Shape-morphing robots can change their morphology to fulfill different tasks in varying environments, but existing shape-morphing capability is not embedded in a robot’s body, requiring bulky supporting equipment. Here, we report an embedded shape-morphing scheme with the shape actuation, sensing, and locking, all embedded in a robot’s body. We showcase this embedded scheme using three morphing robotic systems: 1) self-sensing shape-morphing grippers that can adapt to objects for adaptive grasping; 2) a quadrupedal robot that can morph its body shape for different terrestrial locomotion modes (walk, crawl, or horizontal climb); 3) an untethered robot that can morph its limbs’ shape for amphibious locomotion. We also create a library of embedded morphing modules to demonstrate the versatile programmable shapes (e.g., torsion, 3D bending, surface morphing, etc.). Our embedded morphing scheme offers a promising avenue for robots to reconfigure their morphology in an embedded manner that can adapt to different environments on demand. 形状变形机器人可以改变其形态以适应不同环境中的不同任务，但现有的形状变形能力并未嵌入到机器人身体中，需要庞大的支持设备。在这里，我们报告了一种嵌入式形状变形方案，其中形状驱动、传感和锁定都嵌入到机器人身体中。我们通过三个变形机器人系统展示了这种嵌入式方案：1）自感知形状变形夹爪，可以适应物体进行自适应抓取；2）一种四足机器人，可以变形其身体形状以适应不同的陆地运动模式（行走、爬行或水平攀爬）；3）一种无绳机器人，可以变形其肢体形状以适应两栖运动。我们还创建了一个嵌入式变形模块库，以展示多功能的可编程形状（例如，扭转、3D 弯曲、表面变形等）。我们的嵌入式变形方案为机器人以嵌入式方式重新配置其形态提供了有希望的途径，可以根据需要适应不同的环境。
Abstract 摘要
Biological organisms can actively adapt or transform their shapes, whether in response to external environments or as part of their evolutionary life cycles, exemplifying nature’s prowess in shapemorphing. Consider metamorphosis: frogs evolve from aquatic tadpoles with elongated bodies to terrestrial adults with four limbs, while butterflies transform from caterpillars with segmented forms to airborne wonders with delicate wings. Such dramatic morphological changes, rooted in their evolutionary paths, enable them to master diverse modes of locomotion in varied habitats ^(1){ }^{1}. Such shape-morphing capabilities have been recently exploited by researchers in many disciplines, ranging from mechanical metamaterials with programmable material properties ^(2){ }^{2} to human-machine interfaces that can change shapes for immersive haptic experiences ^(3){ }^{3}. For robotic systems, shape morphing is particularly useful since it can enhance a robot’s capability by morphing the same physical structure into different shapes to achieve multiple functions. Shape morphing has been leveraged for robots to change their morphology for adaptive manipulation or locomotion ^(4){ }^{4}. For instance, a robot can adapt its morphology to enable different locomotion modes in different environments ^(5,6){ }^{5,6} or overcome 生物体可以主动适应或改变其形状，无论是对外部环境的反应还是其进化生命周期的组成部分，这展示了自然界在形态变化方面的能力。以变态为例：青蛙从细长的水生蝌蚪进化为有四条腿的陆生成体，而蝴蝶则从分节的毛毛虫变成拥有精致翅膀的空中奇迹。这种基于其进化路径的显著形态变化，使它们能够在不同的栖息地掌握多种运动方式。这种形状变化的能力最近被许多学科的研究人员所利用，从具有可编程材料属性的机械超材料到可以改变形状以实现沉浸式触觉体验的人机界面。对于机器人系统来说，形状变化特别有用，因为它可以通过将相同的物理结构变形为不同的形状来增强机器人的能力，以实现多种功能。形状变化已被用于使机器人改变其形态以进行适应性操作或运动。 例如，机器人可以根据不同的环境调整其形态，以实现不同的运动模式 ^(5,6){ }^{5,6} 或克服
