Conference Paper

Design and Modeling of a Series Elastic Element for Snake Robots

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Abstract

In this work, we detail the design, fabrication, and initial modeling of a compact, high-strength series elastic element designed for use in snake robots. The spring achieves its elasticity by torsionally shearing a rubber elastomer that is bonded to two rigid plates, and it is able to achieve mechanical compliance and energy storage that is an order of magnitude greater than traditional springs. Its novel design features a tapered conical cross-section that creates uniform shear stress in the rubber, improving the ultimate strength. Tests show that the torque-displacement profile of these springs is approximately linear, and initial results are reported on creating more accurate models that account for the element’s hysteresis and viscoelastic properties. Low-bandwidth force control is demonstrated by measuring the element’s torsional deflection to estimate the torque output of one of our snake robot modules.

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... For instance, Kong and Jeon proposed a compact RSEA design by using a coil spring and worm gears together, which is used for a knee joint assistance system [21]; in our previous work [22], the elastic element was a set of disc springs mounted at both sides of a lever. More recently, new elastic materials have also been investigated in the design of the SEAs: A magnetic nonlinear torsion spring is for instance integrated into a resonant parallel elastic actuator by Sudano et al. [23] for biorobotic applications; a torsionally-sheared rubber component is utilized by a team at the Carnegie Mellon University in their elastic actuator developed for a snake robot [24]. While many effects are reported in the studies of the new design, these elastic actuators still often suffer from poor linearity, which is derived from mechanical effects such as the properties of the rubber materials and different initial spring pre-compression. ...
... Traditionally, the spring elements of the SEAs are modelled with the Hooke's law in a linearized form as presented for instance in [19]. The linear model fits the single spring system accurately, however, it cannot address the nonlinear effects that can be observed from more complex spring sets [22] or novel rubber elastic elements [24]. Therefore, a precise model of the elastic element is needed and has been in the last years investigated. ...
Article
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This paper describes data-driven modelling methods and their use for the control of a novelset of series-elastic actuators (SEAs). A set of elastic actuators was developed in order to fulfill theend-user needs for tailored industrial collaborative robot manipulators of different morphologiesand payloads. Three different types of elastic actuation were investigated, namely, disc springs,coil springs and torsion bars. The developed algorithms were validated both on single actuators andon a 6-DOF robotic arm composed of such actuators.
... The robot features a versatile mounting point on the front of the body, which allows for the attachment of a camera. The joint-modules themselves fully provide the robot's on-board sensing capabilities; each contains an inertial measurement unit (IMU) and encoders [20]. ...
... To keep the CPG stable even when the center of rotation is far from the robot and r 0 is large, the θ values of the CPG are scaled by a factor of r 0 + 1. Specifically, in practice, we rewrite Eq. (20) to read: ...
Conference Paper
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In this paper, we focus on the problem of directing the gaze of a vision system mounted to the body of a high-degree-of-freedom (DOF) legged robot for active perception deployments. In particular, we consider the case where the vision system is rigidly attached to the robot's body (i.e., without any additional DOF between the vision system and robot body) and show how the supernumerary DOFs of the robot can be leveraged to allow independent locomotion and gaze control. Specifically, we augment a workspace central pattern generator (CPG) with omnidirectional capabilities by coupling it with a body pose control mechanism. We leverage the smoothing nature of the CPG framework to allow online adaptation of relevant locomotion parameters, and obtain a stable mid-level controller that translates desired gaze orientation and body velocity directly into joint angles. We validate our approach on an 18-DOF hexapod robot, in a series of indoor and outdoor trials, where the robot inspects an environmental feature or follows a pre-planned path relative to a visually-tracked landmark, demonstrating simultaneous locomotion and directed vision.
... To meet the growing need for robotic mobility implementations such as disaster rescue, factory pipe maintenance, and terrorism surveillance, a considerable number of snake-like robots for ground locomotion have been developed in the past decades [1][2][3]. Early versions of snake-like robots were equipped with passive wheels, which could achieve stable and fast planar locomotion by swinging their bodies. Such robots, however, lacked the ability of moving in varied topography [2,4]. ...
... Due to this drawback, more attention has been focused on snake-like robots with 3D locomotion ability. By changing the internal shape of their bodies, snake-like robots with lateral and dorsal connected modules can achieve 3D locomotion, which make them more adaptive to different kinds of terrain [3,5]. ...
... To meet the growing need for robotic mobility implementations such as disaster rescue, factory pipe maintenance, and terrorism surveillance, a considerable number of snake-like robots for ground locomotion have been developed in the past decades [1][2][3]. Early versions of snake-like robots were equipped with passive wheels, which could achieve stable and fast planar locomotion by swinging their bodies. Such robots, however, lacked the ability of moving in varied topography [2,4]. ...
... Due to this drawback, more attention has been focused on snake-like robots with 3D locomotion ability. By changing the internal shape of their bodies, snake-like robots with lateral and dorsal connected modules can achieve 3D locomotion, which make them more adaptive to different kinds of terrain [3,5]. ...
