 to 51.1°C), given ow conditions of 11 cc/min and 2 Hz.This behavior can be understood through Fourier's law of heat conduction, which states that heat transfer is ampli ed with greater temperature differences and that higher temperatures result in increased heat losses.The relevant equation is presented subsequently: where ΔQ denotes the heat transfer, Δt represents the time change, k represents thermal conductivity, ΔT is the temperature gradient between two entities, A is the cross-sectional area in contact, and x denotes the distance.Fundamentally, as the temperature of the internal water rises, the consequent heat loss intensi es.This manifests in a growing disparity between the temperature of the water and that of the ber, with differences of 2.7, 6.3, 10.5, 11.7, and 17.9°C corresponding to the paired water and ber temperatures of 30/27.3,40/33.7,50/39.5, 60/48.3, and 70/52.Furthermore, the temperature of the heated water tends to diminish as it courses through the ber resembling a blood vessel.The longer the water resides within the ber, the more pronounced the heat dissipation.Hence, an increased ow rate accelerates the entry and circulation of the heated water via the peristaltic pump, minimizing the time the heated water stays-and subsequently cools-within the ber.This culminates in a rise in the ber's temperature, as elucidated in Supplementary Fig. 2. It is noteworthy that even when the water temperature remains consistent, adjustments to the ow rate can modulate the ber's temperature.
Figures 2f and 2g display thermal infrared images and a corresponding temperature chart, respectively, revealing the degree of heat dissipation within the ber as dictated by the ow frequency of the internal water.Altering the frequency, while retaining a uniform ow rate, results in a variable volume of water being infused into the ber per cycle.At higher frequencies, smaller water volumes are introduced more often, while at lower frequencies, a greater volume is introduced less frequently.For example, with a ow of 4.47 cc/min at 1 Hz, approximately 0.075 cc of water is infused 60 times per minute.In contrast, maintaining this ow rate but with an 8 Hz frequency, approximately 0.009 cc/min of water is infused a remarkable 480 times per minute.With increasing frequency, a corresponding gradual decrease in the temperature of the ber mimicking a blood vessel is observed.At a 60°C ow rate of 4.47 cc/min, the ber's temperatures were approximately 41.4, 41.3, 40.2, 38.5, and 38.3°C for frequencies of 1, 2, 4, 6, and 8 Hz, respectively.At a 60°C ow rate spanning from 1.10-11.0cc/min, and with frequency variations from 1 to 8 Hz, the average alteration in ber temperature was − 3.3 ± 0.59°C, as depicted in Supplementary Fig. 3.This information corroborates the feasibility of nely tuning the temperature of the ber simulating a blood vessel through meticulous management of ow frequency.
Figure 2h depicts the time-dependent temperature variations of the ber resembling a blood vessel, based on the activation or deactivation of the water ow.Both the water temperature and frequency were maintained at 60°C and 2 Hz, respectively.Upon initiating water circulation, the temperature of the ber promptly started to rise.A signi cant observation was that an increased ow rate expedited the ber's reaching of its peak temperature, which then stabilized.Following the cessation of water circulation, the temperature swiftly decreased, settling around 25°C after 100 s.
Within the realm of human physiology, when the core body temperature drops below 37°C, the hypothalamus, responsible for thermoregulation, triggers arteriolar vasoconstriction via the sympathetic nervous system.This action reduces blood ow to the skin, thereby minimizing temperature loss through radiation and convection.Conversely, if the body temperature surpasses 37°C, the hypothalamus induces vasodilation, increasing blood ow to the skin and subsequently enhancing heat dissipation (Fig. 3a). 26ranslating this to vascular heat dissipation dynamics: vasoconstriction is synonymous with decreased heat loss, whereas vasodilation intensi es it.
The selected material for the ber simulating a blood vessel, silicone rubber, possesses notable elasticity.When water ows through the ber, it induces internal pressure, causing the ber to dilate (Fig. 3b).Torricelli's theorem elucidates the relationship between ow rate and pressure: where is the ow rate, g represents gravitational acceleration, P is the pressure, and represents the speci c gravity.It is apparent that an increase in ow rate leads to a quadratic rise in pressure.Figure 3c documents the volume changes relative to the internal water ow rate of the ber simulating a blood vessel (as note in Supplementary Video 1).At a ow rate of 11 cc/min, a maximal volume uctuation of 3.5% was observed (operating conditions: 60°C, 2 Hz).Notably, the temperature of the water had no impact on volume alterations.Modifying the frequency, while sustaining a uniform ow rate, results in varying volumes of water being introduced per cycle, thereby adjusting the internal pressure.Elevated frequencies lead to smaller water volumes being introduced more often, resulting in a decrease in internal pressure.As illustrated in Fig. 3d, under the operating conditions of 60°C and 5.39 cc/min, the volume change of the ber reduced from 1.9-1.3%as the frequency increased from 1 Hz to 8 Hz (refer to Supplementary Fig. 4).Concurrently, the temperature of the ber dropped from 43.2°C (at 1 Hz) to 40.0°C (at 8 Hz).Hence, by controlling the extent of dilation in the ber simulating a blood vessel, similar to the physiological processes of vasoconstriction and vasodilation, heat dissipation can be effectively modulated.