obstacles ^(7){ }^{7}, adjust its leg length to maximize its speed when traversing different terrain ^(8){ }^{8}, or reconfigure its limb shape and motion for amphibious locomotion ^(9){ }^{9}. 障碍物 ^(7){ }^{7} ，调整其腿长以最大化其在不同地形上的速度，或者重新配置其肢体形状和运动以实现两栖运动 ^(9){ }^{9} 。
Although various shape-morphing robots have been developed, the required functionalities of shape-morphing are usually not embedded into the robots. To leverage shape-morphing for robotic systems, it is critical to change, assess, and maintain different shapes, necessitating three core strategies: an actuation strategy to drive the shape change, a sensing strategy to measure the shape change, and a locking strategy to hold the robot’s shape. Various schemes have been explored with different locking strategies (e.g., thermal ^(9-15){ }^{9-15}, jamming ^(16-19){ }^{16-19}, etc.) and actuation strategies (e.g., dielectric ^(14,1,5,20-22){ }^{14,1,5,20-22}, magnetic ^(10,11,16,23-28){ }^{10,11,16,23-28}, pneumatic ^(5,7,9,12,17,29-35){ }^{5,7,9,12,17,29-35}, thermal ^(36-46){ }^{36-46}, etc.), but they are generally not “embedded” since they need bulky external equipment for either shape locking or actuation, such as large magnetic coils or heavy pneumatic pumps, leading to robotic systems that are either constrained inside magnetic coils or tethered from pneumatic sources. Additionally, these schemes require external sensors (e.g., motion tracking systems) to enable closed-loop control and have limited 尽管已经开发了各种形状变形机器人，但形状变形所需的通常并未嵌入到机器人中。为了利用形状变形于机器人系统，改变、评估和维护不同形状至关重要，需要三种核心策略：驱动形状变化的驱动策略、测量形状变化的感觉策略以及保持机器人形状的锁定策略。已经探索了各种方案，采用了不同的锁定策略（例如，热 ^(9-15){ }^{9-15} 、堵塞 ^(16-19){ }^{16-19} 等）和驱动策略（例如，介电 ^(14,1,5,20-22){ }^{14,1,5,20-22} 、磁性 ^(10,11,16,23-28){ }^{10,11,16,23-28} 、气动 ^(5,7,9,12,17,29-35){ }^{5,7,9,12,17,29-35} 、热 ^(36-46){ }^{36-46} 等），但它们通常不是“嵌入”的，因为它们需要笨重的外部设备来进行形状锁定或驱动，例如大型磁线圈或重型气动泵，导致机器人系统要么被限制在磁线圈内，要么从气动源中拉扯。此外，这些方案需要外部传感器（例如，运动跟踪系统）来实现闭环控制，并且具有有限的
morphing modes, primarily relying on planar bending and only being able to morph to a single pre-defined shape. Although some existing schemes have partial “embeddedness”, such as embedded actuation using dielectric elastomer actuators (DEAs) ^(14,15){ }^{14,15} without bulky peripherals, DEAs can only be actuated with high-voltages (hundreds to kilo volts), necessitating additional high-voltage converters. Further, DEAs are generally required to be fabricated into different configurations (e.g., stacked, rolled, tubular, etc.) to generate different deformation modes using the same basic element. A scheme with embedded shape actuation, sensing, and locking that can be controlled to lock into versatile, precise shapes has yet to be developed due to incompatibility between various shape actuation, sensing, and locking methods. Therefore, achieving animal-like embedded shape morphing remains a grand challenge (see Supplementary Table 1 for a detailed list of existing shape-morphing schemes). 变形模式，主要依赖于平面弯曲，并且只能变形为单个预定义的形状。尽管一些现有方案具有部分“嵌入式”，例如使用介电弹性体致动器（DEAs）的嵌入式驱动，无需笨重的外围设备，但 DEAs 只能通过高压（数百到千伏）驱动，需要额外的电压转换器。此外，DEAs 通常需要制造成不同的配置（例如，堆叠、卷曲、管状等），以使用相同的基本元素生成不同的变形模式。由于各种形状驱动、传感和锁定方法之间的不兼容性，一种具有嵌入式形状驱动、传感和锁定功能的方案，可以控制以锁定到多种多样的精确形状，尚未开发出来。因此，实现类似动物的嵌入式形状变形仍然是一个巨大的挑战（有关现有形状变形方案的详细列表，请参阅补充表 1）。