Article
Snake-like robots with 3D locomotion ability have significant advantages of adaptive travelling in diverse complex terrain over traditional legged or wheeled mobile robots. Despite numerous developed gaits, these snake-like robots suffer from unsmooth gait transitions by changing the locomotion speed, direction, and body shape, which would potentially cause undesired movement and abnormal torque. Hence, there exists a knowledge gap for snake-like robots to achieve autonomous locomotion. To address this problem, this paper presents the smooth slithering gait transition control based on a lightweight central pattern generator (CPG) model for snake-like robots. First, based on the convergence behavior of the gradient system, a lightweight CPG model with fast computing time was designed and compared with other widely adopted CPG models. Then, by reshaping the body into a more stable geometry, the slithering gait was modified, and studied based on the proposed CPG model, including the gait transition of locomotion speed, moving direction, and body shape. In contrast to sinusoid-based method, extensive simulations and prototype experiments finally demonstrated that smooth slithering gait transition can be effectively achieved using the proposed CPG-based control method without generating undesired locomotion and abnormal torque.
... To meet the growing need for robotic mobility implementations such as disaster rescue, factory pipe maintenance, and terrorism surveillance, a considerable number of snake-like robots for ground locomotion have been developed in the past decades [1][2][3]. Early versions of snake-like robots were equipped with passive wheels, which could achieve stable and fast planar locomotion by swinging their bodies. Such robots, however, lacked the ability of moving in varied topography [2,4]. ...
... Due to this drawback, more attention has been focused on snake-like robots with 3D locomotion ability. By changing the internal shape of their bodies, snake-like robots with lateral and dorsal connected modules can achieve 3D locomotion, which make them more adaptive to different kinds of terrain [3,5]. ...
Article
Full-text available
Snake-like robots with 3D locomotion ability have significant advantages of adaptive travelling in diverse complex terrain over traditional legged or wheeled mobile robots. Despite numerous developed gaits, these snake-like robots suffer from unsmooth gait transitions by changing the locomotion speed, direction, and body shape, which would potentially cause undesired movement and abnormal torque. Hence, there exists a knowledge gap for snake-like robots to achieve autonomous locomotion. To address this problem, this paper presents the smooth slithering gait transition control based on a lightweight central pattern generator (CPG) model for snake-like robots. First, based on the convergence behavior of the gradient system, a lightweight CPG model with fast computing time was designed and compared with other widely adopted CPG models. Then, by reshaping the body into a more stable geometry, the slithering gait was modified, and studied based on the proposed CPG model, including the gait transition of locomotion speed, moving direction, and body shape. In contrast to sinusoid-based method, extensive simulations and prototype experiments finally demonstrated that smooth slithering gait transition can be effectively achieved using the proposed CPG-based control method without generating undesired locomotion and abnormal torque.
... To meet the growing need for robotic mobility implementations such as disaster rescue, factory pipe maintenance, and terrorism surveillance, a considerable number of snake-like robots for ground locomotion have been developed in the past decades [1][2][3]. Early versions of snake-like robots were equipped with passive wheels, which could achieve stable and fast planar locomotion by swinging their bodies. Such robots, however, lacked the ability of moving in varied topography [2,4]. ...
... Due to this drawback, more attention has been focused on snake-like robots with 3D locomotion ability. By changing the internal shape of their bodies, snake-like robots with lateral and dorsal connected modules can achieve 3D locomotion, which make them more adaptive to different kinds of terrain [3,5]. ...
... По этой причине во многих конструкциях змеевидных манипуляторов компланарность осей осознанно не реализуется [18][19][20][21][22][23]. На рисунке 4 приведено изображение конструкции змеевидного робота на основе одностепенных модулей, разработанного в Carnegie Mellon University [18,24]. ...
... [20][21] позволяют определить шарнирные координаты змеевидного манипулятора, шарниры − 1 и которого лежат на заданной пространственной кусочно-гладкой кривой. Пусть = ( ) -параметрически заданная кривая. ...
Article
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In the paper, we have formulated the invariant description form for geometry of a spatial, kinematically redundant manipulator with the orthogonal non-coplanar axes of rotation of the joints. We have obtained the explicit equations for determining the angular coordinates from the condition that points of joints belong to the smooth parametrically given curve. Inequality constraints on the relative position of neighboring parts of the manipulator have been formulated. We have proposed an algorithm for solving equations and the method of planning changes for hinge coordinates for the movement of joints points along the spatial curve that is formed by incremental addition of target points for the head link positions of the manipulator. The method has been applied for planning movements of a hyper-redundant manipulator with a fixed root link and a snakelike robot when moving along the path built on the basis of current and forecasted positions of joints in the Cartesian space.
... Rubber is an alternative to commercial linear metal springs as the elastic element in NLS designs. Although rubber has some disadvantages when compared to metal springs, such as increased hysteresis and van der Waal force-dependent stiffness characteristics [16][17], it tolerates large stretches before plastic deformation and can be molded with custom form factors. Due to these advantages, rubber is already being used in SEAs when actuator size matters [18]. In contrast to metal springs, rubber springs can be nonlinear, especially at large stretches [19]. ...
... The average relative error between the camencoded and measured torque is 63%. Compared to other rubbers, the NLS' urethane rubber has large hysteresis [18]. To decrease NLS hysteresis, we plan to investigate use of other rubbers as NLS elastic elements in the future. ...
Conference Paper
Full-text available
Series elastic actuators often use linear metal springs in their drivetrains, which requires design compromises between torque resolution and actuation bandwidth. Nonlinear springs (NLSs), with variable stiffness, overcome this limitation, enabling both high torque resolution and high bandwidth. Current NLS designs combine variable cam structures with off-the-shelf linear springs, which increases the overall size of these torque transmitting elements. NLS size could be reduced by using other materials as an elastic element. We present an optimization-based synthesis method for NLSs that are compact and encode a user-defined torque-deflection profile using elastic elements with an arbitrary stiffness profile. We experimentally validate the proposed method by creating a NLS prototype and testing it on an actuator testbed. The prototype uses rubber as the elastic element, resulting in a compact design that generates the desired torque profile, although hysteresis of the rubber material partially compromises performance. The results suggest that the proposed method successfully generates compact NLS designs, but that rubber elements need to be carefully chosen to mitigate hysteresis.
