Elastic Legs Research Articles

Piezoelectric energy harvesting from walking motion of a passive biped robot model with flexible legs

Passive dynamic walking biped robots utilize the inherent dynamics of their structure to achieve walking motion without continuous actuation, enhancing energy efficiency and stability. Replacing conventional rigid legs with flexible elastic beams in the simplest passive walker will be associated with undesirable vibrations. Despite the positive effect of the damper in reducing vibrations, the current research has used the piezoelectric energy harvesting with the aim of reducing the wasted energy of the gait cycle and improving its stability range. For this purpose, the electromechanical Lagrange equations are determined by applying Hamilton's principle and the assumed mode method and then, the new definition of the step function is obtained through numerical methods, solving a boundary value problem to establish proper initial conditions for stable walking. Numerical simulations indicate that the piezoelectric energy harvester can create a stable period-one gait cycle by optimizing the length of the piezo layers attached to the undamped elastic legs despite the presence of small vibrations. Additional results are presented in bifurcation diagrams, investigating the effect of important physical and structural parameters such as slope angle, length and thickness of the piezo layer.

Emerging Gaits for a Quadrupedal Template Model With Segmented Legs

Abstract Energy-efficient gaits in walking robots can be obtained by designing elastic systems that exhibit naturally emerging locomotion patterns. Biological legged locomotion serves as inspiration, as animals use different gaits to move at certain speeds while minimizing energy consumption. To understand the underlying dynamics of biological locomotion, simplified models have been proposed. The most common one, the SLIP (spring loaded inverted pendulum) model, can explain the effect of the radial elasticity of linear legs and helps to explain locomotion patterns, especially for running behaviors, in different legged systems. However, the SLIP model is inappropriate for the study of stability of limit cycles in systems with articulated legs, which are most commonly used in real robots. This paper introduces a novel quadrupedal template model featuring articulated elastic legs, non-constant leg stiffness, and dynamic leg swing. Numerical simulation with a continuation approach is used to discover the gaits emerging from the natural dynamics of the model, without imposing any contact sequence a priori. The stability of those gaits is also characterized, in order to facilitate the exploitation of the natural model dynamics for generating locomotion patterns for quadrupedal robots.

Learning plastic matching of robot dynamics in closed-loop central pattern generators

Animals achieve agile locomotion performance with reduced control effort and energy efficiency by leveraging compliance in their muscles and tendons. However, it is not known how biological locomotion controllers learn to leverage the intelligence embodied in their leg mechanics. Here we present a framework to match control patterns and mechanics based on the concept of short-term elasticity and long-term plasticity. Inspired by animals, we design a robot, Morti, with passive elastic legs. The quadruped robot Morti is controlled by a bioinspired closed-loop central pattern generator that is designed to elastically mitigate short-term perturbations using sparse contact feedback. By minimizing the amount of corrective feedback on the long term, Morti learns to match the controller to its mechanics and learns to walk within 1 h. By leveraging the advantages of its mechanics, Morti improves its energy efficiency by 42% without explicit minimization in the cost function.

Passive walking biped robot model with flexible viscoelastic legs

To simulate the complex human walking motion accurately, a suitable biped model has to be proposed that can significantly translate the compliance of biological structures. In this way, the simplest passive walking model is often used as a standard benchmark for making the bipedal locomotion so natural and energy efficient. This paper is devoted to a presentation of the application of internal damping mechanism to the mathematical description of the simplest passive walking model with flexible legs. This feature can be taken into account by using the viscoelastic legs, which are constituted by the Kelvin–Voigt rheological model. Then, the update of the impulsive hybrid nonlinear dynamics of the simplest passive walker is obtained based on the Euler–Bernoulli’s beam theory and using a combination of Lagrange mechanics and the assumed mode method, along with the precise boundary conditions. The main goal of this study is to develop a numerical procedure based on the new definition of the step function for enforcing the biped start walking from stable condition and walking continuously. In our previous work, it was shown that the period-one gait cycle can be produced by adding the proportional damping model with high damping ratio to the elastic legs. The present paper overcomes the practical limitations of this damping model and similarly demonstrates the stable period-one gait cycles for the viscoelastic legs. The study of the influence of various system parameters is carried out through bifurcation diagrams, highlighting the region of stable period-one gait cycles. Numerical simulations clearly prove that the overall effect of viscoelastic leg on the passive walking is efficient enough from the viewpoint of stability and energy dissipation.

BirdBot achieves energy-efficient gait with minimal control using avian-inspired leg clutching.