This work reports the shape-morphing scheme with embedded shape actuation, sensing, and locking, distinguishing itself from other methods (see Supplementary Fig. 1 for a comparison). The embedded scheme is accomplished by integrating a Twisted-and-Coiled Actuator (TCA), a lightweight artificial muscle that contracts with applied electricity while sensing its own deformation, and a customized shape memory polymer (SMP) that can switch between rigid and soft states to lock and release a robot’s shape. What sets our approach apart is that it achieves these functions entirely within the morphing body, without the need for external bulky equipment and sensors. Such “embeddedness” paves the way for untethered or self-contained shape-morphing robots. Furthermore, our method can achieve different programmable final shapes through versatile morphing modes, such as torsion and 3D-bending, by strategically arranging TCAs in different patterns and embedding them onto various substrates (e.g., spines, surfaces). 本工作报道了一种嵌入形状驱动、传感和锁定的形状变形方案，与其它方法（参见补充图 1 的比较）区别开来。嵌入方案是通过集成一种扭曲和卷曲驱动器（TCA），一种轻质人工肌肉，在施加电流时收缩并感知其自身的变形，以及一种定制的形状记忆聚合物（SMP），能够在刚性和软性状态之间切换以锁定和释放机器人的形状来实现的。我们的方法与众不同的地方在于，它完全在变形体内实现这些功能，无需外部笨重的设备和传感器。这种“嵌入性”为无缆或自包含的形状变形机器人铺平了道路。此外，我们的方法可以通过灵活的变形模式（如扭转和 3D 弯曲）通过策略性地排列 TCAs 并嵌入到各种基材（例如，脊柱、表面）上，实现不同的可编程最终形状。
To showcase the capabilities of our embedded scheme, we first develop a morphing module that can move and lock into a desired angle in two-dimensional (2D) space using embedded sensing capability. Using the module (Fig. 1), we then demonstrate the versatility of 为了展示我们嵌入式方案的特性，我们首先开发了一个可以在二维（2D）空间中移动并锁定到所需角度的变形模块，该模块利用嵌入式传感能力。使用该模块（图 1），然后我们展示了其多功能性。
our approach by creating a range of morphing robotic systems, including grippers for adaptive grasping, a quadruped robot that can morph its body shape for adaptive terrestrial locomotion (e.g., walk, crawl, and horizontal climb) in different environments, and an amphibious robot that can morph its limb shape for amphibious locomotion (swim and walk). Finally, we create a library of morphing modules with programmable modes by strategically placing TCAs on various geometries (beams, grid surface), further highlighting the versatility of our embedded scheme. 我们的方法是通过创建一系列变形机器人系统，包括用于自适应抓取的夹爪、一种可以变形其身体形状以适应陆地行走的四足机器人（例如，行走、爬行和水平攀爬）以及一种可以变形其肢体形状以适应两栖行走的两栖机器人。最后，我们通过在多种几何形状（梁、网格表面）上战略性地放置 TCA，创建了一个具有可编程模式的变形模块库，进一步突显了我们嵌入式方案的通用性。
Results 结果
A 2D bending shape-morphing module (SMM) 二维弯曲形状变形模块（SMM）