... In a very recent version of our robot (AIRo-5.1) [24], only the middle one of the three joints is a torque-controllable joint with a built-in series elastic actuator (SEA) [25], [26], and the remaining two joints are passive joints with torsional springs. ...
Article
Full-text available
The present paper proposes an automatic T-branch travel method of an articulated wheeled in-pipe inspection robot, AIRo-5.2, using its joint angle response to environmental changes. The robot joints are composed of two passive elastic joints with torsional springs and a single active joint using a polyurethane-based series elastic actuator (SEA). By switching from torque control to angle control of this SEA, the AIRo-5.2 can pass through vertical T-branches. However, the timing needed to switch them has not yet been defined, and thus it was necessary to train the operators. Therefore, a method that uses the middle joint angle change was proposed for automatic T-branch travel. To elucidate the phenomenon of this angle change and to determine the effects of a robot's mechanical parameters, a partial dynamic model was constructed when only the head link contact was released at a T-branch. Finally, the travel performance of our developed in-pipe robot was tested on 10 types of T-branches with different gravity directions. From the experiments, although the probability of completing the course was not 100% in all cases, the effectiveness of our proposed principle and algorithm for automatic T-branch travel was confirmed.
... The proposed SEA consists of a rubber elastomer, which is bonded between two tapered plates and torsionally sheared during actuation. In [12], the design, fabrication, and modelling of this compact, high-strength series elastic element designed for use in snake robots were presented, which was able to achieve mechanical compliance and energy storage that was an order of magnitude greater than traditional springs. Koopaee et al. introduced another design variant for SEAs in [10] where a water-jet-cut polyurethanebased elastic element was used. ...
Article
Full-text available
The term perception-driven obstacle-aided locomotion (POAL) was proposed to describe locomotion in which a snake robot leverages a sensory-perceptual system to exploit the surrounding operational environment and to identify walls, obstacles, or other structures as a means of propulsion. To attain POAL from a control standpoint, the accurate identification of push-points and reliable determination of feasible contact reaction forces are required. This is difficult to achieve with rigidly actuated robots because of the lack of compliance. As a possible solution to this challenge, our research group recently presented Serpens, a low-cost, open-source, and highly compliant multi-purpose modular snake robot with a series elastic actuator (SEA). In this paper, we propose a new prototyping iteration for our snake robot to achieve a more dependable design. The following three contributions are outlined in this work as a whole: the remodelling of the elastic joint with the addition of a damper element; a refreshed design for the screw-less assembly mechanism that can now withstand higher transverse forces; the re-design of the joint module with an improved reorganisation of the internal hardware components to facilitate heat dissipation and to accommodate a larger battery with easier access. The Robot Operating System (ROS) serves as the foundation for the software architecture. The possibility of applying machine learning approaches is considered. The results of preliminary simulations are provided.
... Considering the constraints and arrangement of links, the mechanical advantage of Salto is created by a optimized single DOF eight-bar revolute linkage. The series-elastic actuator includes a torsional latex spring designed for an SEA snake [215] that took advantage of the energy storage capability of latex and a geared brushless motor to drive the linkage. Before a jump, Salto maintains a a low mechanical advantage state to store energy. ...
Article
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Purpose of Review Soft robotics enables unprecedented capabilities for mobile robots that could not be previously achieved using rigid mechanisms. This article serves as a reference for researchers working in soft robotic locomotion, provides classifications and trends in this field, and looks ahead to make recommendations for future developments. Recent Findings Soft robotic locomotion tends to be heavily bioinspired. Consequently, we provide a taxonomy of soft robotic locomotion according to locomotion mode, including crawling, flying, swimming, legged locomotion, jumping, and alternative locomotion techniques. For each locomotion mode, we investigate fundamental aspects including actuation type, speed, locomotion gaits, control type, and power autonomy to present an accurate snapshot of soft robotic locomotion research. During the investigation, we focus primarily on the robotics literature from 2016 to 2021, while including some of the seminal work from previous years. Summary In this article, we provide a comprehensive overview of recent soft robotic locomotion research including a broad overview of soft robotic research in several aspects, such as locomotion applications, flexible substrates, and compliant mechanisms, as part of the larger domain of soft robotic locomotion. We also discuss the research trend recent years in this area, possible future research focus, and application of soft locomotion research in human-robot interaction occasions.
... where Z t k , v and ψ respectively represent real observations value, observed noise and quantitative confidence function defined in Equation (15). The loss function is selected in our case because changing R t parameter greatly during the operation process is not conducive to the stability of the updating algorithm. ...
