Real-world embodied Al through a morphologically adaptive quadruped robot 真实世界中的具身化 AI 通过形态适应性四足机器人
Tønnes F. Nygaard , Charles P. Martin , Jim Torresen , Kyrre Glette and David Howard Tønnes F. Nygaard ，Charles P. Martin ，Jim Torresen ，Kyrre Glette 和 David Howard
Abstract 摘要
Robots are traditionally bound by a fixed morphology during their operational lifetime, which is limited to adapting only their control strategies. Here we present the first quadrupedal robot that can morphologically adapt to different environmental conditions in outdoor, unstructured environments. Our solution is rooted in embodied Al and comprises two components: (1) a robot that permits in situ morphological adaptation and (2) an adaptation algorithm that transitions between the most energy-efficient morphologies on the basis of the currently sensed terrain. We first build a model that describes how the robot morphology affects performance on selected terrains. We then test continuous adaptation on realistic outdoor terrain while allowing the robot to constantly update its model. We show that the robot exploits its training to effectively transition between different morphological configurations, exhibiting substantial performance improvements over a non-adaptive approach. The demonstrated benefits of real-world morphological adaptation demonstrate the potential for a new embodied way of incorporating adaptation into future robotic designs. 传统上，机器人在其运行寿命期间受固定形态的限制，仅能适应其控制策略。在这里，我们介绍了第一个四足机器人，它可以在户外、非结构化环境中形态适应不同的环境条件。我们的解决方案根植于具身智能，并包括两个组成部分：（1）一个允许就地形态适应的机器人和（2）一个根据当前感知到的地形在最节能的形态之间过渡的适应算法。我们首先建立了一个模型，描述了机器人形态如何影响在选定地形上的性能。然后我们在真实的户外地形上进行连续适应测试，同时允许机器人不断更新其模型。我们展示了机器人利用其训练有效地在不同的形态配置之间过渡，表现出比非自适应方法更大的性能改进。实现的真实世界形态适应的好处展示了将适应性纳入未来机器人设计的新具身方式的潜力。
obots inspecting the damaged Fukushima reactor were presented with a daunting task: to pass through a narrow duct to enter the area, traverse gaps between platforms, move over and through various types of debris and even swim through murky water. Designing a robot to work across such diverse and unstructured environments is a challenging task as environmental conditions may change, sometimes drastically, during operation. These challenges-chiefly multimodality and unpredictability-are characteristic of the type of unstructured environment that robotic systems as a whole continue to struggle with. In Fukushima, technological limitations meant that the eventual solution required numerous highly specialized traditional robots, with correspondingly high numbers of deployments and extended mission times . Shapeshifting (or morphological adaptation) presents a more attractive, albeit more technically challenging solution that is capable of achieving more complex mission outcomes. Able to vary both body and controller, a morphologically adaptive robot would be able to match its capabilities to its immediate needs: having at one time a large span to traverse gaps, yet at another time being able to shrink and squeeze through narrow openings in debris fields. The underlying principle is that variable morphology provides additional degrees of freedom to more strongly tie a robot's behaviour to its immediate environment for improved mission performance, increasing the likelihood that the robot can adapt and survive in the face of unpredictable environmental conditions. In principle then, morphologically adaptive robots are a promising enabling technology to unlock operation to adapt to a broad swathe of unpredictable environments and tasks on the fly, without having to be redesigned and rebuilt each time they face something unexpected. Due to this promise, morphological adaptation is an area of increasing scientific focus that encompasses a range of research from variable stiffness robot limbs to elegant origami-inspired morphing structures . 检查受损的福岛反应堆的机器人面临着艰巨的任务：通过狭窄的管道进入区域，穿过平台之间的间隙，移动和穿越各种类型的碎片，甚至在浑浊的水中游泳。设计一个能够在如此多样化和无结构的环境中工作的机器人是一项具有挑战性的任务，因为环境条件在操作过程中可能会发生变化，有时变化剧烈。这些挑战，主要是多模态性和不可预测性，是整体上机器人系统继续努力应对的无结构环境的特征。在福岛，技术限制意味着最终解决方案需要大量高度专业化的传统机器人，相应地需要大量的部署和延长的任务时间 。变形（或形态适应）提供了一个更有吸引力但技术上更具挑战性的解决方案，能够实现更复杂的任务结果。 能够改变身体和控制器，形态适应机器人能够根据其即时需求匹配其能力：一次具有跨越间隙的大跨度，另一次能够缩小并挤过碎片场地中的狭窄开口。基本原则是可变形态提供额外的自由度，更牢固地将机器人的行为与其即时环境联系起来，以提高任务性能，增加机器人能够适应和在面对不可预测的环境条件时生存的可能性。因此，形态适应机器人原则上是一种有前途的启用技术，可以解锁对各种不可预测环境和任务的即时适应，而无需每次面对意外情况时重新设计和重建。由于这一前景，形态适应是一个日益受到科学关注的领域，涵盖了从可变刚度机器人肢体到优雅的受折纸启发的变形结构的一系列研究。
We postulate that the key to developing such flexible, adaptable robots may lie in a specific subfield of machine intelligence called embodied artificial intelligence . Embodied AI is a subfield of embodied cognition that states that the brain (software) is not the sole source of cognition, but rather that orchestration of interactions between brain (software), body (hardware) and environment are key to producing intelligent action . Viewed through the lens of embodied cognition, the physical manifestation of a robot is a crucial adaption tool that could be vital in achieving resilient robots that can operate across challenging real-world environments . In some cases, changing the robot's morphology might be the only viable option to elicit suitable in-environment behaviours . 我们假设开发这种灵活、适应性强的机器人的关键可能在于一种称为具身人工智能的机器智能特定子领域。具身人工智能是具身认知的一个子领域，它指出大脑（软件）并非认知的唯一来源，而是大脑（软件）、身体（硬件）和环境之间的互动协调对于产生智能行为至关重要。通过具身认知的视角来看，机器人的物理表现是一个至关重要的适应工具，可能对实现能够在具有挑战性的现实环境中运行的弹性机器人至关重要。在某些情况下，改变机器人的形态可能是引发适当环境行为的唯一可行选项。
In this paper we present our own morphologically adaptive quadruped robot for unstructured environments, seen in Fig. 1a. The dynamic robot for embodied testing, DyRET, provides a powerful proof of concept that harnesses a variable morphology to adapt to realistic real-world conditions in outdoor settings . Morphological adaptation is provided through variable-length legs, whereby the length of both femur and tibia can be adjusted on the fly to enable different walking behaviours while also tilting the central body (Fig. 1b). A novel terrain-adaptation algorithm tailors morphology to the current terrain. Bootstrapped with knowledge from controlled experimentation in indoor terrain boxes, it alters the morphological configuration of the robot online to optimize energy efficiency when traversing unstructured terrains based on sensed terrain characteristics. 在本文中，我们展示了我们自己的形态适应四足机器人，用于非结构化环境，如图 1a 所示。这款动态机器人 DyRET 用于实体测试，提供了一个强有力的概念证明，利用可变形态来适应户外真实环境条件 。形态适应是通过可变长度的腿来实现的，大腿和胫骨的长度可以实时调整，以实现不同的行走行为，同时也可以倾斜中央身体（图 1b）。一种新颖的地形适应算法根据当前地形调整形态。通过室内地形箱中的控制实验知识，它在线改变机器人的形态配置，以优化在感知地形特征的基础上穿越非结构化地形时的能量效率。
This work is inspired by multiple fields including legged robotics, embodied cognition and AI, and evolutionary robotics. We can broadly segregate the literature into three topics: (1) controller adaptation with static morphology, (2) offline morphological adaptation and (3) online morphological adaptation. 这项工作受到多个领域的启发，包括腿式机器人技术、体现认知和人工智能，以及进化机器人技术。我们可以将文献大致分为三个主题：（1）静态形态的控制器适应，（2）离线形态适应和（3）在线形态适应。
Biologically inspired legged robots are a promising solution for unstructured environments. Adaptation can be realized purely through software, primarily adapting gait patterns and foot-tip arcs. Techniques that allow locomotion on challenging terrain include evolutionary approaches , reinforcement learning and 生物启发的有腿机器人是应对非结构化环境的一个有前途的解决方案。适应性可以纯粹通过软件实现，主要是通过调整步态模式和脚尖弧线。允许在具有挑战性的地形上移动的技术包括进化方法、强化学习。
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Fig. 1 | The morphologically adaptive robot used in this study. , An overview of the main components of the robot. , The robot with the shortest (left) and longest (right) leg configuration. AHS, attitude and heading reference system; GPS, global positioning system; RGB-D, red, green, blue and depth. 图 1 | 本研究中使用的形态适应机器人。 ，机器人主要组件的概述。 ，具有最短（左）和最长（右）腿配置的机器人。AHS，姿态和航向参考系统；GPS，全球定位系统；RGB-D，红、绿、蓝和深度。
Bayesian optimization , as well as perception-less and hybrid approaches . Online adaptation to terrains of different compliance under aggressive manoeuvres and external disturbances has been studied , as well as walking posture adaptation for navigation in confined spaces ; however, these approaches are implemented on a static morphology which limits the level of attainable environmental adaptation. 贝叶斯优化 ，以及无感知 和混合方法 。已研究在激烈机动和外部干扰下对不同顺应性地形的在线适应，以及在狭窄空间中导航时的步行姿势适应 ；然而，这些方法是在静态形态上实现的，限制了可达到的环境适应水平。