We first illustrate the working principle for the embedded shapemorphing scheme using a 2D bending module ( 115mmxx6.5mm115 \mathrm{~mm} \times 6.5 \mathrm{~mm}xx5mm\times 5 \mathrm{~mm} ) that can morph to and hold different bending angles (Fig. 2a). We realize the locking strategy (Fig. 2b) by casting a spine using a customized shape memory polymer (SMP). SMP is chosen because 1 ) its elastic stiffness significantly decreases after being heated above its glass transition temperature {:T_(g)(100^(@)C);2)\left.T_{\mathrm{g}}\left(100^{\circ} \mathrm{C}\right) ; 2\right) it can return to the original shape after being heated up because of its shape memory effect. The temperature of the SMP spine is controlled by embedded Joule heating through a resistance heating wire wrapped on the spine and a thermistor embedded inside the spine to measure the spine’s temperature. 首先，我们通过一个二维弯曲模块（ 115mmxx6.5mm115 \mathrm{~mm} \times 6.5 \mathrm{~mm}xx5mm\times 5 \mathrm{~mm} ）来说明嵌入式形状变形方案的工作原理，该模块可以变形并保持不同的弯曲角度（图 2a）。我们通过使用定制的形状记忆聚合物（SMP）铸造脊柱来实现锁定策略（图 2b）。选择 SMP 的原因是：1）其弹性刚度在加热至玻璃化转变温度以上时显著降低；2）由于其形状记忆效应，加热后可以恢复到原始形状。通过在脊柱上缠绕电阻加热线并嵌入脊柱内部的温度传感器，通过嵌入式焦耳加热来控制 SMP 脊柱的温度。
The actuation and sensing (Fig. 2b) for the module are both accomplished by a twisted-and-coiled actuator (TCA), a thermal-driven artificial muscle that can contract when heated up and relax after cooling down. A TCA is chosen for the actuation because 1) it can be actuated by electricity with a low voltage (a few volts) but with a large energy density (larger than human muscles); 2 ) it can serve both as an actuator and a sensor (i.e., self-sensing) at the same time ^(47);3{ }^{47} ; 3 ) it is soft and can be embedded into a structure in any shapes ^(48){ }^{48}. The self-sensing avoids embedding extra sensors, which is almost impossible due to the heat created by the TCA. To integrate the TCA with the SMP spine, we enclose it inside a soft silicone tube, bend the tube with the TCA into a UU shape, and glue the tube onto the protrusions of the SMP spine 模块的驱动和传感（图 2b）都由一种扭曲螺旋驱动器（TCA）完成，这是一种热驱动的人工肌肉，加热时可以收缩，冷却后可以放松。选择 TCA 进行驱动的原因是：1）它可以用低电压（几伏）进行驱动，但能量密度大（大于人类肌肉）；2）它可以同时作为驱动器和传感器（即自感知） ^(47);3{ }^{47} ; 3 ；3）它是柔软的，可以嵌入到结构中的任何形状 ^(48){ }^{48} 。自感知避免了嵌入额外的传感器，这在 TCA 产生的热量下几乎是不可能的。为了将 TCA 与 SMP 脊柱集成，我们将它包裹在一个柔软的硅胶管内，将管子弯曲成 UU 形状，并将管子粘接到 SMP 脊柱的突出部分。
Fig. 1∣1 \mid Embedded shape morphing can enable morphologically adaptive robots. The new shape morphing has embedded shape actuation, sensing, and locking within the morphing body. It can compactly enable robot base shape change for adaptive grasping, robot body and limb shape change for locomotion in various environments. 图 1∣1 \mid 嵌入形状变形可以使形态适应性机器人成为可能。新的形状变形具有嵌入变形体内的形状驱动、感知和锁定功能。它能够紧凑地实现机器人基座形状变化以适应抓取，以及机器人身体和肢体形状变化以适应各种环境中的运动。
Fig. 2 | Design and working principle of the shape-morphing module (SMM). a Schematic of the 2D bending SMM. The module includes an SMP spine wrapped with heating wires, an elastic tube (sheath), and the Twisted-and-Coiled Actuator (TCA) (middle). b\mathbf{b} The actuation and sensing are both realized through the TCA, which contracts under electricity (U_(t))\left(U_{t}\right) and relaxes after cooling down. Its resistance RR changes with respect to the displacement DD. The shape locking is realized through the shape memory polymer (SMP) spine, whose stiffness can be controlled by the Joule Heating through a heating wire (U_(s))\left(U_{s}\right). c Photographs of the module during the morphing process. It can rigidly stay at a shape to hold a weight (left). Once the spine is softened, it turns into a soft robot that can move to different 图 2 | 形状变形模块（SMM）的设计和工作原理。