Article
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Adding damping such as viscoelastic element in series elastic actuators (SEA) can improve the force control bandwidth of the system and suppression of high frequency oscillations induced by the environment. Thanks to such advantages, series viscoelastic actuators (SVA) have recently gained increasing research interests from the community of robotic device design. Due to the inconvenience of mounting torque sensors, employing the viscoelastic elements to directly estimate the output torque is of great significance regarding the real-world applications of SVA. However, the nonlinearity and time-varying properties of viscoelastic materials would degrade the torque estimation accuracy. In such a case, it is paramount to simultaneously estimate the output torque state and viscoelastic model coefficients in order to enhance the torque estimation accuracy. To this end, this paper first completed the design of a rubber-based SVA device and used the Zenner linear viscoelastic model to model the viscoelastic element of the rubber. Subsequently, this paper proposed a dual extended Kalman filter- (DEFK) based torque estimation method to estimate the output torque and viscoelastic model coefficients simultaneously. The noisy observations of two Kalman filters were provided by motor current-based estimated torque. Moreover, the dynamic friction of harmonic drive of the designed SVA was modeled and compensated to enhance the reliability of current-based torque estimation. Finally, a number of experiments were carried out on SVA, and the experimental results confirmed the DEFK effectiveness of improving torque estimation accuracy compared to only-used rubber and only-used motor current torque estimation methods. Thus, the proposed method could be considered as an effective alternative approach of torque estimation for SVA.
... Thereafter, the design and control of SEA has been widely exploited in the fields of legged locomotion [20,21], humanoid robots [22] and manipulators [23]. Regarding snake robots, different methods of achieving compliant motion by controlling the torques exerted by the joints of the robot were presented by the Robotics Institute at the Carnegie Mellon University [10,24]. These control strategies are implemented on a snake robot that includes SEA and torque sensing at each joint, and demonstrate compliant locomotion that adapts naturally to the robot's surrounding terrain. ...
Article
Full-text available
Snake robot locomotion in a cluttered environment where the snake robot utilises a sensory-perceptual system to perceive the surrounding operational environment for means of propulsion is defined as perception-driven obstacle-aided locomotion (POAL). From a control point of view, achieving POAL with traditional rigidly-actuated robots is challenging because of the complex interaction between the snake robot and the immediate environment. To simplify the control complexity, compliant motion and fine torque control on each joint is essential. Accordingly, intrinsically elastic joints have become progressively prominent over the last years for a variety robotic applications. Commonly, elastic joints are considered to outperform rigid actuation in terms of peak dynamics, robustness, and energy efficiency. Even though a few examples of elastic snake robots exist, they are generally expensive to manufacture and tailored to custom-made hardware/software components that are not openly available off-the-shelf. In this work, Serpens, a newly-designed low-cost, open-source and highly-compliant multi-purpose modular snake robot with series elastic actuator (SEA) is presented. Serpens features precision torque control and stereoscopic vision. Only low-cost commercial-off-the-shelf (COTS) components are adopted. The robot modules can be 3D-printed by using Fused Deposition Modelling (FDM) manufacturing technology, thus making the rapid-prototyping process very economical and fast. A screw-less assembly mechanism allows for connecting the modules and reconfigure the robot in a very reliable and robust manner. The concept of modularity is also applied to the system architecture on both the software and hardware sides. Each module is independent, being controlled by a self-reliant controller board. The software architecture is based on the Robot Operating System (ROS). This paper describes the design of Serpens and presents preliminary simulation and experimental results, which illustrate its performance.
... The robot is blind, meaning that no on-board vision system is used to close the loop; on-board sensing is provided by the joint modules themselves, each containing an IMU and encoders [17]. ...
... The robot is blind, meaning that no on-board vision system is used to close the loop; on-board sensing is provided by the joint modules themselves, each containing an IMU and encoders [17]. ...
Preprint
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Inspired by the locomotor nervous system of vertebrates, central pattern generator (CPG) models can be used to design gaits for articulated robots, such as crawling, swimming or legged robots. Incorporating sensory feedback for gait adaptation in these models can improve the locomotive performance of such robots in challenging terrain. However, most CPG models to date have been developed exclusively for open-loop gait generation for traversing level terrain. In this paper, we present a novel approach for incorporating inertial feedback into the CPG framework for the control of body posture during legged locomotion on steep, unstructured terrain. That is, we adapt the limit cycle of each leg of the robot with time to simultaneously produce locomotion and body posture control. We experimentally validate our approach on a hexapod robot, locomoting in a variety of steep, challenging terrains (grass, rocky slide, stairs). We show how our approach can be used to level the robot's body, allowing it to locomote at a relatively constant speed, even as terrain steepness and complexity prevents the use of an open-loop control strategy.
... Several research groups have taken a biomimetic or bioinspired approach in an attempt to match (or exceed) biological performance using an engineered device. This approach has led to new techniques for robotic manipulation [10,13,16,17], the ability to move robots on difficult terrain [9,14,15], and has been used to test scientific hypotheses about locomotion [11,13,14]. However, these engineered devices are typically larger than biological organisms, and the fastest organisms have a greater kinematic performance than currently achievable by small robots using elastic elements to perform repeatable motions [8]. ...
Article
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Elastically-driven motion has been used as a strategy to achieve high speeds in small organisms and engineered micro-robotic devices. We examine the size-scaling relations determining the limit of elastic energy release from elastomer bands with mechanical properties similar to the biological protein resilin. The maximum center-of-mass velocity of the elastomer bands was found to be size-scale independent, while smaller bands demonstrated larger accelerations and shorter durations of elastic energy release. Scaling relationships determined from these measurements are consistent with the performance of small organisms which utilize elastic elements to power motion. Engineered devices found in the literature do not follow the same size-scaling relationships, which suggests an opportunity for improved design of engineered devices.
... In contrast our controllers achieve a bandwidth of 70 Hz. The study on [10] accomplishes reasonably good torque control Luis Sentis is a professor in Aerospace Engineering, University of Texas at Austin, Austin, TX, 78712, USA performance, but the range of achievable torques is small to ensure that the elastomer operates in the linear region; our design and control methods described here achieve more than an order of magnitude higher range of torques with high fidelity tracking. ...