Evolutionary robotics and artificial life have deep links to embodied AI, and are concerned with investigating and understanding biological processes, including adaptive bodies . Although a robotic adaptation process would ideally be embodied , most works in adaptive robotic morphology are carried out in physics simulation and not on physical robots . Examples include soft robots , modular robots and legged robots . Recent work has studied co-optimization of control and morphology using gradient approaches in differentiable physics simulators , which has strong potential to efficiently couple control, morphology and environment. So far these efforts are only simulated and run in simple environments. 进化机器人学和人工生命与具身人工智能有深刻联系，关注于研究和理解生物过程，包括适应性身体。虽然理想情况下机器人的适应过程应该是具身的，但大多数自适应机器人形态学的研究是在物理模拟中进行的，而不是在实际机器人上。例如软体机器人、模块化机器人和有腿机器人。最近的研究使用可微分物理模拟器中的梯度方法研究了控制和形态的协同优化，这有望有效地将控制、形态和环境结合起来。到目前为止，这些努力仅在简单环境中进行模拟和运行。
The next step up from pure simulation of adaptive morphology is selecting a few virtual robots for real-world manufacture and testing. The manufacturing process can involve three-dimensional printing , assembly from building blocks or even silicone mould techniques for soft robots ; however, the performance of these robots is often limited due to the inaccuracies in the simulation or models used, referred to as the reality gap . This discrepancy means that robots with morphologies optimized in simulation are not fully adapted to the intricate physical environments they will eventually operate in, but to a simplified version of it. 从纯自适应形态模拟的下一个阶段是选择一些虚拟机器人进行现实世界的制造和测试。制造过程可以涉及三维打印，从积木组装，甚至是软机器人的硅胶模具技术；然而，这些机器人的性能通常受到模拟或模型中的不准确性的限制，被称为现实差距。这种差异意味着在模拟中优化形态的机器人并没有完全适应它们最终将在其中运行的复杂物理环境，而是适应了其简化版本。
Our approach to morphological adaptation is performed exclusively in hardware, which is guaranteed to work in reality. Other examples where the body of a robot is optimized or changed in the real world directly are relatively rare, including manual assem or an external mechanism for reconfiguration . Such approaches require extensive time, external apparatus or human intervention and are not suitable for continuous adaptation during independent operation. Few examples exist of robots with a built-in ability to morphologically adapt, mainly due to the challenges associated with designing, building and maintaining a robot with a complex dynamic morphology . Many of these robots are therefore relatively small with no payload capacity, and are limited in their ability to function in real-world unstructured settings (for example, ref. ). More complicated robots possess a higher potential to solve real-world problems, including morphing drones , multimodal legged-wheeled and wheeled-flying robots . These more advanced robots typically discretely change between a couple of predefined morphologies, whereas in this paper we sample morphologies from a continuous range. 我们对形态适应的方法完全在硬件中执行，这可以保证在现实中正常工作。其他一些例子中，机器人的身体在现实世界中直接进行优化或改变的情况相对较少，包括手动组装或外部机制进行重构。这些方法需要大量时间、外部设备或人为干预，并且不适合在独立运行期间进行持续适应。目前存在的具有形态适应能力的机器人的例子很少，主要是由于设计、建造和维护具有复杂动态形态的机器人所面临的挑战。因此，许多这些机器人相对较小，没有有效载荷能力，并且在现实世界中的非结构化环境中的功能受到限制。更复杂的机器人具有更高的潜力来解决现实世界的问题，包括变形无人机、多模式腿轮机器人和轮式飞行机器人。 这些更先进的机器人通常在几种预定义的形态之间离散地变化，而在本文中，我们从一个连续范围中采样形态。
Compared with the identified literature, our approach is the first to continuously optimize the morphology of a real legged robot with the capability to hold a reasonable payload and, in principle, carry out various missions outdoors in the real world. It also makes DyRET the first fully featured robot of its size, with software, sensing and actuation, to close the embodiment brain-body-environment loop in a challenging real-world setting. We fill large boxes with real terrain material and train a simple regression model relating the sensed terrain to the performance of the different morphological configurations of the robot to demonstrate this ability. We validate this model in a simple scenario indoors. Finally, we run the robot in realistic terrains outside, where we test continuous adaptation of morphology while simultaneously updating the regression model in the wild. Continuous adaptation outperforms a challenging baseline of the best static configuration discovered during the bootstrapping phase. 与已识别的文献相比，我们的方法是第一个能够持续优化真实四足机器人形态的方法，具有承载合理负载的能力，并且原则上能够在现实世界的户外执行各种任务。它还使 DyRET 成为其尺寸的第一个功能齐全的机器人，具有软件、传感和执行功能，以在具有挑战性的现实世界环境中关闭实体大脑-身体-环境循环。我们用真实地形材料填充大箱子，并训练一个简单的回归模型，将传感到的地形与机器人不同形态配置的性能相关联，以展示这种能力。我们在室内的一个简单场景中验证了这个模型。最后，我们在现实地形中让机器人运行，在那里我们测试形态的持续适应，同时在野外更新回归模型。持续适应胜过在引导阶段发现的最佳静态配置的具有挑战性的基线。
Results 结果
We start by gathering a baseline dataset used to bootstrap the subsequent adaptive process. Our system is then evaluated in two different scenarios: (1) adapting in a controlled indoor environment and (2) adapting in a realistic outdoor environment. In both, we compare the performance of the adaptation algorithm to the best-performing static morphologies from the baseline dataset. 我们首先收集一个基线数据集，用于启动后续的自适应过程。然后我们在两种不同的场景中评估我们的系统：（1）在受控的室内环境中进行自适应和（2）在现实的室外环境中进行自适应。在这两种情况下，我们将自适应算法的性能与基线数据集中表现最佳的静态形态进行比较。
Gathering the dataset. A baseline dataset was collected to prelearn a model of how the robot's morphology affects its performance on different terrains, facilitating efficient adaptation in real-world environments by avoiding potentially poor-performing morphologies. The baseline model bootstraps the subsequent learning process and, in our final experiment, is updated continuously as the robot operates in new environments. 收集数据集。收集了一个基准数据集，用于预先学习机器人形态如何影响其在不同地形上的表现，从而通过避免潜在的性能较差的形态，在现实环境中实现高效适应。基准模型启动了后续的学习过程，并在我们的最终实验中，随着机器人在新环境中运行而持续更新。
Wooden boxes were filled with terrain materials purchased from a landscaping supplier, as seen in Fig. 2a. Our robot senses both the hardness and roughness of its terrain, and thus we selected three materials with a spread in these two terrain characteristics (details can be found in Supplementary Table 3). Sand is soft with low roughness, gravel is hard with high roughness and a fibre-reinforced concrete sheet provides a hard surface with low roughness (please refer to the Methods for our definitions of roughness and hardness). Each box consists of two halves filled with different terrain materials. This allows the robot to walk on the separate terrains, as well 木箱里装满了从园艺供应商购买的地形材料，如图 2a 所示。我们的机器人能感知地形的硬度和粗糙度，因此我们选择了三种具有这两种地形特征差异的材料（详细信息请参见附表 3）。沙子柔软且粗糙度低，碎石坚硬且粗糙度高，纤维增强混凝土板提供了硬表面且粗糙度低（请参阅方法部分了解我们对粗糙度和硬度的定义）。每个木箱由两半填充不同的地形材料。这使得机器人可以在不同的地形上行走，
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Fig. 2 | Environments and results for indoor and outdoor experiments. a, The terrain boxes used for the experiment in the controlled indoor environment are shown; they contain sand, gravel and concrete. , The COT for the two best static morphologies (gravel-specialized in green and concrete-specialized in orange) and the adaptation (blue) when walking on concrete and then gravel; the vertical dashed grey line denotes the approximate point where the middle of the robot crosses between the two terrain types. The front legs step onto the new terrain for a few steps before this line. The solid lines show the mean of twelve repeats, whereas the shaded areas show the confidence intervals. c, The outdoor area used in the experiment in a realistic outdoor environment, with the red line showing a typical walking path for the robot. It starts on grass, walks onto the road and then back onto the grass. , Standard boxplots of the energy efficiencies (COT) of the adapting (blue) and best all-round static morphology (orange) on the outside test track. The boxes extend from the lower to upper quartile, with horizontal lines showing the median. The whiskers on both sides of the boxes show the extreme values. *Statistically significant differences from a two-sided Mann-Whitney test on each parameter with Holm-Bonferroni -value correction ( (adaptive), (static all-rounder); ). 图 2 | 室内和室外实验的环境和结果。a，显示了用于受控室内环境实验的地形箱；它们包含沙子、碎石和混凝土。 ，在混凝土和碎石上行走时，两种最佳静态形态（绿色专门化为碎石和橙色专门化为混凝土）和适应性（蓝色）的 COT；垂直虚线灰线表示机器人中间穿越两种地形类型的大致点。前腿在此线之前几步踏上新地形。实线显示了十二次重复的平均值，而阴影区域显示了 置信区间。c，实验中在现实室外环境中使用的室外区域，红线显示了机器人的典型行走路径。它从草地开始，走上马路，然后再回到草地。 ，适应性（蓝色）和最佳全能静态形态（橙色）在室外测试赛道上的能源效率（COT）的标准箱线图。箱子从下四分位延伸到上四分位，水平线显示了中位数。 盒子两侧的胡须显示出极端值。*在每个参数上进行双侧 Mann-Whitney 检验，使用 Holm-Bonferroni -值校正进行统计学上显著的差异（ （自适应）， （静态全能手）; ）。
allowing us to test terrain transitions. The boxes were placed in a motion capture facility for high accuracy indoor positioning. 允许我们测试地形过渡。这些箱子被放置在一个动作捕捉设施中，用于高精度室内定位。