Similar to the positioning of blood vessels beneath human skin for temperature regulation, silicone rubber simulates the role of skin by covering the ber that mimics a blood vessel, creating a synthetic skin with thermoregulatory properties.The thermal conductivity of silicone rubber is approximately 0.2 W/m•K, 29 which closely parallels the thermal conductivity of human skin at 0.21 W/m•K. 30The thermal infrared temperature and distribution within this synthetic skin are determined by its thickness and the organization of the underlying bers that resemble blood vessels.The thermal characteristics of the synthetic skin in relation to its thickness and the thermal interference effects resulting from the arrangement of the bers must be elucidated in order to accurately reproduce the thermal infrared temperature and distribution seen in human planar skin.
Figure 4 illustrates the thermal infrared temperature and distribution patterns of the thermoregulatory arti cial skin, dependent on the skin's thickness and the arrangement of the bers mimicking blood vessels (operating conditions: 60°C, 4.47 cc/min, 2 Hz).Positioned beneath the thermoregulatory arti cial skin, these bers' resulting thermal infrared temperature and distribution were analyzed on the skin's surface.The 80 × 80 mm 2 arti cial skin segment, composed of silicone rubber, had varying thicknesses: 0.5, 1.0, 2.0, and 3.0 mm.A single 400 mm-long ber, designed in a serpentine pattern, underwent spacing adjustments at 15, 10, and 5 mm intervals to study the thermal dynamics (Fig. 4a).
Heat radiating from the ber resembling a blood vessel spreads radially, moving from the base to the surface of the arti cial skin.As a result, an increase in the synthetic skin's thickness leads to a noticeable reduction in its thermal temperature.Additionally, the representation of the ber in the thermal distribution images becomes increasingly blurred (Figs.4b-4d).Reduced spacing between the bers ampli es the thermal interference effect, leading to a temperature rise in the sections of the synthetic skin situated between bers (Fig. 4e).The thermal infrared images suggest that an even temperature distribution arises when the ber spacing is limited to 5 mm and the synthetic skin's thickness is 1.0 mm or greater.
Prosthetic hands and humanoid robots tted with thermoregulatory arti cial skin contain numerous semiconductor devices and actuating components.These elements can generate localized heat.Our study examined conditions where a thermal temperature close to 36.5°C, akin to human skin, can be consistently maintained, even in the presence of indirect heat sources.A square frame, measuring 2 mm in thickness and covering an area of 40 mm 2 , was placed over either a heating source (with temperatures of 30, 50, or 70°C) or a cooling source set at 0°C.Centered on this frame, within a 25 mm 2 space, a ber imitating a blood vessel was arranged in a serpentine pattern, with 5 mm intervals between each loop, as shown in Fig. 5a.This con guration was subsequently enveloped by an arti cial skin layer, 1 mm in thickness and spanning an area of 40 mm 2 , as illustrated in Fig. 5b.
After letting the assembly sit for 5 min without any water circulation, the registered temperatures on the arti cial skin were 13.5 ± 0.8, 26.4 ± 0.1, 38.0 ± 0.4, and 47.4 ± 0.5°C, aligning with source temperatures of 0, 30, 50, and 70°C, respectively.Evidently, the temperature of the arti cial skin is in uenced by the thermal conditions of the source below it.However, by initiating water ow through the ber that simulates a blood vessel under speci c ow conditions, we stabilized the temperature of the arti cial skin near the optimal 36.5°C.Within the arti cial skin's surface, the areas directly above the ber -the primary sites of thermoregulation -were clearly identi able (marked by a white dotted-line perimeter).
Using a cooling source at 0°C, the thermoregulated area maintained a temperature of 36.1 ± 1.3°C under ow conditions of 70°C, 4.47 cc/min, and 2 Hz.When the heating source was set to temperatures of 30, 50, and 70°C, the temperature measurements for the thermoregulated area registered at 36.2 ± 0.6, 36.2 ± 0.4, and 36.7 ± 1.0°C, respectively, under their speci c ow parameters.