Article
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We design, build, and empirically test a robotic leg prototype using a new type of high performance device dubbed a viscoelastic liquid cooled actuator (VLCA). VLCAs excel in the following five critical axes of performance, which are essential for dynamic locomotion of legged systems: energy efficiency, torque density, mechanical robustness, position and force controllability. We first study the design objectives and choices of the VLCA to enhance the performance on the needed criteria. We follow by an investigation on viscoelastic materials in terms of their damping, viscous and hysteresis properties as well as parameters related to the long-term performance. As part of the actuator design, we configure a disturbance observer to provide high-fidelity force control to enable a wide range of impedance control capabilities. After designing the VLCA, we proceed to design a robotic system capable to lift payloads of 32.5 kg, which is three times larger than its own weight. In addition, we experiment with Cartesian trajectory control up to 2 Hz with a vertical range of motion of 32 cm while carrying a payload of 10 kg. Finally, we perform experiments on impedance control by studying the response of the leg testbed to hammering impacts and external force interactions.
... For example, Kong and Jeon developed a compact RSEA with a coil spring and worm gears for knee joint assistance [7]; Stienen et al. developed a rotational hydroelastic actuator with a symmetric torsion spring for a powered exoskeleton [8]; or the elastic element of the CAPIO actuator [9] includes a set of small disc springs placed at both sides of a lever which connects to the link. In recent years, new elastic materials are also utilized: scientists at the Carnegie Mellon University used nonlinear rubber as the elastic element of the actuators for their snake robots [10]; Sudano et al. integrated a magnetic nonlinear torsion spring in a rotary elastic actuator for biorobotic applications [11]. However, due to mechanical effects caused by the construction itself, by the structure of the spring system (e.g. ...
Chapter
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Series elastic actuators (SEAs) have been frequently used in torque control mode by using the elastic element as torque measuring device. In order to precisely control the torque, an ideal torque source is critical for higher level control strategies. The elastic elements are traditionally metal springs which are normally considered as linear elements in the control scheme. However, many elastic elements are not perfectly linear, especially for an elastic element built out of multiple springs or using special materials and thus their nonlinearities are very noticeable. This paper presents two data-driven methods for learning the spring model of a series-elastic actuator: (1) a Dynamic Gaussian Mixture Model (DGMM) is used to capture the relationship between actuator torque, velocity, spring deflection and its history. Once the DGMM is trained, the spring deflection can be estimated by using the conditional probability function which later is used for torque control. For comparison, (2) a deep-learning approach is also evaluated which uses the same variables as training data for learning the spring model. Results show that the data-driven methods improve the accuracy of the torque control as compared to traditional linear models.
... The compliant nature of muscles can automatically reject perturbations and significantly reduce the burden on the control system (Loeb et al., 1999;Jindrich and Full, 2002). To take advantage of this, actuators which add compliance and greater control of force are being developed (Pratt and Williamson, 1995;Thorson and Caldwell, 2011;Rollinson et al., 2013;Schilling et al., 2013b). A compliant actuator combined with the tri-segmented shape of the legs (Fischer and Blickhan, 2006) produces a mechanical system which is robust to perturbations capable of performing dynamic walking with open-loop control (Spröwitz et al., 2014). ...
Article
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Animals dynamically adapt to varying terrain and small perturbations with remarkable ease. These adaptations arise from complex interactions between the environment and biomechanical and neural components of the animal's body and nervous system. Research into mammalian locomotion has resulted in several neural and neuro-mechanical models, some of which have been tested in simulation, but few " synthetic nervous systems " have been implemented in physical hardware models of animal systems. One reason is that the implementation into a physical system is not straightforward. For example, it is difficult to make robotic actuators and sensors that model those in the animal. Therefore, even if the sensorimotor circuits were known in great detail, those parameters would not be applicable and new parameter values must be found for the network in the robotic model of the animal. This manuscript demonstrates an automatic method for setting parameter values in a synthetic nervous system composed of non-spiking leaky integrator neuron models. This method works by first using a model of the system to determine required motor neuron activations to produce stable walking. Parameters in the neural system are then tuned systematically such that it produces similar activations to the desired pattern determined using expected sensory feedback. We demonstrate that the developed method successfully produces adaptive locomotion in the rear legs of a dog-like robot actuated by artificial muscles. Furthermore, the results support the validity of current models of mammalian locomotion. This research will serve as a basis for testing more complex locomotion controllers and for testing specific sensory pathways and biomechanical designs. Additionally, the developed method can be used to automatically adapt the neural controller for different mechanical designs such that it could be used to control different robotic systems.
... 3 Peak torque refers to the maximum achievable instantaneous torque at the SEA joint motor to allow for accurate and stable force control, lower reflected inertia and greater shock tolerance [2]. Several other SEAs have been presented for different applications that fall under the same categories of a structural torsion spring as elastic element and a locally situated motor (electric or hydraulic) [33,[36][37][38][39]. A limitation of such a design is that structural torsion springs need to be custom designed for each application and therefore, an explicit characterization is needed experimentally to validate the torque-deflection behavior for such springs. ...