Designers of legged robots are challenged with creating mechanisms that allow energy-efficient locomotion with robust and minimalistic control. Sources of high energy costs in legged robots include the rapid loading and high forces required to support the robot's mass during stance and the rapid cycling of the leg's state between stance and swing phases. Here, we demonstrate an avian-inspired robot leg design, BirdBot, that challenges the reliance on rapid feedback control for joint coordination and replaces active control with intrinsic, mechanical coupling, reminiscent of a self-engaging and disengaging clutch. A spring tendon network rapidly switches the leg's slack segments into a loadable state at touchdown, distributes load among joints, enables rapid disengagement at toe-off through elastically stored energy, and coordinates swing leg flexion. A bistable joint mediates the spring tendon network's disengagement at the end of stance, powered by stance phase leg angle progression. We show reduced knee-flexing torque to a 10th of what is required for a nonclutching, parallel-elastic leg design with the same kinematics, whereas spring-based compliance extends the leg in stance phase. These mechanisms enable bipedal locomotion with four robot actuators under feedforward control, with high energy efficiency. The robot offers a physical model demonstration of an avian-inspired, multiarticular elastic coupling mechanism that can achieve self-stable, robust, and economic legged locomotion with simple control and no sensory feedback. The proposed design is scalable, allowing the design of large legged robots. BirdBot demonstrates a mechanism for self-engaging and disengaging parallel elastic legs that are contact-triggered by the foot's own lever-arm action.

Trot gait control of a quadruped robot with elastic legs

Trot gait control of a quadruped robot with elastic legs

Gait cycles of passive walking biped robot model with flexible legs

Passive dynamic walking of bipeds exhibits a new concept of robot locomotion that is well- known for its success in human mimicry. Many efforts have been devoted in the literature to implement flexible and anthropomorphic passive bipeds. However, utilization of flexible characteristics of elastic structures has not been considered yet. This paper presents a modified simplest passive walking model with flexible legs which are a pair of elastic beams with small deflections instead of usual rigid links. The main contributions of this paper lie in modeling the impulsive hybrid dynamics of the flexible passive biped and applying a numerical technique based on finite difference formula to seek for appropriate initial conditions of walking gait cycles. Extended Hamilton's principle and assumed mode method along with Euler–Bernoulli's beam theory and updated transition rules at impact are used to derive the mathematical model of this biped. Numerical simulations reveal non-periodic patterns of motion for small slope angles due to vibrations of elastic legs. It is also shown that the period-one gait cycles with quicker steps can be generated on slower slopes for different values of elasticity and damping coefficients compared to the rigid model.

Foot terrain impact modeling and motion performance research of hexapod robot based on passive elastic leg

In order to improve the performance of the multi-legged robot, the impact of foot-terrain is an important target to measure the performance of the robot. In order to ensure the compliance contact of foot-terrain for the legged robot, it is essential to add passive spring between the calf and foot. The mechanical structure makes the leg of hexapod robot retractable passive elastic structure. For multi-legged robots with passive elastic legs, the foot-terrain impact model is presented to measure the dynamic performance and provide theoretical support for the low impact force motion planning. The traditional planning method will cause additional impact for the switching case between the swing and stance phase. This paper presents a motion planning method that considers the deformable leg structure and impact performance. The experiments have been carried out, and the results have demonstrated the effectiveness of the foot terrain impact model and motion planning method in comparison with a conventional method.

Study on impact energy absorption and adhesion of biomimetic buffer system for space robots

Space buffer landers offer the unique promise of ensuring that high-speed flying space robots steadily attach to the surface of the target spacecraft for repairs and rescues. A stable attachment and an easy detachment mechanism of the robot are required to enable space buffer landers to land smoothly on spacecraft in space environments. In this paper, we present an approach to fabricate a buffer lander with an elastic multi-leg configuration and adhesive feet with a microarray structure. We set up a theoretical model of a buffer lander with six elastic legs and adhesive feet. We analyze the influence of the initial position of the lander on the buffer kinetic energy absorption characteristics by theoretical modeling. Based on this model, we establish a discrete element multibody dynamics coupling simulation platform. Through the simulation, we analyze the factors influencing the buffer kinetic energy absorption characteristics and optimize the parameters of the buffer. We obtain the contact force of the adhesion feet and the torque of each joint of the buffer during the cushioning process with EDEM-ADAMS coupling simulations. Finally, we build a launching platform for the buffer collision test and simulate a high-temperature and high-vacuum space environment with a heating cage and a vacuum tank, respectively. Then, the effects of the high-temperature and high-vacuum environment on the kinetic energy absorption and adsorption characteristics of the buffer are analyzed.

Development of Octopus Robot with High Object Manipulability and Mobility

An octopus has multiple degrees of freedom and elastic legs that can skillfully perform various actions. In this study, we propose an octopus type robot with multiple limb, multiple degrees of freedom and the adsorption function. We made a prototype robot with multiple degrees of freedom legs. We also carried out experiments about rod climbing, ladder climbing, brachiation, and caterpillar type movement using the robot. Because the link length of the multiple degrees of freedom leg is shorter than the link length of a fewer degrees of freedom leg, the robot has small moment arm. These experiments show examples of various behaviors by the robot with small moment arm.