A minimum change in leg length is needed before observing a notable effect on robot behaviour; each leg segment was therefore limited to five uniformly sampled discrete lengths, giving 25 different morphological combinations in total. The robot walks forward for per morphology, covering all 25 combinations. The velocity varies greatly, but the theoretical speed is for the shortest-legged robot and for the longest-legged robot. The walking surface typically reduces the speed, but it can in some cases also increase it due to the complex effects of the dynamics of the mechanical system. Each morphology is tested at five different starting locations per terrain type to cancel out any local variation in the surface. The robot does not traverse any transitions at this stage. The dataset contains approximately 90 min of pure walking data. 需要在观察到机器人行为上有显著影响之前，腿长需要进行最小变化；因此，每个腿段被限制为五个均匀采样的离散长度，总共给出了 25 种不同的形态组合。机器人每种形态向前行走 ，覆盖所有 25 种组合。速度变化很大，但理论速度为最短腿机器人为 ，最长腿机器人为 。行走表面通常会降低速度，但在某些情况下也会增加速度，这是由于机械系统动力学复杂效应的影响。每种形态在每种地形类型下的五个不同起点位置进行测试，以消除表面上的任何局部变化。机器人在这个阶段不会穿越任何过渡。数据集包含大约 90 分钟的纯行走数据。
The measured cost of transport (COT) for each morphology on the three surfaces can be seen in Fig. 3. When walking on concrete, the robot achieves the best energy efficiency with a long femur and short tibia, as well as a medium femur and medium tibia. On sand the robot achieves a high efficiency for short to medium length tibias, with femur length having less of an effect. There is much less consistency in gravel, but the lowest COT is observed for the shortest possible legs. 在三种表面上，每种形态的运输成本（COT）如图 3 所示。在混凝土上行走时，机器人通过长股骨和短胫骨，以及中等股骨和中等胫骨实现最佳能源效率。在沙子上，机器人对短到中等长度的胫骨具有高效率，而股骨长度的影响较小。在碎石上一致性较低，但最低的 COT 是在可能最短的腿部观察到的。
Adapting in a controlled indoor environment. In this preliminary experiment we demonstrate a simplified case where morphology is adjusted on the basis of sensed terrain characteristics, but terrains are present in the training data and discretely separated within terrain boxes (Fig. 4a). In this case there is also no need to continuously change the leg lengths as the terrains are highly uniform throughout. As the terrains are known, the adaptation algorithm takes the form of a classifier (see the Methods for details). The robot is brought to a standstill before the morphology is changed, which is triggered by the onboard sensors detecting a 在受控的室内环境中适应。在这个初步实验中，我们展示了一个简化的情况，其中形态根据感知到的地形特征进行调整，但地形存在于训练数据中，并在地形框内离散分开（图 4a）。在这种情况下，由于地形在整个区域内高度统一，也无需不断改变腿的长度。由于地形是已知的，适应算法采用分类器的形式（详见方法部分）。在改变形态之前，机器人被停止，这是由机载传感器检测到触发的。
Fig. 3 | The COT of different leg lengths on the three terrains. The lower the COT value (yellow), the more efficiently the robot is at walking. Please note that the ranges-as seen in the bottom of the figure-are not the same for each surface, to better highlight local differences within each terrain. 图 3 | 不同腿长在三种地形上的 COT。 COT 值（黄色）越低，机器人行走效率越高。 请注意，如图底部所示，每个表面的范围并不相同，以更好地突出每个地形内的局部差异。
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Fig. 4 | Diagram showing the two adaptation methods used. a, The adaptation principle for the controlled indoor environment: , the robot walks forward while sensing its environment; , once a terrain change has been detected, it stops walking; , the robot changes the length of its legs to the optimal morphology for the new terrain; , it starts walking with the new morphology, repeating from . , The adaptation principle for realistic outdoor terrains: , the robot predicts the best-performing morphology on the basis of sensor readings and its internal model; 2 , it changes the length of its legs to this new morphology while walking; , when the legs have reached their goal length, the robot measures its performance and the terrain characteristics; , it adds the new measurements to its internal model, before repeating the process from step . 图 4 | 显示使用的两种适应方法的图表。a，受控室内环境的适应原则： ，机器人在感知环境的同时向前行走； ，一旦检测到地形变化，它停止行走； ，机器人改变腿的长度以适应新地形的最佳形态； ，它开始以新形态行走，重复从 。 ，适应现实户外地形的原则： ，机器人根据传感器读数和内部模型预测表现最佳的形态；2，机器人在行走时改变腿的长度到这个新形态； ，当腿达到目标长度时，机器人测量其表现和地形特征； ，它将新的测量结果添加到内部模型中，然后从步骤 重复该过程。
step onto a new terrain type. This serves as a simplified validation of our final, continuous, adaptation method performed in a realistic outdoor environment. 踏上新的地形类型。这是我们在现实户外环境中进行的最终连续适应方法的简化验证。
We used the same terrain boxes as those in Fig. 2a to collect the baseline dataset. The first half of the box was covered in a concrete sheet, with the other half comprising gravel. The lowest-COT 我们使用与图 2a 中相同的地形箱来收集基线数据集。 箱子的前半部分覆盖着混凝土板，另一半由碎石组成。 最低 COT
a
Fig. | Analysis of the adaptation algorithm. a, The prediction error for each evaluated morphology as the robot walks on grass, road and then back onto the grass. The plot shows a locally weighted regression with unweighted fit, whereas the shaded areas shows the confidence interval of the regression. , The number of times each morphology was evaluated on the three terrain sections, summed over the whole experiment. The initial grass section is to the left, the road is in the middle and the final grass section to the right. 图 | 适应算法分析。a，当机器人在草地上行走，然后在路上行走，再回到草地时，对每个评估形态的预测误差。图中显示了局部加权回归和未加权拟合，而阴影区域显示了回归的 置信区间。 ，每个形态在三个地形部分上评估的次数，整个实验中总和。初始草地部分在左侧，道路在中间，最终草地部分在右侧。
morphology for each surface is chosen from our baseline dataset (femur and tibia for concrete; femur and tibia for gravel) and serves as a comparison for the adaptive morphology. Each morphology begins on concrete and walks onto gravel, triggering a change in morphology in the adaptive case. More details on the experiment design can be found in the Methods. 每个表面的形态都是从我们的基线数据集中选择的（对于混凝土，股骨 和胫骨 ；对于碎石，股骨 和胫骨 ），并作为自适应形态的比较。每种形态都从混凝土开始，走到碎石上，触发自适应情况下形态的变化。有关实验设计的更多细节，请参阅方法部分。
Figure shows that morphologies specialized on one terrain do not transfer well to the other, and that no single morphology is best across both terrains. This is expected given our terrain selection method tried to use terrains with different characteristics. The concrete-specialized morphology achieves a mean COT of 23 while walking on concrete, which rises to 37 after the transition, resulting in a reduction in energy efficiency of approximately . The gravel-specialized morphology starts with a mean COT of 36 , but achieves 26 on gravel, showing an improvement of approximately after stepping onto the optimal terrain for the morphology. The adaptive morphology is shown to perform consistently well across these known terrains and the change detection algorithm triggers a switch in morphology at the appropriate time. 图 显示，专门针对一种地形的形态不适合转移到另一种地形，并且没有一种形态在两种地形上表现最佳。这是因为我们的地形选择方法试图使用具有不同特征的地形。专门针对混凝土的形态在混凝土上行走时达到平均 COT 为 23，过渡后上升到 37，导致能效降低约 。专门针对碎石的形态起始平均 COT 为 36，但在碎石上达到 26，显示在最适合该形态的地形上步入后改善约 。自适应形态表现出在这些已知地形上始终良好，并且变化检测算法在适当时刻触发形态切换。
Adapting in a realistic outdoor environment. Figure describes an extended method that takes into consideration the additional challenges of a realistic outdoor environment. As these terrains are highly dynamic and unstructured, we cannot assume that all of the terrains that the robot will encounter are present in the baseline dataset. We therefore replace terrain classification (used in our previous approach) with characterization (see the Methods for more details). Realistic outdoor terrains can also change substantially, even over small areas, and potentially for every single step that the robot takes. With this extended method, the robot does not stop to change morphology at any point, but operates continuously while the morphology slowly adapts and new experiences are added to the (now adaptive) model. 在现实的户外环境中适应。图 描述了一种考虑到现实户外环境的额外挑战的扩展方法。由于这些地形高度动态且无结构，我们不能假设机器人将遇到的所有地形都包含在基准数据集中。因此，我们用特征化替换了地形分类（在我们先前的方法中使用），详细信息请参见方法部分。现实户外地形也可能发生相当大的变化，即使是在小范围内，甚至可能是机器人每一步都会发生变化。通过这种扩展方法，机器人在任何时候都不会停止改变形态，而是在形态缓慢适应并将新经验添加到（现在是自适应的）模型中的同时持续运行。
An outside test track was selected (Fig. 2c). The route starts with a section of grass, before the robot steps onto a concrete road and then back onto the grass. Returning to the same surface again shows to what degree the algorithm is able to adapt its model based on previous experience of walking on grass. 选择了一个室外测试赛道（图 2c）。路线从一段草地开始，然后机器人踏上混凝土路，再回到草地上。再次返回相同的表面显示算法能够根据之前在草地上行走的经验调整其模型的程度。