a 2D 弯曲 SMM 的示意图。该模块包括一个包裹着加热线的 SMP 脊柱、一个弹性管（套管）和扭曲卷曲执行器（TCA）（中间）。 b\mathbf{b} 驱动和传感都通过 TCA 实现，TCA 在通电时收缩 (U_(t))\left(U_{t}\right) ，冷却后放松。其电阻 RR 随位移 DD 变化。形状锁定是通过形状记忆聚合物（SMP）脊柱实现的，其刚度可以通过加热线进行焦耳加热 (U_(s))\left(U_{s}\right) 来控制。c 形状变形过程中的模块照片。它可以刚性保持形状以承受重量（左侧）。一旦脊柱变软，它就变成了可以移动到不同
shapes (middle). Once the spine recovers its rigidity, the module can rigidly stay at another shape (right). d The shape-morphing processes. Initially, the module stays at the shape AA. It morphs to another shape BB through the following process: i) when U_(s)U_{\mathrm{s}} is applied, the resistance wire heats the spine to soften the spine after the temperature passes its glass transition temperatures T_(g)T_{\mathrm{g}}; ii) once the spine is completely soft, U_(t)U_{\mathrm{t}} is applied to the TCA that contracts to deform the module; iii) after the target shape is arrived, the new shape will be maintained by the TCA while U_(s)U_{\mathrm{s}} is removed to cool the spine; iv) after the spine’s stiffness is recovered (temperature below 80^(@)C80^{\circ} \mathrm{C} ), U_(t)U_{t} will be removed, and the module rigidly stays at the shape B to function as a different structure. 形状（中间）。一旦脊柱恢复其刚性，模块可以刚性保持在另一个形状（右侧）。d 形状变形过程。最初，模块保持在形状 AA 。它通过以下过程变形为另一个形状 BB ：i)当应用 U_(s)U_{\mathrm{s}} 时，电阻丝加热脊柱，使其在温度超过其玻璃化转变温度 T_(g)T_{\mathrm{g}} 后变软；ii)一旦脊柱完全变软， U_(t)U_{\mathrm{t}} 应用于 TCA，使其收缩变形模块；iii)到达目标形状后，新形状将由 TCA 保持，同时移除 U_(s)U_{\mathrm{s}} 以冷却脊柱；iv)脊柱的刚度恢复（温度低于 80^(@)C80^{\circ} \mathrm{C} ）后，移除 U_(t)U_{t} ，模块刚性保持在形状 B，作为不同的结构进行功能。
(Supplementary Fig. 4). The protrusions are critical to minimize the thermal interference between the TCA and the spine since both are thermally driven. Details about the fabrication and assembly of the module can be found in Supplementary Note 1. (补充图 4)。突出部分对于最小化 TCA 和脊柱之间的热干扰至关重要，因为两者都是热驱动的。有关模块的制造和组装的详细信息，请参阅补充说明 1。
With the actuation, sensing, and locking, the morphing process is demonstrated by morphing the module from an initially straight shape, through an intermediate soft state, to a desired curved shape (Fig. 2c, d and Supplementary Movie 1). At the initially straight "shape A^('')A^{\prime \prime}, it functions as a rigid structure to hold a mass of 15 g close to the free end. After removing the mass, we can soften the spine by applying a voltage of U_(s)=25VU_{\mathrm{s}}=25 \mathrm{~V} to the heating wire wrapped around the spine (Fig. 2d i). With the softened spine, the module turns into a soft robot, and it can freely bend to any angle when the TCA is actuated (Fig. 2d ii). For instance, if we apply a constant voltage of U_(t)=3VU_{t}=3 \mathrm{~V} to the TCA, the module will eventually bend to an angle of ∼140^(@)\sim 140^{\circ}. We then stop applying voltage to the spine (i.e., U_(s)=0U_{s}=0 ) to let the spine cool down to recover its rigidity (Fig. 2d iii). After turning off the voltage applied to the TCA (i.e., U_(t)=0U_{\mathrm{t}}=0 ), the module maintains its new "shape BB " (Fig. 2d iv). This “shape B” can again function as a rigid structure to hold a mass of 15 g without additional energy input. Under this new shape, we can heat up the spine again to let the module return to the 通过驱动、感知和锁定，通过将模块从初始的直线形状，通过中间的柔软状态，变为所需的弯曲形状（图 2c、d 和补充电影 1）来演示变形过程。