Human skin contains a complex network of blood vessels responsible for distributing heat, oxygen, and nutrients throughout the body.Figure 6a presents a depiction of the primary blood vessels distributed across the human face.To simulate the thermal infrared temperature and distribution of a human face, six segments of bers mimicking blood vessels were arranged on a mannequin's face, as illustrated in Figs.6b and 6c.These bers were then covered by the speci cally designed arti cial skin, creating a thermoregulatory layer for the mannequin's facial region.These bers were connected to two peristaltic pumps, each handling three ber segments, to facilitate the circulation of heated water.
An infrared image captured using an infrared camera displays the temperature distribution across an actual human face (Fig. 6d).Notably, higher temperatures are observed around the eyes, nose, and mouth compared to the cooler regions of the cheeks.The temperatures recorded around the eyes and nose averaged around 34.2°C, while the cheeks remained at a relatively cooler 31.1°C.Figure 6e presents both conventional and thermal infrared images of the mannequin's face equipped with the thermoregulatory skin.The bers mimicking blood vessels were strategically arranged: three segments surrounding the eyes, lips, and chin with spacing ranging from 1 to 3 mm, and another three segments traversing the cheeks, eyes, nose, and lips, spaced 4 to 5 mm apart.By circulating water at temperatures of 54 and 52°C at speci c ow rates through these bers, certain facial regions, particularly around the eyes and nose, exhibited higher temperatures, registering approximately 34.5 and 33.9°C respectively (as noted in Supplementary Fig. 5).In contrast, the cheeks remained cooler at about 31.2°C.Figure 6f presents both conventional and thermal infrared images of a human right hand, highlighting that the extremities, especially the ngertips, are warmer than the dorsal (back) region of the hand.Speci cally, the thumb and middle nger tips showed temperatures of 33.4 and 33.1°C respectively, while the dorsal region remained cooler, with temperatures between 30.0 and 31.2°C.Figure 6g offers a comparison between the thermoregulatory skin on a robotic hand and the thermal distribution of a human hand.Without the thermoregulatory skin, the robotic hand did not produce discernible infrared radiation (as noted in Supplementary Fig. 6).To simulate the infrared temperature and distribution consistent with a human hand, a thermoregulatory skin comprising nine segments of the blood vesselmimicking bers was crafted and attached to the robot hand.Two bers were designated for the thumb, while the remaining ngers received one ber each, spaced between 1 to 4 mm apart.On the dorsal side, three ber segments were distributed at intervals between 2 to 5 mm (as noted in Supplementary Fig. 7).
With water heated to prede ned temperatures being directed through these bers at established ow rates, the thermoregulatory skin on the robotic hand effectively mirrored the thermal distribution of a human hand.The thumb and middle ngertips recorded temperatures around 33.5 and 33.1°C respectively, while the dorsal hand ranged between 30.0 and 31.1°C.

Conclusion
In summary, we developed a thermoregulatory arti cial skin that replicates the thermal infrared temperatures and distributions found in human skin, targeting its application for humanoid robots and prosthetic hands.Our approach simulated the crucial components of the human circulatory system, including the heart and vascular network.We represented blood vessels using bers mimicking their structure, made of elastic silicone material with a hollow con guration measuring a diameter of 500 µm.Since water acts as the heat medium, it was circulated through these bers using pumps that operated under varied conditions.These conditions covered temperature intervals of 30-70°C, ow rates from 1.10 to 11.0 cc/min, and frequency variations between 1 and 8 Hz, to observe the resultant thermal attributes on the ber's surface.
Drawing parallels with the temperature regulation performed by the human heart through blood circulation, we adjusted the temperature of the mimicked bers by modifying water ow rates.Employing 60°C water with ow rates ranging from 1.10 to 11.0 cc/min allowed the ber temperatures to span between 23.8 and 48.3°C.More nuanced temperature control was achieved by adjusting the ber's dilation, reminiscent of the arteriole's vasoconstriction and vasodilation mechanisms.By introducing water at 60°C with a ow rate of 5.39 cc/min and frequencies between 1 and 8 Hz, we observed ber volume changes between 1.9% and 1.2%, which correlated with temperatures ranging from 43.2 to 40.0°C.
To complete the design, we constructed an arti cial skin layer from silicone rubber, which possessed a thermal conductivity of 0.2 W/m•K, similar to human skin.We then assessed the thermal infrared temperature and distribution properties of this thermoregulatory arti cial skin, considering variances in skin thickness (0.5-3.0 mm) and the spacing between bers at the base of the arti cial skin (5-15 mm).The successful integration of this innovative skin on a mannequin's face and a robot's hand effectively simulated the thermal infrared temperatures and distributions seen in humans, underscoring its practical application potential.This advancement represents a signi cant milestone in the rapidly advancing eld of robotics.It offers a solution to minimize the subtle discomfort felt during human-robot interactions, thereby promoting a smoother integration of robotic technology into everyday human tasks and fostering a more harmonious coexistence.

Con of Interest
The authors declare no completing nancial interests.