Article
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Torque control of small-scale robotic devices such as hand exoskeletons is challenging due to the unavailability of miniature and compact bidirectional torque actuators. In this work, we present a miniature Bowden-cable-based series elastic actuator (SEA) using helical torsion springs. The three-dimensional (3D) printed SEA is 38mm×38mm×24mm in dimension and weighs 30 g, excluding motor which is located remotely. We carry out a thorough experimental testing of our previously presented linear compression spring SEA (LC-SEA) (Agarwal et al. 2015, "An Index Finger Exoskeleton With Series Elastic Actuation for Rehabilitation: Design, Control and Performance Characterization," Int. J. Rob. Res., 34(14), pp. 1747-1772) and helical torsion spring SEA (HT-SEA) and compare the performance of the two designs. Performance characterization on a test rig shows that the two SEAs have adequate torque source quality (RMSE < 12% of peak torque) with high torque fidelities ( > 97% at 0.5 Hz torque sinusoid) and force tracking bandwidths of 2.5 Hz and 4.5 Hz (0.2 N.m), respectively, which make these SEAs suitable for our application of a hand exoskeleton.
... elastic element because it is compact, can tolerate large deflections, and can be easily molded to a custom shape and size. For these reasons, rubber has been incorporated into actuator designs where weight and volume is a concern [10]. Compared to metal springs, viscoelastic materials like rubber have the disadvantage of exhibiting hysteresis due to viscous effects, though others have overcome this challenge by using state observers to account for hysteresis [11]. ...
Conference Paper
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Series elastic actuators primarily use linear springs in their drivetrains, which introduces a design tradeoff: soft springs provide higher torque resolution at the cost of system bandwidth, whereas stiff springs provide a fast response but lower torque resolution. Nonlinear springs (NLSs) potentially incorporate the benefits of both soft and stiff springs, but such springs are often large. An NLS design was recently proposed that combines a variable radius cam with a rubber elastic element, enabling a compact spring design. However, the rubber introduces hysteresis, which can lead to poor torque tracking if not accounted for in the controller. To overcome this limitation, we here propose a state observer that captures hysteretic effects exhibited by the rubber to provide an accurate estimate of actuator torque. We perform torque-control experiments with this observer on an actuator testbed and compare the performance of the NLS to both soft and stiff linear metal springs. Experiments show that the NLS exhibits improved output impedance compared to both linear springs, and comparable bandwidth to the stiff linear spring up to 1.5 Hz. However, the hysteresis in the urethane rubber introduces instability in higher-frequency conditions, suggesting that future NLS designs can be improved by use of a different rubber as the elastic element.
... We have recently developed a new snake robot where each joint contains a series-elastic actuator [Rollinson et al., 2013b], enabling the robot to accurately sense and control the true output torque of each joint [Pratt and Williamson, 1995]. This should allow the shape of the robot to be much more sensitive to the terrain it contacts and allow these compliant controllers to work in a wider range of environments. ...
Article
We present a method of achieving whole-body compliant motions with a snake robot that allows the robot to automatically adapt to the shape of its environment. This feature is important to pipe navigation because it allows the robot to adapt to changes in diameter and junctions, even though the robot lacks mechanical compliance or tactile sensing. Rather than reasoning in the configuration space of robot joint angles, the compliant controller estimates the overall state of the robot in terms of the parameters of a low-dimensional control function, i.e., a gait. The controller then commands new gait parameters relative to that estimated state. Performing closed-loop control in this lower-dimensional parameter space, rather than the robot's full configuration space, exploits the intuitive connection between the gait parameters and higher-level robot behavior. Furthermore, the ability to automatically adjust gait parameters with this controller enables more sophisticated motions that would previously have been too complex to be controlled manually.
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Legged robots can negotiate unstructured environments and have applications in education, environmental inspection, space exploration, and cargo transportation. As a powerful form of legged robots, jumping robots have attractive features due to their high efficiency, mobility, traverse obstacles, and low cost of transport. Although spring is the core component of the energy system, little related work explores the value selection of spring stiffness and the effect of different spring placements for jumping robots. In this article, we present a systematic method to select the stiffness of spring based on static analysis, jumping linkage configuration and multi-objective optimization for jumping robots. Also, to predict the motion behavior of jumping robots, we provide a comprehensive dynamic model of the robotic jumping in different phases according to the Lagrange method and the principle of virtual work, which considers the motion constraints and configuration constraints simultaneously. The proposed method and dynamic model can validate by designing a spring-linkage-based jumping robot as a showcase. The experimental results show performance improvements in jumping height in terms of both different springs’ stiffness and arrangement, which is possible to appraise a maximal enhancement of 57.88%.
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Kinematic and kinetic requirements for robotic actuators are subject to uncertainty in the motion of the load. Safety factors account for uncertainty in the design stage, but defining factors that translate to reliable systems without over-designing is a challenge. Bulky or heavy actuators resulting from overdesign are undesirable in wearable or mobile robots, which are prone to uncertainty in the load due to human–robot or robot–environment interaction. In this paper, we use robust optimization to account for uncertainty in the design of series elastic actuators. We formulate a robust-feasible convex optimization program to select the optimal compliance–elongation profile of the series spring that minimizes one or multiple of the following objectives: spring elongation, motor energy consumption, motor torque, or motor velocity. To preserve convexity when minimizing energy consumption, we lump the energy losses in the transmission as viscous friction losses, which is a viable approximation for series elastic actuators powered by direct or quasi-direct drives. Our formulation guarantees that the motor torque, winding temperature, and speed are feasible despite uncertainty in the load kinematics, kinetics, or manufacturing of the spring. The globally optimal spring could be linear or nonlinear. As simulation case studies, we design the optimal compliance–elongation profiles for multiple series springs for a robotic prosthetic ankle. The simulation case studies illustrate examples of our methodology, evaluate the performance of robust feasible designs against optimal solutions that neglect uncertainty, and provide insight into the selection of different objective functions. With this framework the designer specifies uncertainty directly in the optimization and over the specific kinematics, kinetics, or manufacturing parameters, aiming for reliable robots that reduce overdesign.