The robot uses the model detailed in the Methods to predict the best-performing morphology on its current terrain. As changing the length of the legs takes a considerable amount of time, only neighbouring morphologies are considered (within for the femur and for the tibia). The terrain and performance are not evaluated while the legs are changing length, but after the morphology has been achieved. The robot takes three steps per leg to get a representative measure, and we refer to this as an evaluation. It only reconfigures if any of the neighbours are predicted to outperform the efficiency it just achieved with its current morphology. If not, it simply evaluates the same morphology again. Evaluations are therefore not based on discrete terrain changes or time passing, but are performed continuously. Further evaluations will improve the model, even for repeat measurements for the optimal morphology. The algorithm was allowed 32 evaluations on each terrain section, before being led onto the next. The best all-round static morphology (lowest COT across all three terrain types from the baseline dataset: femur , tibia ) served as a comparison. 机器人使用方法中详细描述的模型来预测其当前地形上表现最佳的形态。由于改变腿的长度需要相当长的时间，因此只考虑相邻的形态（股骨为 ，胫骨为 ）。在腿长改变时不评估地形和性能，而是在形态达到后进行评估。机器人每条腿走三步以获得代表性的测量，我们称之为评估。如果预测到任何相邻形态的效率将超过当前形态所达到的效率，机器人将重新配置。否则，它只是再次评估相同的形态。因此，评估不是基于离散的地形变化或时间流逝，而是持续进行。进一步的评估将改进模型，即使是对于最佳形态的重复测量。算法在每个地形区段上允许进行 32 次评估，然后再进行下一步。最佳的全面静态形态（基线数据集中三种地形类型中 COT 最低的形态：股骨 ，胫骨 ）用作比较。
Figure shows the energy efficiency (COT) of every morphology evaluated while adapting. For the first grass section, we observe 图 显示了在适应过程中评估的每种形态的能效（COT）。对于第一个草坪部分，我们观察到
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Fig. 6 | Model transformation during adaptation. The first row shows the predicted energy efficiency (COT) map of all leg lengths for the grass surface, whereas the second row is for the road surface. Data from all five iterations of the algorithm are included. To indicate where the model was updated, all visited cells resulting in a change in COT higher than one are marked with a red square. 图 6 | 自适应过程中的模型转换。第一行显示了所有腿长在草地表面的预测能效（COT）地图，而第二行是在路面上的。包括算法的所有五次迭代的数据。为了指示模型何时被更新，所有访问的单元格中，导致 COT 高于 1 的变化的单元格都标记为红色方块。
that adaptation gives a median COT of 22, whereas the static morphology has 27 -a reduction in efficiency of approximately . We see similar reductions in the median of approximately and for the road and second grass surface, respectively. The adaptation outperforms the all-round best-performing morphology on all three terrain sections. 适应性给出了一个中位数 COT 为 22，而静态形态为 27，效率降低约 0。我们看到在道路和第二草地表面的中位数分别约为 1 和 2 的类似降低。适应性在所有三个地形部分上表现优于全面表现最佳的形态。
Figure 5a shows the difference between the predicted energy efficiency (COT) for the selected morphology and the actual efficiency measured after walking. The error in COT starts very high at approximately 25 , falls below six after trying 16 different morphologies, before ending at approximately 2.5 at the end of the first grass section. The error spikes to about eight as the robot steps onto the road and ends up at around four at the end of the section. When stepping back onto the grass, the error spikes up to 11 , but that is still much less than initially encountered on the first grass section. It very quickly converges and reaches below six in eight more evaluations before ending at an error of about five. These statistics are based on a locally weighted regression on five repeats of the adaptive run, and contain uncertainty reflected in the confidence intervals in the figure. 图 5a 显示了所选形态的预测能效（COT）与实际步行后测得的效率之间的差异。COT 的误差在开始时非常高，约为 25，尝试了 16 种不同的形态后降至 6 以下，然后在第一段草地结束时约为 2.5。当机器人踏上道路时，误差急剧上升至约 8，最终在该段结束时约为 4。当再次踏上草地时，误差上升至 11，但仍远低于最初在第一段草地上遇到的情况。在接下来的 8 次评估中，误差非常快地收敛并降至 6 以下，最终误差约为 5。这些统计数据基于自适应运行的五次重复的局部加权回归，并包含在图中置信区间中反映的不确定性。
Figure 5b shows which morphologies are used on each terrain type. Mostly short femur with long-tibia combinations are evaluated while the robot walks on the initial grass section, as seen to the left of the figure. When it steps onto the road (shown in the middle) there is a shift to long-femur, long-tibia combinations. The morphologies tested on the final grass section are similar to those used on the road. The adaptation algorithm exploits almost the entire morphological range. The algorithm also delineates the benefit of having an adaptive morphology-the best generalist static morphology is consistently outperformed by adaptation. 图 5b 显示了每种地形类型上使用的形态。大多数短股骨与长胫骨组合在机器人行走在初始草地部分时进行评估，如图左侧所示。当它踏上道路（中间显示）时，会转变为长股骨、长胫骨组合。在最后的草地部分测试的形态与道路上使用的形态类似。适应算法几乎利用了整个形态范围。该算法还说明了具有自适应形态的好处-最佳的广义静态形态始终被适应性超越。
Figure 6 shows how the model's understanding of the two outdoor terrains changes during the adaptation runs. The mean terrain characteristics from the outside test track (with a roughness of and hardness of for grass, and a roughness of and hardness of for the road) was used to visualize the model output at four different stages of the adaptation process. The initial maps generated solely on the baseline dataset contain many extreme COT values (at 0 and above 40). The optimal morphologies in the baseline dataset achieved COT values in the range of approximately 18 to 25 , whereas the worst morphologies were above 35 , giving us a reference for realistic COT values. After walking on the first grass section, multiple prediction updates are seen in red in the second column of the figure. Cost of transport values for the updated grass model are in the range of 21-26, which can be considered realistic. The road predictions are more varied, with COT values as low as 12, which are considered unrealistic. After walking on the road, similarly large updates to the road model are seen in the third column, where we now have COT values between 19 and 25 ; the grass model is also slightly updated. After this section the model has experienced both terrain types, so when transitioning to the final grass section we see that only seven squares are updated for grass and five for the road. Only two of 25 possible leg-length combinations (femur , with tibia lengths and ) were updated both in the first grass section and the last. The fact that no more than two morphologies were updated shows that the adaptation algorithm has successfully integrated the experience from new terrains with the baseline dataset to rapidly generate low-error predictions. Figure 6 also serves as a demonstration of how the algorithm explores the space of available morphologies. We see from the grass map after the first grass section that the best-predicted COT is in the top right area (femur , tibia ). The adaptation algorithm is limited to only selecting the next morphology from neighbouring cells due to the time taken to transition between morphologies. Although this provides an opportunity to test a range of different morphologies in a short amount of time in a stable, controllable manner, it also means that an area such as this is left unexplored as it is surrounded by high-COT cells. We see, however, that the area is visited when the robot returns to the grass section for a second time, and that it does in fact outperform the morphologies tested initially. 图 6 显示了模型在适应运行期间对两个户外地形的理解如何变化。从外部测试赛道（草地粗糙度 和硬度 ，道路粗糙度 和硬度 ）的平均地形特征被用来可视化适应过程的四个不同阶段的模型输出。最初仅基于基准数据集生成的地图包含许多极端的 COT 值（在 0 及以上 40）。基准数据集中的最佳形态实现了大约 18 到 25 的 COT 值范围，而最差的形态超过 35，为我们提供了现实 COT 值的参考。在第一段草地上行走后，图中第二列中的红色显示了多次预测更新。更新后的草地模型的运输成本值在 21-26 的范围内，可以被认为是现实的。道路的预测更加多样化，COT 值低至 12，被认为是不现实的。 在路上行走后，我们在第三列中看到了类似的大更新，现在我们的 COT 值在 19 到 25 之间；草地模型也略有更新。在这一部分之后，模型经历了两种地形类型，因此当过渡到最后的草地部分时，我们看到只有七个方块更新为草地，五个更新为道路。在第一个草地部分和最后一个部分，只有两种可能的腿长组合（股骨 ，胫骨长度 和 ）被更新。没有超过两种形态被更新的事实表明，适应算法成功地将新地形的经验与基线数据集整合在一起，快速生成低误差的预测。图 6 也展示了算法如何探索可用形态的空间。我们从第一个草地部分后的草地地图中看到，最佳预测的 COT 在右上角区域（股骨 ，胫骨 ）。适应算法仅限于从相邻单元格中选择下一个形态，因为在形态之间过渡需要时间。 尽管这为在短时间内以稳定、可控的方式测试一系列不同的形态提供了机会，但也意味着这样一个区域被高 COT 细胞包围，因此未被探索。然而，我们看到当机器人第二次返回草地区时，这个区域被访问了，并且事实上表现出了比最初测试的形态更好的性能。
Discussion 讨论
This work serves as an important step in the direction of morphologically adaptive robots and the overall goal of robotic operation in unstructured environments. We have demonstrated the validity of our approach, which harnesses morphological adaptation in an 这项工作是朝着形态适应机器人和在非结构化环境中实现机器人操作的总体目标迈出的重要一步。我们已经证明了我们的方法的有效性，利用形态适应。
embodied AI context to provide substantially improved performance compared with the best single static morphology. 具体化的 AI 背景可大幅提高性能，与最佳单一静态形态相比。