在初始的直线“形状 A^('')A^{\prime \prime} ”中，它作为一个刚性结构，可以承载 15 克的重量，接近自由端。移除重量后，我们可以通过施加 U_(s)=25VU_{\mathrm{s}}=25 \mathrm{~V} 电压到围绕脊柱的加热线（图 2d i）来软化脊柱。有了柔软的脊柱，模块变成了软体机器人，当 TCA 被驱动时，它可以自由弯曲到任何角度（图 2d ii）。例如，如果我们对 TCA 施加一个恒定的电压 U_(t)=3VU_{t}=3 \mathrm{~V} ，模块最终会弯曲到 ∼140^(@)\sim 140^{\circ} 的角度。然后我们停止对脊柱施加电压（即 U_(s)=0U_{s}=0 ），让脊柱冷却以恢复其刚性（图 2d iii）。关闭施加到 TCA 的电压（即 U_(t)=0U_{\mathrm{t}}=0 ）后，模块保持其新的“形状 BB ”（图 2d iv）。这个“形状 B”可以再次作为一个刚性结构，承载 15 克的重量，而无需额外的能量输入。在这个新形状下，我们可以再次加热脊柱，让模块返回到
original “shape A” due to the shape memory effect of the SMP spine (Supplementary Movie 1). Note that the residual temperature in the TCA prevents it from fully returning to “shape A” in Supplementary Movie 1, but this can be solved by completely cooling the TCA before returning. Our shape-morphing scheme can be realized using small and common off-the-shelf electronics in a self-contained manner as demonstrated by a minimal system, whose control unit is 7xx8cm7 \times 8 \mathrm{~cm} and weighs 25 g without a battery (Supplementary Fig. 5). 原始形状 A 是由于 SMP 脊柱（补充电影 1）的形状记忆效应。请注意，TCA 中的残余温度阻止它在补充电影 1 中完全恢复到“形状 A”，但在返回之前完全冷却 TCA 可以解决这个问题。我们的形状变形方案可以通过使用小型和常见的现成电子设备以自包含的方式实现，如最小系统所示，其控制单元为 7xx8cm7 \times 8 \mathrm{~cm} ，不带电池重 25 克（补充图 5）。
Characterization, modeling, and control of the 2D shapemorphing module 表征、建模和控制二维形状变形模块
The technology underpinning the embedded morphing module is the shape locking using the SMP spine, and the actuation and sensing using the TCA. To better understand the module, we conduct experiments to characterize the SMP’s stiffness variation and TCA’s actuation and self-sensing, respectively. For the SMP’s stiffness variation, we measure the SMP’s storage modulus with respect to temperature through a Dynamic Mechanical Analysis (DMA) modulus scan (Supplementary Fig. 6A). The SMP spine becomes ∼67\sim 67 times softer (storage modulus E=20MPa\mathrm{E}=20 \mathrm{MPa} ) at 110^(@)C110^{\circ} \mathrm{C} than the rigid state (E=1350MPa)(\mathrm{E}=1350 \mathrm{MPa}) at room temperature. Based on these measurements, we plot the 支撑嵌入式变形模块的技术是使用 SMP 脊柱进行形状锁定，以及使用 TCA 进行驱动和传感。为了更好地理解该模块，我们进行了实验，分别表征了 SMP 的刚度变化和 TCA 的驱动和自传感。对于 SMP 的刚度变化，我们通过动态力学分析（DMA）模量扫描测量了 SMP 的储存模量与温度的关系（补充图 6A）。在室温下，SMP 脊柱的刚度变为 ∼67\sim 67 倍（储存模量 E=20MPa\mathrm{E}=20 \mathrm{MPa} ）比刚性状态 (E=1350MPa)(\mathrm{E}=1350 \mathrm{MPa}) 软。基于这些测量结果，我们绘制了
^(1){ }^{1} Adaptive Robotics Lab, Department of Mechanical Engineering, Colorado State University, Fort Collins, CO, USA. ^(2){ }^{2} Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT, USA. e-mail: jiefeng.sun@yale.edu; jianguo.zhao@colostate.edu 自适应机器人实验室，机械工程系，科罗拉多州立大学，科罗拉多斯普林斯，科罗拉多州，美国。 ^(2){ }^{2} 机械工程与材料科学系，耶鲁大学，纽黑文，康涅狄格州，美国。电子邮件：jiefeng.sun@yale.edu；jianguo.zhao@colostate.edu