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This paper presents the concept of a new rubber compression mechanism for rotary compact series elastic elements, which can be used in robotic joints in human–machine interaction devices. A compact elastic element is realized using rubber materials with a higher specific energy and energy density than steel or fiberglass, which are commonly used in commercial springs. To overcome the nonlinearity and hysteresis of the proposed compression mechanism, a mathematical Bouc–Wen model developed through parameter identification is proposed. This paper describes the working principle of the new elastic element and presents the modeling method. Experiments on the Bouc–Wen model conducted to demonstrate the suggested mechanism are reported, and the results show that the proposed elastic element can be used for robotic joints in human–machine interaction devices.
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We present the Visiflex, an inexpensive compliant tactile fingertip capable of contact localization and 6-dof contact force and torque measurement. Because manipulation of rigid or nearly-rigid objects requires compliance at the contact, we build compliance directly into the Visiflex in the form of a well characterized 6-dof flexure between the fingertip and the base of the Visiflex. This compliance also allows the use of a 6-dof position sensor to measure forces and torques transmitted through the fingertip. The position sensor is a camera, and the same camera is used to detect contact locations on the fingertip via frustrated total internal reflection (FTIR). Our tests indicate that typical errors in contact location detection are less than 1 mm and typical errors in force sensing are less than 0.3 N. A video of the Visiflex can be found online.
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This paper presents the design and control of a cable-actuated mobile snake robot composed of modular coupled linkages. The goal of this research is to reduce the size of snake robots and improve their locomotive efficiency by simultaneously actuating groups of links to fit optimized curvature profiles. The basic functional unit of the snake is a four-link, single degree of freedom module that bends using an antagonistic cable-routing scheme. The mechanical and electrical designs of the module are first presented, with emphasis on the cable-routing scheme, key optimizations, and the use of elastic elements. A simplified model of serpentine locomotion is then presented and used to derive some properties of this locomotion gait. Control strategies for snake robots with coupled joints are also developed, including a feedback linearization of the pulley dynamics using the coupled cable equations. Experiments using a fully integrated prototype are presented and compared with simulated results.
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Highly articulated systems are capable of executing a variety of behaviors by coordinating their many internal degrees of freedom to help them move more effectively in complex terrains. However, this inherent variety poses significant challenges that have been the subject of a great deal of previous work: What are the most effective or most efficient methods for achieving the intrinsic coordination necessary to produce desired global objectives? This work takes these questions one step further, asking how different levels of coordination, which we quantify in terms of kinematic coupling, affect articulated locomotion in environments with different degrees of underlying structure. We introduce shape functions as the analytical basis for specifying kinematic coupling relationships that constrain the relative motion among the internal degrees of freedom for a given system during its nominal locomotion. Furthermore, we show how shape functions are used to derive shape-based controllers (SBCs) that manage the compliant interaction between articulated bodies and the environment while explicitly preserving the inter-joint coupling defined by shape functions. Initial experimental evidence provides a comparison of the benefits of different levels of coordination for two separate platforms in environments with different degrees of inherent structure. The experimental results show that decentralized implementations, where there is relatively little inter-joint coupling, perform well across a spectrum of different terrains but that there are potential benefits to higher degrees of coupling in structured terrains. We discuss how this observation has implications related to future planning and control approaches that actively “tune” their underlying structure by dynamically varying the assumed level of coupling as a function of task specification and local environmental conditions.
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The leg mechanism of the novel jumping robot, Salto, is designed to achieve multiple functions during the sub-200 ms time span that the leg interacts with the ground, including minimizing impulse loading, balancing angular momentum, and manipulating power output of the robot's series-elastic actuator. This is all accomplished passively with a single degree-of-freedom linkage that has a coupled, unintuitive design which was synthesized using the technique described in this paper. Power delivered through the mechanism is increased beyond the motor's limit by using variable mechanical advantage to modulate energy storage and release in a series-elastic actuator. This power modulating behavior may enable high amplitude, high frequency jumps. We aim to achieve all required behaviors with a linkage composed only of revolute joints, simplifying the robot's hardware but necessitating a complex design procedure since there are no pre-existing solutions. The synthesis procedure has two phases: (1) design exploration to initially compile linkage candidates, and (2) kinematic tuning to incorporate power modulating characteristics and ensure an impulse-limited, rotation-free jump motion. The final design is an eight-bar linkage with a stroke greater than half the robot's total height that produces a simulated maximum jump power 3.6 times greater than its motor's limit. A 0.27m tall prototype is shown to exhibit minimal pitch rotations during meter high test jumps.
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Several arboreal mammals have the ability to rapidly and repeatedly jump vertical distances of 2 m, starting from rest. We characterize this performance by a metric we call vertical jumping agility. Through basic kinetic relations, we show that this agility metric is fundamentally constrained by available actuator power. Although rapid high jumping is an important performance characteristic, the ability to control forces during stance also appears critical for sophisticated behaviors. The animal with the highest vertical jumping agility, the galago (Galago senegalensis), is known to use a power-modulating strategy to obtain higher peak power than that of muscle alone. Few previous robots have used series-elastic power modulation (achieved by combining series-elastic actuation with variable mechanical advantage), and because of motor power limits, the best current robot has a vertical jumping agility of only 55% of a galago. Through use of a specialized leg mechanism designed to enhance power modulation, we constructed a jumping robot that achieved 78% of the vertical jumping agility of a galago. Agile robots can explore venues of locomotion that were not previously attainable. We demonstrate this with a wall jump, where the robot leaps from the floor to a wall and then springs off the wall to reach a net height that is greater than that accessible by a single jump. Our results show that series-elastic power modulation is an actuation strategy that enables a clade of vertically agile robots.