Key experimental takeaways are (1) we can build a model of how COT is affected by terrain and morphology, (2) we can use this model to adapt in a controlled indoor environment (a proof of concept) and, most importantly, (3) we can combine the model with an adaptation algorithm, allowing the robot to continually vary its morphology in response to previously unseen environments in live outdoor experiments over natural, unstructured terrains, using the previously learned model as a reference point. In our testing, the system quickly learned high-performance morphologies on grass, even though it had only previously experienced sand, gravel and concrete. This dynamic morphology strategy is shown to achieve better energy efficiency than any single static morphology during testing and highlights adaptive morphology as an advantageous trait for robots operating in unstructured terrains. 关键实验结果是（1）我们可以建立一个模型，了解地形和形态对 COT 的影响，（2）我们可以利用这个模型在受控的室内环境中进行适应（概念验证），最重要的是，（3）我们可以将模型与适应算法结合起来，使机器人能够根据先前未见的环境在自然、非结构化地形上进行实时户外实验，并将先前学习的模型作为参考点。在我们的测试中，系统很快学会了在草地上的高性能形态，尽管之前只接触过沙子、碎石和混凝土。这种动态形态策略被证明在测试中比任何单一静态形态都具有更好的能源效率，并突显了适应形态作为机器人在非结构化地形中操作时的有利特征。
By contrast to the relatively controllable indoor experiments, the realistic outdoor environment exposed our system to many sources of noise and inaccuracy. Outdoor experimentation also precluded the use of motion-capture equipment for position tracking. To compensate for these difficulties, we used separate regression models for each morphology to keep noisy measurements contained. Each of these submodules is continually updated with new data, increasing the accuracy of the model with each new evaluation. Overly optimistic measurements would probably be selected for a new evaluation and subsequently be adjusted to a more realistic level. Overly pessimistic measurements can quickly be overlooked in favour of neighbouring morphologies, leading to premature convergence to local optima. This is addressed by only using the previously recorded COT when comparing with the predicted performance of the neighbours, enabling a single measurement to force exploration of an otherwise ignored neighbour. Noisy terrain measurements also aid the algorithm, as walking outside exposes the robot to a range of different terrain examples very quickly, and the model will therefore gradually be filled out until it has the coverage needed for realistic prediction for its entire operating environment. This ability to exploit noise and inaccurate measurements is a strength of our adaptation mechanism allowing it to cope with complex and changing outdoor environments. 与相对可控的室内实验相比，现实的户外环境让我们的系统暴露于许多噪音和不准确性来源。户外实验也排除了使用运动捕捉设备进行位置跟踪。为了弥补这些困难，我们为每种形态使用单独的回归模型来保持嘈杂的测量结果。每个子模块都会不断更新新数据，提高模型的准确性。过于乐观的测量可能会被选中进行新的评估，随后会被调整到更现实的水平。过于悲观的测量可能会很快被忽视，以邻近形态为优先，导致过早收敛到局部最优解。这通过仅在与邻居的预测性能进行比较时使用先前记录的 COT 来解决，从而使单个测量强制探索一个被忽略的邻居。 嘈杂的地形测量也有助于算法，因为在户外行走会迅速让机器人接触到各种不同的地形示例，因此模型将逐渐填充，直到具备对整个操作环境进行现实预测所需的覆盖范围。利用噪声和不准确的测量能力是我们适应机制的优势，使其能够应对复杂和不断变化的户外环境。
There are a few main limitations to our approach. Primarily, we use a one-to-one mapping of controller to morphology, rather than explicitly searching for effective body-brain combinations-a trade-off of faster adaptation speed for less behavioural diversity. Future efforts may focus on learning more sophisticated models on which to rapidly prototype control schemes before real-world rollout, as explicit controller adaptation may facilitate a more diverse behavioural repertoire for a broader range of terrains. We could also consider more advanced morphological adaptation mechanisms . To balance reconfigurability with mechanical simplicity and stability, our adaptation actuator mechanism has a speed of approximately . Faster adaptation would be advantageous in highly dynamic environments, where the robot has to constantly play catch-up between its instantaneous morphological configuration and the best configuration as predicted by the model. In practice this was never an issue, as the nearest-neighbour adaptive approach was specifically designed to work on the hardware. Improvements to terrain modelling would also bring benefits. We used second-order polynomial regression models to facilitate analysis and gain an understanding the underlying mechanisms and effects of the adaptation process. We also chose to look at each morphology separately, instead of constructing one model that incorporated all data points. 我们的方法存在一些主要限制。首先，我们使用控制器到形态的一对一映射，而不是明确寻找有效的身体-大脑组合-这是为了更快的适应速度而牺牲了行为多样性。未来的努力可能集中在学习更复杂的模型上，以便在真实世界推出之前快速原型化控制方案，因为明确的控制器适应可能有助于更广泛范围地形的更多行为库。我们还可以考虑更先进的形态适应机制 。为了在重新配置性和机械简单性与稳定性之间取得平衡，我们的适应执行机构的速度约为 。在高度动态环境中，更快的适应速度将是有利的，机器人必须不断追赶其瞬时形态配置和模型预测的最佳配置之间的差距。在实践中，这从未成为问题，因为最近邻自适应方法专门设计用于硬件。改进地形建模也将带来好处。 我们使用二阶多项式回归模型来促进分析并了解适应过程的基本机制和效果。我们还选择单独查看每种形态，而不是构建一个包含所有数据点的模型。
The implications of these results are potentially far-reaching. We hope to inspire the design and adoption of similar mechanisms, for example, in commercially available platforms, to further increase their range, the tasks they can complete and their possible operational environments. Our key takeaway is that morphological adaptation to real-world environments is a powerful and promising technique for conquering unstructured terrains, with considerable benefits over the static morphologies that are ubiquitous within current robotics literature. We hope that our research helps pave the way towards flexible hardware platforms that are capable of performing a variety of useful missions in outdoor, unstructured terrains. 这些结果的含义可能具有深远影响。我们希望激发类似机制的设计和采用，例如在商业可用平台中，以进一步扩大它们的范围、它们可以完成的任务以及它们可能的操作环境。我们的关键收获是，形态适应真实环境是征服无序地形的强大且有前途的技术，相比于当前机器人学文献中普遍存在的静态形态，具有相当大的优势。我们希望我们的研究有助于铺平道路，使硬件平台能够在户外、无序地形中执行各种有用任务。
Methods 方法
Robot platform design. Our robotic platform, DyRET, can be seen in Fig. 1. It is a quadrupedal mammal-inspired robot with the ability to change the length of its legs during operation and a fully certified open-source hardware project . The body weighs approximately , measures by , and stands between and tall, depending on the pose and leg length. The robot is powered by a three-cell LiPo battery that supplies an unregulated voltage of when fully charged. It has previously been used in laboratory settings, for example, in refs. . 机器人平台设计。我们的机器人平台 DyRET 如图 1 所示。它是一款四足哺乳动物灵感设计的机器人，具有在运行过程中改变腿部长度的能力，并且是一个完全认证的开源硬件项目。机器人的重量约为 ，尺寸为 乘 ，高度在 和 之间，具体取决于姿势和腿部长度。该机器人由一个三节 LiPo 电池供电，充满电时提供 的不稳定电压。它以前曾在实验室环境中使用，例如在参考文献 中。
Figure la shows the main components of the hardware design. The central body consists mainly of carbon fibre tubing, milled aluminium and three-dimensionally printed plastic parts, as well as commercial off-the-shelf available parts where possible. An RGB-D camera is mounted at the front of the robot, pointing vertically down and measuring the roughness of the terrain surface under the front legs. Force sensors are mounted at the tip of each leg and report the perceived surface hardness of the robot. 图 1a 显示了硬件设计的主要组件。中央主体主要由碳纤维管、铣削铝和三维打印的塑料部件组成，同时尽可能使用商用现成零件。一个 RGB-D 相机安装在机器人的前部，垂直指向下方，测量前腿下方地形表面的粗糙度。力传感器安装在每条腿的末端，并报告机器人感知到的表面硬度。
For indoor experiments, the position was measured using a 26-camera motion capture system from Qualisys with four reflective markers placed on the robot this achieves a subcentimetre precision. Outdoors, we use a Ublox C94-M8P differential GPS mounted on the chassis, with the real-time kinematic base station consistently placed within of the robot. The outdoor system typically achieves a precision of less than , which is considered adequate for accurate speed estimation. 对于室内实验，使用 Qualisys 的 26 摄像头运动捕捉系统测量位置，机器人上放置了四个反射标记，实现亚厘米精度。在室外，我们使用安装在底盘上的 Ublox C94-M8P 差分 GPS，实时动态基站始终放置在机器人的 内。室外系统通常实现小于 的精度，被认为足以进行准确的速度估计。
Four legs are attached to the chassis, each with three rotational joints. The proximal joint consists of a Dynamixel MX-64 servo from Robotis, whereas the two distal joints use a MX-106 servos. Two prismatic joints vary the lengths of the femur and tibia, using a geared direct current motor and custom linear actuator as shown in Extended Data Fig. 2a. Each femur can lengthen by and each tibia by . The longest transition-from the minimum to the maximum length of the tibia-takes approximately at a speed of around . Increasing the length of the legs serves as a mechanical gearing of the servos. Longer legs mean higher movement speed at the end of the leg given the same rotational velocity at the joint; however, they come at the cost of less force at the end of the leg, given the same torque at the joint. Being able to change the length of its legs during operation allows the robot to make this trade-off between speed and stability as needed. 四条腿连接到底盘上，每条腿都有三个旋转关节。近端关节由 Robotis 的 Dynamixel MX-64 舵机组成，而两个远端关节使用 MX-106 舵机。两个棱柱关节通过齿轮直流电机和自定义线性执行器改变股骨和胫骨的长度，如扩展数据图 2a 所示。每根股骨可以延长 ，每根胫骨可以延长 。从胫骨的最小长度到最大长度的最长过渡大约需要 ，速度约为 。增加腿部长度相当于对舵机进行机械齿轮传动。较长的腿意味着在腿末端以相同的关节旋转速度下移动速度更快；然而，这会以牺牲末端力量为代价，即在关节扭矩相同的情况下。在运行过程中能够改变腿部长度使机器人能够根据需要在速度和稳定性之间进行权衡。
Our adaptive morphology mechanism alters the available workspace, as seen in Extended Data Fig. 3b. The longest available leg length increases the workspace volume by approximately , and lifts the body about away from the ground, consequently affecting the robot's balance. Only of the workspace for the shortest legs, and 6% for the longest legs, overlap. This shared area is too small for an effective gait, making it impossible for a static robot without adaptive leg lengths to replicate the behaviour of our platform 我们的自适应形态机制改变了可用的工作空间，如扩展数据图 3b 所示。最长可用腿长将工作空间体积增加约 ，并将身体抬离地面约 ，从而影响机器人的平衡。最短腿的工作空间仅占 ，而最长腿的工作空间仅占 6%。这个共享区域对于有效的步态来说太小，使得静态机器人无法复制我们平台的行为。
The COT provides a straightforward and informative means of assessing energy efficiency when walking, taking into account key metrics such as energy expenditure as well as mass and distance travelled. A dimensionless parameter, COT allows for ready comparison with other robots as well as biological life ; it is specifically very popular in the legged-robotics community (see ref. ). The formula for COT is given in equation (1), where is the energy, is the mass of the robot, is standard gravity of Earth and is the distance travelled. In our case, energy is solely based on the energy expended for locomotion by the servos, which is measured by an onboard current sensor in each servo. The power used for control and sensing is assumed to be independent of the morphological configuration and is therefore not included. COT 提供了一种直接且信息丰富的评估能效的方法，考虑了关键指标，如能量消耗、质量和行驶距离。无量纲参数 COT 可与其他机器人以及生物生活进行方便比较；它在有腿机器人社区中特别受欢迎（参见参考文献 1）。COT 的公式如方程式（1）所示，其中 2 是能量，3 是机器人的质量，4 是地球的标准重力，5 是行驶距离。在我们的情况下，能量仅基于舵机用于运动的能量消耗，由每个舵机上的板载电流传感器测量。用于控制和感知的功率被假定与形态配置无关，因此未包括在内。
Terrain sensing. Our system uses two different methods to sense its terrain: classification and characterization. The goal of the classification is to find out which class the perceived terrain belongs to, out of a few number of example terrains. In our indoor experiments, we only have three classes: concrete, sand and gravel. The goal in characterization is to instead measure some features of the terrain that are useful for the adaptation process; the perceived terrain is not classified as a specific type but is given a set of quantitative measurements that describe it. Terrains may be characterized in a multitude of ways; here we use hardness and roughness as they strongly inform the morphology. 地形感知。我们的系统使用两种不同的方法来感知地形：分类和表征。分类的目标是找出感知地形属于哪个类别，从几个示例地形中选择。在我们的室内实验中，我们只有三个类别：混凝土、沙子和砾石。表征的目标是测量地形的一些特征，这些特征对于适应过程是有用的；感知地形不被分类为特定类型，而是给出一组描述它的定量测量。地形可以以多种方式进行表征；在这里，我们使用硬度和粗糙度，因为它们强烈影响形态。
Hardness and roughness are often sensed indirectly, for example, using vision . Precise definitions also vary slightly across the literature. Here we evaluate 硬度和粗糙度通常是间接感知的，例如，使用视觉 。在文献中，精确的定义也略有不同。在这里，我们评估
perceived hardness by measuring the force of the impact as the front feet hit the ground. Roughness is evaluated by measuring the deviation from a perfectly flat ground plane for a number of points in front of the robot. Our methods for terrain measurement are informed by our available sensing hardware. Hardness is inferred from the impact force measured by the sensors in the front feet (Optoforce OMD-20-SH-80N) at . The back foot sensors are ignored to reduce the ambiguities that arise from crossing between two terrain types (front feet on terrain , back feet on terrain B). Raw sensor data is run through a median filter of size five for noise reduction, along with the removal of obvious erroneous force measurements of several times the weight of the complete robot . The final hardness value reported is the summed maximum value measured on each of the force axes on both sensors in a six-second sliding window from the start of the measurement. Details are available in the Supplementary Information. Only looking at the maximum from a sliding window means that increases in hardness are immediately represented in the hardness estimate, whereas reductions will take some time to propagate through the system. There is a slight dependency on environmental factors like the friction of the surface, but these are considered minor contributors compared to the high level of noise in the measurements and natural variance in the terrains the robot operates in 通过测量前脚着地时的冲击力来感知硬度。通过测量机器人前方多个点相对于完全平坦地面的偏差来评估粗糙度。我们的地形测量方法受到可用传感硬件的启发。硬度是通过前脚传感器（Optoforce OMD-20-SH-80N）测量的冲击力推断出来。忽略后脚传感器，以减少由于穿越两种地形类型（前脚在地形 上，后脚在地形 B 上）而产生的歧义。原始传感器数据通过大小为五的中值滤波器进行噪声减少处理，同时移除明显错误的力测量值，这些值是完整机器人重量的数倍 。报告的最终硬度值是从测量开始的六秒滑动窗口中在两个传感器的每个力轴上测量的最大值之和。详细信息请参阅补充信息。 仅仅从滑动窗口中查看最大值意味着硬度的增加会立即在硬度估计中表示出来，而减少则需要一些时间才能传播到整个系统中。环境因素（如表面摩擦）对机器人的运行有一定影响，但与测量中的高噪音水平和机器人操作地形的自然变化相比，这些因素被认为是次要的贡献者
Roughness is inferred using the point-cloud from an Intel Realsense D435 RGB-D camera mounted at the front of the robot and pointing down, providing a three-dimensional representation of the ground at . A ground plane is fit to the measured points; all points that have a distance to the plane of more than are discarded to filter out the legs and other parts of the robot from the scene. The mean of the square distances from each point to the plane is used as a roughness estimate, where zero would imply walking on a perfectly flat surface. 使用安装在机器人前部并向下指向的 Intel Realsense D435 RGB-D 相机的点云来推断粗糙度，为 提供地面的三维表示。对测量点拟合地面平面；所有距离平面距离超过 的点都被丢弃，以过滤出机器人的腿部和其他部分。每个点到平面的平方距离的平均值被用作粗糙度估计，其中零意味着在完全平坦的表面上行走。
These methods for extracting terrain features are both relatively simple, but have been considered adequate for our needs. Details on the sensors and measurement ranges are available in Supplementary Table 4, and a plot showing the distribution of terrain measurements for the indoor boxes is shown in Extended Data Fig. 3. Sensor measurements from walking for on the different boxed terrains are also available in Extended Data Fig. 5. The measurement methods were evaluated on a number of terrains inside and outside during development, and corresponded well with perceived terrain features by the researchers. Varying the morphology does have some impact on the measurements of the walking surface, but quite large changes to the morphology are needed before differences are found. For hardness, increased speed of the legs, reduced force from the servos, and more flexibility in the mechanism as the distance between the body and the end of the leg increase are important factors. For roughness, the distance to the ground has an effect, as well as the increased motion blur from higher speeds. Extended Data Fig. 4 shows terrain measurements for different speeds, which is directly correlated with overall leg length 这些提取地形特征的方法都相对简单，但已被认为能够满足我们的需求。传感器和测量范围的详细信息可在附表 4 中找到，显示室内箱子地形测量分布的图表可在扩展数据图 3 中看到。不同箱式地形上行走的传感器测量数据也可在扩展数据图 5 中找到。在开发过程中，测量方法在室内和室外的多种地形上进行了评估，并与研究人员感知到的地形特征相吻合。改变形态确实会对行走表面的测量产生一定影响，但在发现差异之前需要进行相当大的形态变化。对于硬度，腿部速度增加、伺服减少力量以及机构中身体与腿部末端之间距离增加的灵活性更重要。对于粗糙度，与地面的距离会产生影响，同时高速运动会导致运动模糊增加。扩展数据图。4 显示了不同速度的地形测量，这与总体腿长直接相关
Terrain characterization-used for adaptation in realistic outdoor environments-is performed via these two features directly. Classification-used for adaptation in the controlled indoor environment-is performed by calculating the Euclidean distance to the mean value for each terrain group in the dataset, and selecting the closest match. The pseudocode for both terrain measurement methods are included in the Supplementary Methods. 地形特征描述-用于在现实户外环境中进行适应性调整-是通过这两个特征直接执行的。分类-用于在受控室内环境中进行适应性调整-是通过计算数据集中每个地形组的均值的欧几里德距离，并选择最接近的匹配项来执行的。这两种地形测量方法的伪代码包含在补充方法中。