Conference Paper
Compliant actuation methods are popular in robotics applications where interaction with complex and unpredictable environments and objects is required. There are a number of ways of achieving this, but one common method is Series Elastic Actuation (SEA). In a recent version of their Unified Snake robot, Choset et al. incorporated a Series Elastic Element (SEE) in the form of a rubber torsional spring. This paper explores the possibility of using multi-material 3D printing to produce similar SEEs. This approach would facilitate the fabrication and testing of different springs and minimize the assembly required. This approach is evaluated by characterizing the behavior of two configurations of SEE, 3d printed with different dimensions. The springs exhibit predictable viscoelastic behavior that is well described by a five element Wiechert model. We find that individual springs behave predictably and that multiple copies of the same spring design exhibit good consistency.
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This paper details the design and architecture of a series elastic actuated snake robot, the SEA Snake. The robot consists of a series chain of 1-DOF modules that are capable of torque, velocity and position control. Additionally, each module includes a high-speed Ethernet communications bus, internal IMU, modular electro-mechanical interface, and ARM based on-board control electronics.
Conference Paper
We present three methods of achieving compliant motion with a snake robot by controlling the torques exerted by the joints of the robot. Two strategies command joint torques based solely on the robot's local curvature (i.e. joint angles). A third strategy commands joint angles, velocities, and torques based on the recorded feedback from the robot while executing a previously defined motion under position control. The three control strategies are implemented and compared on a snake robot that includes series elastic actuation (SEA) and torque sensing at each joint, and demonstrate compliant locomotion that adapts automatically to the robot's surrounding terrain.
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Biomimetic engineering takes the principles of biological organisms and copies, mimics or adapts these in the design and development of new materials and technologies. Biomimetic Technologies reviews the key materials and processes involved in this groundbreaking field, supporting theoretical background by outlining a range of applications Beginning with an overview of the key principles and materials associated with biomimetic technologies in Part One, the book goes on to explore biomimetic sensors in more detail in Part Two, with bio-inspired tactile, hair-based, gas-sensing and sonar systems all reviewed. Biomimetic actuators are then the focus of Part Three, with vision systems, tissue growth and muscles all discussed. Finally, a wide range of applications are investigated in Part Four, where biomimetic technology and artificial intelligence are reviewed for such uses as bio-inspired climbing robots and multi-robot systems, microrobots with CMOS IC neural networks locomotion control, central pattern generators (CPG's) and biologically inspired antenna arrays - Includes a solid overview of modern artificial intelligence as background to the principles of biomimetic engineerin - Reviews a selection of key bio-inspired materials and sensors, highlighting their current strengths and future potentia - Features cutting-edge examples of biomimetic technologies employed for a broad range of applications
Conference Paper
Our lab has developed new capabilities for snake robots that allow them to successfully navigate networks of pipes. Recent developments in the control and state estimation of snake robots have enabled these capabilities. The development of a gait-based compliant controller enables us to develop more complex motions while at the same time simplifying the controls for the operator. Additionally, new state estimation techniques that exploit the robot's redundant sensing allow accurate estimation of the robot's orientation and kinematic configuration, even when significant amounts of sensor feedback is missing or corrupted.
Conference Paper
We present a method for the online calibration of a compact series elastic actuator installed in a modular snake robot. Calibration is achieved by using the measured motor current of the actuator's highly geared motor and a simple linear model for the spring's estimated torque. A heuristic is developed to identify operating conditions where motor current is an accurate estimator of output torque, even when the motor is heavily geared. This heuristic is incorporated into an unscented Kalman filter that estimates a spring constant in real-time. Using this method on a prototype module of a series elastic snake robot, we are able accurately estimate the module's output torque, even with a poor initial calibration.
Conference Paper
Full-text available
The design of a hyper-redundant serial-linkage snake robot is the focus of this paper. The snake, which consists of many fully enclosed actuators, incorporates a modular architecture. In our design, which we call the Unified Snake, we consider size, weight, power, and speed tradeoffs. Each module includes a motor and gear train, an SMA wire actuated bistable brake, custom electronics featuring several different sensors, and a custom intermodule connector. In addition to describing the Unified Snake modules, we also discuss the specialized head and tail modules on the robot and the software that coordinates the motion.
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It has long been the dream to build robots which could walk and run with ease. To date, the stance phase of walking robots has been characterized by the use of either straight, rigid legs, as is the case of passive walkers, or by the use of articulated, kinematically-driven legs. In contrast, the design of most hopping or running robots is based on compliant legs which exhibit quite natural behavior during locomotion.
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This paper considers the kinematics of hyper-redundant (or “serpentine”) robot locomotion over uneven solid terrain, and presents algorithms to implement a variety of “gaits”. The analysis and algorithms are based on a continuous backbone curve model which captures the robot's macroscopic geometry. Two classes of gaits, based on stationary waves and traveling waves of mechanism deformation, are introduced for hyper-redundant robots of both constant and variable length. We also illustrate how the locomotion algorithms can be used to plan the manipulation of objects which are grasped in a tentacle-like manner. Several of these gaits and the manipulation algorithm have been implemented on a 30 degree-of-freedom hyper-redundant robot. Experimental results are presented to demonstrate and validate these concepts and our modeling assumptions