Gathering the baseline dataset. A small dataset of walking performance for the different morphological configurations on selected terrains needed to be generated. To limit the extent of the data collection, we tested 25 leg-length combinations of the femur and ) and tibia ( and ). A full list of morphologies are available in Supplementary Table 2. The terrain boxes shown in Fig. 2a contains a mix of gravel, sand and concrete surfaces. The gravel and sand were filled to an approximate depth of , but half of a box with concrete was not possible due to the high weight. A flat sheet of fibre-reinforced concrete was instead placed on top of highly compacted dirt and mulch. These materials were selected to give a wide spread in the hardness and roughness features we use, as seen in Supplementary Table 3. 收集基线数据集。需要生成一个关于不同形态配置在选定地形上行走表现的小数据集。为了限制数据收集的范围，我们测试了 25 种股骨（ 和 ）和胫骨（ 和 ）的长度组合。形态学的完整列表可在附表 2 中找到。图 2a 中显示的地形箱包含了混合的碎石、沙子和混凝土表面。碎石和沙子的填充深度约为 ，但由于重量过大，无法用混凝土填充一半的箱子。相反，我们在高度压实的土壤和覆盖物上放置了一块纤维增强混凝土平板。这些材料被选择出来，以便在我们使用的硬度和粗糙度特征中产生广泛分布，如附表 3 所示。
Each evaluation consists of the robot walking forwards on a single surface at a velocity of about for . All of this time was spent on the same surface This was performed five times for each morphology, starting on different parts of each surface to account for local variations in the terrain material. Twenty-five morphologies walking on three different surface types for five iterations of of walking each yielded approximately of walking data in total, which were collected over two consecutive days. 每次评估都包括机器人以大约 的速度在单一表面上向前行走 。所有时间都花在同一表面上。对于每种形态，这个过程重复进行了五次，从每个表面的不同部分开始，以考虑地形材料的局部变化。在三种不同类型的表面上，共有二十五种形态进行了五次 的行走迭代，总共产生了大约 的行走数据，这些数据是在连续两天内收集的。
Baseline modelling. Evaluating how each morphology performs in the real world can take a long time, so testing all possible leg lengths each time the terrain changes is impossible. A baseline model allows the robot to efficiently adapt its body during operation by providing some predictive knowledge of which morphologies might perform well. While walking, the sensed terrain characteristics are used to generate a map of predicted performance for all possible morphologies. In our case we limit the number of morphologies to 25 and treat them all independently when learning the model. 基线建模。评估每种形态在现实世界中的表现可能需要很长时间，因此每次地形变化时测试所有可能的腿长是不可能的。基线模型允许机器人通过提供一些预测性知识，有效地在操作过程中调整其身体，以了解哪些形态可能表现良好。在行走时，传感到的地形特征被用来生成所有可能形态的预测性能地图。在我们的情况下，我们将形态数量限制为 25 个，并在学习模型时将它们全部独立对待。
The whole model is a collection of 25 fully independent submodels, one for each of the leg-length pairs in the dataset. A diagram can be seen in Extended Data Fig. 1. Each submodel is made using second-order polynomial regression to approximate the relationship between the two terrain characteristics and the energy efficiency of each leg-length pair. The output is clamped to provide a COT prediction between 0 and 40 , as values beyond this are considered unrealistic. The parameters for all the submodels after indoor data collection can be seen in Supplementary Table 5. Each time the robot tests a new morphology, the terrain measurements and performance are added to the model to incorporate new knowledge continuously. When a new terrain is encountered, the corresponding point from each of the 25 submodels is used to generate a full predicted map for the given terrain. Examples of generated maps can be seen in Fig. 6, where they were made from data at different points throughout the adaptation algorithm. 整个模型是由 25 个完全独立的子模型组成的，每个子模型对应数据集中的每对腿长。在扩展数据图 1 中可以看到一个图表。每个子模型都是使用二阶多项式回归来近似两个地形特征与每对腿长的能效之间的关系。输出被夹紧以提供在 0 到 40 之间的 COT 预测，因为超出这个范围的值被认为是不现实的。室内数据收集后所有子模型的参数可以在补充表 5 中看到。每次机器人测试新的形态时，地形测量和性能都会被添加到模型中，以持续整合新知识。当遇到新地形时，从 25 个子模型中的每个对应点用于为给定地形生成完整的预测地图。生成的地图示例可以在图 6 中看到，这些地图是根据适应算法中不同点的数据生成的。
Selection of the next morphology can be performed globally in the generated map; however, as changing the length of the legs can require a lot of time, we always select from neighbouring morphologies in the model, where the new morphology is the neighbour with the best-predicted efficiency (lowest-predicted COT) given the measured terrain features. To prioritize more current information, the actual current performance is used when comparing to new morphologies, and not the theoretical prediction for the current morphology from the map. 在生成的地图中可以全局执行下一个形态的选择；然而，由于改变腿的长度可能需要很长时间，我们总是从模型中的相邻形态中进行选择，其中新形态是根据测量的地形特征给出的最佳预测效率（最低预测 COT）的邻居。为了优先考虑更多的当前信息，在比较新的形态时使用实际的当前性能，而不是来自地图的当前形态的理论预测。
Indoor adaptation experiment. Our goal was to test the simple adaptation method in a controlled indoor environment. This serves as a precursor to continuous adaptation in unstructured terrains outside by evaluating the feasibility of our methods on a simpler problem. One of the boxes in Fig. 2a was used, with the first half covered with a concrete sheet and the second half with gravel. We compare the adaptation method, detailed below, to walking across the whole box with each of the two optimal static morphologies from the baseline datase (concrete-specialized, with a femur and tibia; and gravel-specialized, with a femur and tibia). 室内适应性实验。我们的目标是在受控室内环境中测试简单的适应方法。这作为在结构化地形外部进行持续适应的前导，通过评估我们的方法在更简单问题上的可行性。图 2a 中的一个箱子被使用，前半部分覆盖着混凝土板，后半部分覆盖着碎石。我们将下面详细描述的适应方法与从基线数据集中的两种最佳静态形态（混凝土专用，具有 股骨和 胫骨；和碎石专用，具有 股骨和胫骨）中的每一种在整个箱子上行走进行比较。
The robot was initially positioned to walk eight steps on the concrete before stepping onto the gravel for the last eight steps. When using the two optimal static morphologies, the robot walks the full 16 steps without stopping. In the adaptive case, the robot uses terrain classification to detect the transition between the two terrain types. When a change has been detected, the robot stops walking and changes the length of its legs. The new morphology is taken from the best performers in the baseline dataset. Once the desired leg length has been reached, it recommences walking the rest of the 16 steps. The tests were repeated 12 times to get an accurate representation of the actual performance; 12 iterations of 16 steps gives a total of 192 steps for each morphology. Walking across the box with the adaptive and two static morphologies gives a total of 576 steps for the indoor experiment 机器人最初被定位为在混凝土上走八步，然后在最后八步踏上碎石。在使用两种最佳静态形态时，机器人可以连续走完 16 步而不停下来。在自适应情况下，机器人使用地形分类来检测两种地形类型之间的过渡。一旦检测到变化，机器人停止行走并改变腿的长度。新的形态取自基线数据集中表现最好的机器人。一旦达到所需的腿长，它将重新开始行走剩下的 16 步。测试重复 12 次以获得实际表现的准确表示；16 步的 12 次迭代为每种形态提供了总共 192 步。在室内实验中，使用自适应和两种静态形态横穿盒子共计 576 步。
Pseudocode for the experiment is available in the Supplementary Methods. 实验的伪代码可在补充方法中找到。
Outdoor adaptation experiment. Our goal was to test the extended adaptation method in a realistic outdoor environment, which is the key experiment for this paper. This experiment was done on the outside test track shown in Fig. 2c, which consists of mixed terrain, dominated by grassy areas and a concrete road. As experiments were conducted in the middle of summer in Australia, the earth was very hard and dry, and the light covering of grass did not contribute much in term of perceived hardness. The road includes cracks and small obstacles like rocks and sticks. No attempt was made to clean up or prepare the outdoor environments in any way. The adaptation method is compared to the best all-performing static morphology from the baseline dataset (femur , tibia ). 户外适应实验。我们的目标是在现实的户外环境中测试扩展适应方法，这是本文的关键实验。这个实验是在图 2c 所示的室外测试赛道上进行的，该赛道由混合地形组成，以草地区域和混凝土道路为主。由于实验是在澳大利亚夏季中期进行的，土地非常干燥硬实，浅浅的草覆盖并没有在感知硬度方面起到太大作用。道路上有裂缝和小障碍物，如岩石和树枝。没有尝试清理或以任何方式准备户外环境。适应方法与基线数据集中表现最佳的静态形态学（股骨 ，胫骨 ）进行了比较。
When adapting, the robot is initially positioned on the grass section with its most conservative morphology (femur , tibia ). With a target forward velocity of about , the robot is manually steered onto the grass, onto the road, then back on the grass. The adaptation algorithm is given the chance to change its morphology 32 times on each terrain section, referred to as evaluations. The static morphology evaluates the same morphology 64 times on each section without any reconfiguration, resulting in approximately the same time spent walking on each terrain section for the two approaches. This ensures similar battery conditions for all tests. The adaptation algorithm was tested five times since results can vary based on local variations in the terrain. 在适应时，机器人最初以其最保守的形态（股骨 ，胫骨 ）定位在草地区域上。机器人的目标前进速度约为 ，手动将其驶入草地，然后驶上道路，再返回草地。适应算法有机会在每个地形区段上改变其形态 32 次，称为评估。静态形态在每个区段上评估相同的形态 64 次，没有任何重新配置，从而保证了两种方法在每个地形区段上行走的时间大致相同。这确保了所有测试中的电池条件相似。适应算法进行了五次测试，因为结果可能会根据地形的局部变化而有所不同。
When choosing the next morphology to evaluate, the robot only considered neighbouring morphologies (morphologies that only require changing the leg segment lengths by a single increment: for the femur and for the tibia). It decides on the morphology on the basis of the model initialized with the baseline dataset, as well as the features of the current terrain. One evaluation comprises three full steps per leg, during which performance and terrain 在选择下一个要评估的形态时，机器人只考虑相邻的形态（只需要通过单个增量更改腿节长度的形态： 代表股骨， 代表胫骨）。它根据使用基线数据集初始化的模型以及当前地形的特征来决定形态。每次评估包括每条腿三个完整步骤，期间会评估性能和地形。
features are measured. This ensures accurate measurements in the noisy outdoor environment. 特征被测量。这确保了在嘈杂的户外环境中进行准确的测量。
The pseudocode for the experiment is available in Supplementary Methods 1 实验的伪代码可在附录方法 1 中找到
Robot control. The robot uses a high-level spline-based gait controller detailed in ref. . It describes a continuous, regular crawl gait where the body moves at a static speed, and only one leg is lifted at a time. Leg trajectories are identical and represented by a looping cubic Hermite spline. A balancing counter-movement is added to each step where the robot leans to the opposite side of the currently lifted leg. This allows statically stable gaits and is necessary as each leg weighs approximately the same as the central body. Details on all parameters for the gait controller can be found in Supplementary Table 1 . 机器人控制。 机器人使用高级基于样条的步态控制器，详细信息请参阅参考文献 。它描述了一个连续、规律的爬行步态，其中身体以静态速度移动，每次只抬起一条腿。腿部轨迹相同，并由循环立方埃尔米特样条表示。在每一步中添加了一个平衡的反向运动，机器人向当前抬起的腿的对侧倾斜。这样可以实现静态稳定的步态，并且必要，因为每条腿的重量大约与中央身体相同。有关步态控制器的所有参数的详细信息，请参见附表 1。
Step height is a fundamental parameter, and set to on the basis of the terrains the robot will be operating in and a safety margin. Step length can then be maximized within the workspace of the legs (seen in Extended Data Fig. 3b), and step frequency is calculated to keep the rotational velocity of the servos within a safe range. We also have to calculate a scaling factor given our variable leg lengths, as increasing the length of the legs allows longer steps with the same rotational speed for each joint. The step height was kept constant, but step length and width (the sideways movement) was scaled to keep the rotations per minute of the servos consistent throughout the ground movement. The centre of the trajectory spline was kept constant so as not to affect the balance of the robot As the frequency of the gait is kept the same, the increased step length for taller robots leads to slightly higher walking speeds (up to ). The scaling can be found in Supplementary Table 2. 步高是一个基本参数，根据机器人将要操作的地形和安全边际设置为 。然后可以在腿部的工作空间内最大化步长（见扩展数据图 3b），并计算步频以保持舵机的旋转速度在安全范围内。我们还必须计算一个比例因子，考虑到我们可变的腿长，因为增加腿长可以使每个关节以相同的旋转速度迈出更长的步伐。步高保持不变，但步长和宽度（侧向移动）被缩放以保持舵机在地面运动中的每分钟旋转次数一致。轨迹样条的中心保持不变，以不影响机器人的平衡。由于步态的频率保持不变，对于较高的机器人，增加步长会导致略微更高的行走速度（最高可达 ）。比例可以在附表 2 中找到。
Data availability 数据可用性
All JSON-formatted measurements from robot evaluations in this study have been deposited in Figshare . All other relevant data are available from the corresponding author on request. 本研究中来自机器人评估的所有 JSON 格式测量数据已存储在 Figshare 中。其他相关数据可根据请求从对应作者处获得。
Code availability 代码可用性
The code for running the robot is available on the DyRET Github page , and is under a GPL v. 3 license. The code to set-up the experiments and log the results is available is a separate Github repository . Author contributions classified in the CRediT taxonomy . 运行机器人的代码可在 DyRET Github 页面 上找到，并且受 GPL v. 3 许可证保护。设置实验和记录结果的代码可在单独的 Github 存储库 中找到。作者贡献按照 CRediT 分类法 进行分类。
Received: 6 July 2020; Accepted: 11 February 2021; 收到日期：2020 年 7 月 6 日；接受日期：2021 年 2 月 11 日；
Published online: 15 March 2021 在线发布日期：2021 年 3 月 15 日
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Acknowledgements 致谢
This work was partially supported by The Research Council of Norway under grant agreement no. 240862 and its Centres of Excellence scheme, project no. 262762. 这项工作得到了挪威研究委员会的部分支持，根据授予协议编号 240862 和其卓越中心计划，项目编号 262762。
Author contributions 作者贡献
T.F.N. was responsible for conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, visualization, and reviewing and editing the original draft. C.P.M. was responsible for conceptualization, methodology, formal analysis and supervision. J.T. was responsible for supervision and funding acquisition. K.G. was responsible for conceptualization, methodology and supervision. D.H. was responsible for conceptualization, methodology, formal analysis, resources, visualization, supervision, project administration and funding acquisition. C.P.M., J.T., K.G. and D.H. all reviewed and edited the manuscript. T.F.N.负责概念化、方法论、软件、验证、正式分析、调查、资源、数据整理、可视化，以及审查和编辑原始草稿。C.P.M.负责概念化、方法论、正式分析和监督。J.T.负责监督和资金获取。K.G.负责概念化、方法论和监督。D.H.负责概念化、方法论、正式分析、资源、可视化、监督、项目管理和资金获取。C.P.M.、J.T.、K.G.和 D.H.都审查并编辑了手稿。
Competing interests 竞争利益
The authors declare no competing interests. 作者声明没有竞争利益。
Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s42256-021-00320-3. 补充信息 在线版本包含可在 https://doi.org/10.1038/s42256-021-00320-3 获取的补充资料。
Correspondence and requests for materials should be addressed to T.F.N. 信件和资料请求应寄至 T.F.N.
Peer review information Nature Machine Intelligence thanks Agoston Eiben, and the other anonymous reviewer(s), for their contribution to the peer review of this work. 《自然机器智能》感谢 Agoston Eiben 和其他匿名审稿人对本文的审稿贡献。
Reprints and permissions information is available at www.nature.com/reprints. 转载和权限信息请访问 www.nature.com/reprints。
Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 出版商注意施普林格自然对已发表的地图和机构隶属保持中立。
Extended Data Fig. 1| A diagram of the prediction model used, instantiated with the baseline data set measurements from the indoor boxes. The full model with the 25 sub-models for each leg length combination. , The sub-model for femur tibia which shows the predicted energy efficiency (COT) of that leg-length combination for different terrains. The 15 points are the actual measurements from the indoor data collection (square from concrete, circle from sand, and diamond from gravel). When the robot encounters a new terrain, each sub-model is queried at the given roughness/ hardness values to form a predicted COT map similar to the ones shown in Figure 2 in the main text. 扩展数据图 1 | 使用的预测模型图示，实例化了来自室内箱子的基准数据集测量。完整模型包括每个腿长组合的 25 个子模型。 ，股骨 胫骨 的子模型显示了不同地形下该腿长组合的预测能效（COT）。这 15 个点是室内数据收集的实际测量值（方形代表混凝土，圆形代表沙子，菱形代表碎石）。当机器人遇到新地形时，将在给定的粗糙度/硬度值下查询每个子模型，形成类似于主文中图 2 所示的预测 COT 地图。
a
b
Extended Data Fig. 2 | Reconfigurable mechanism and workspace difference. a, The components of the mechanical adaptation mechanism. , An indication of the difference in workspace for the two extreme leg lengths. 扩展数据图 2 | 可重构机制和工作空间差异。a，机械适应机制的组成部分。 ，两个极端腿长的工作空间差异的指示。
Extended Data Fig. 3 | Terrain features for indoor boxes. Kernel density estimate of the terrain features for the three different surfaces in the indoor terrain boxes, measured during the data set collection. This includes all the different morphologies. Default seaborn.jointplot parameters are used for the estimate. 扩展数据图 3 | 室内盒子的地形特征。室内地形盒子中三种不同表面的地形特征的核密度估计，是在数据集收集期间测量的。这包括所有不同的形态。估计使用默认的 seaborn.jointplot 参数。
Extended Data Fig. 4| Effect of speed on terrain measurements. Terrain characteristics of the three surfaces in the indoor terrain boxes, shown for different walking speeds. The solid lines show the mean, and the shaded areas show the standard deviation. , Perceived roughness from the depth camera in the front of the robot. , Perceived hardness from the force sensors in the feet. 扩展数据图 4| 速度对地形测量的影响。室内地形箱中三种表面的地形特征，显示不同步行速度。实线显示均值，阴影区域显示标准偏差。 ，机器人前方深度摄像头感知的粗糙度。 ，脚部力传感器感知的硬度。
Extended Data Fig. | One walking sequence on the indoor terrains. Generated from single 16 second walking sessions with shortest possible leg length. Roughness to the left is calculated from the depth camera. The middle plot shows the absolute, filtered three axis force measurements used to infer hardness, summed for the two front leg sensors (x-axis, sideways, in blue; -axis, lengthwise, in orange; and z-axis, up, in green). The right plot shows the total current reported by the servos. 扩展数据图 | 室内地形上的一个行走序列。由单个 16 秒行走会话生成，腿部长度尽可能短。左侧的粗糙度是从深度摄像头计算得出的。中间图显示了用于推断硬度的绝对、滤波的三轴力量测量值，这些值是两个前腿传感器的总和（x 轴，侧向，蓝色； -轴，纵向，橙色；z 轴，向上，绿色）。右侧图显示了舵机报告的总电流。
'Department of Informatics, University of Oslo, Oslo, Norway. The Norwegian Defence Research Establishment, Kjeller, Norway. Research School of Computer Science, Australian National University, Canberra, Australian Capital Territory, Australia. RITMO, University of Oslo, Oslo, Norway. 奥斯陆大学信息学系，挪威奥斯陆。 挪威国防研究机构，凯勒，挪威。 澳大利亚国立大学计算机科学研究学院，澳大利亚首都特区堪培拉。 奥斯陆大学 RITMO。
Cyber-Physical Systems Program, CSIRO, Canberra, Queensland, Australia. These authors share senior authorship. Kyrre Glette and David Howard 堪培拉，昆士兰，澳大利亚的 CSIRO 网络物理系统项目。 这些作者共享高级作者资格。Kyrre Glette 和 David Howard