Modeling Legged Microrobot Locomotion Based on Contact Dynamics and Vibration in Multiple Modes and Axes

A dynamic model is developed for small-scale robots with multiple high-frequency actuated compliant elastic legs and a rigid body. The motion of the small-scale robots results from dual-direction motion of piezoelectric actuators attached to the legs, with impact dynamics increasing robot locomotion complexity. A dynamic model is developed to describe the small-scale robot motion in the presence of variable properties of the underlying terrain. The dynamic model is derived from beam theory with appropriate boundary and loading conditions and considers each robot leg as a continuous structure moving in two directions. Robot body motion is modeled in up to five degrees-of-freedom (DOF) using a rigid body approximation for the central robot chassis. Individual modes of the resulting multimode robot are treated as second-order linear systems. The dynamic model is tested with two different centimeter-scale robot prototypes having an analogous actuation scheme to millimeter-scale microrobots. In accounting for the interaction between the robot and ground, a dynamic model using the first two modes of each leg shows good agreement with experimental results for the centimeter-scale prototypes, in terms of both magnitude and the trends in robot locomotion with respect to actuation conditions.

Piezoelectric driven insect‐inspired robot with flapping wings capable of skating on the water

A 165 mg coin-size bionic water-skating robot driven by piezoelectric (PZT) bending actuator is presented. The robot with light weight and elastic legs uses surface tension to keep itself on the water surface. The driving force produced by flapping wings enables it to glide easily due to tiny resistance coefficient of water surface. The robot consists of PZT bending actuator, four-bar transmission structure, two flapping wings, four elastic legs and the body. The actuator bending at resonance frequency of 105 Hz achieves 346 μm displacement at the end of actuator at voltage of 280 V so that the flapping angle of the wings reaches 73° at that frequency. Tests show that, the maximum equivalent payload of robot is 830.6 mg, about five times of its own mass, before breaking the water surface, and the water drag when robot skates on the water surface is about 29 μN, 1.76% of its gravity. The maximum forward speed of the robot is measured as 151 mm/s.

Experimental investigation of wave slamming on an open structure supported elastically

The superstructures of marine structures supported by the elastic legs and located in the splash zone will subject to violent wave slamming and vibrate consequently during storms. A series of model tests are carried out to investigate the wave impacting on the open structures supported elastically. Three kinds of models with different natural frequencies are designed. The characteristics of the wave pressures on the three models are compared. The durations of the uplift forces and the corresponding accelerations of the structure during wave impact are analyzed simultaneously. The distributions of the peak impact pressures on the subfaces of the plates with different supporting stiffness are given. The relationship between the uplift force on the three models and the relative clearance are obtained. The spectral properties of the slamming loads on the three different structures are compared. The experimental results indicate that the behaviors of the impact pressures, the uplift forces and accelerations of the plates with small natural frequencies are obviously different from those of the plates with larger natural frequencies within the range of the experimental parameters.

Vibrot, a Simple Device for the Conversion of Vibration into Rotation Mediated by Friction: Preliminary Evaluation

While “vibrational noise” induced by rotating components of machinery is a common problem constantly faced by engineers, the controlled conversion of translational into rotational motion or vice-versa is a desirable goal in many scenarios ranging from internal combustion engines to ultrasonic motors. In this work, we describe the underlying physics after isolating a single degree of freedom, focusing on devices that convert a vibration along the vertical axis into a rotation around this axis. A typical Vibrot (as we label these devices) consists of a rigid body with three or more cantilevered elastic legs attached to its bottom at an angle. We show that these legs are capable of transforming vibration into rotation by a “ratchet effect”, which is caused by the anisotropic stick-slip-flight motion of the leg tips against the ground. Drawing an analogy with the Froude number used to classify the locomotion dynamics of legged animals, we discuss the walking regime of these robots. We are able to control the rotation frequency of the Vibrot by manipulating the shaking amplitude, frequency or waveform. Furthermore, we have been able to excite Vibrots with acoustic waves, which allows speculating about the possibility of reducing the size of the devices so they can perform tasks into the human body, excited by ultrasound waves from the outside.

A Study on the Resonance Frequency of the Cross-Shaped Piezoelectric Generator According to Change in Elastic Body Thickness and Tip Mass

Over the past few years, research about generating system with piezoelectric ceramics has been conducted. To compensate problem of low generating power than other harvesters, many researchers have studied about piezoelectric generator for obtaining high output. And until now various types of piezoelectric generator has been developed. Cross-shaped piezoelectric generator using only one vibration source has four elastic body legs which have same vibration mode. So they have same resonance frequency under the vibration. Elastic body thickness and tip mass in design parameters influence on the resonance frequency. The parameters have relation to output characteristics. In this paper, the output characteristics depending on the elastic body thickness and tip mass were studied. The elastic body material used here was SUS304 for high output characteristics. As a result, the resonance frequency was decreased with decreasing thickness. The generator is expected to be used as an energy harvest from at vibration source around the human life.

Research on pipeline elbow passing for in-pipe robot

In-pipe robots provide inspection and maintenance services to various pipelines. This article proposes an algorithm to calculate the required radial variations for in-pipe robots to pass through pipeline elbows smoothly. It first gives a full overview of a robot passing through a U-shaped elbow and identifies the problem location where the radial dimension changes the most. It then presents a detailed analysis on the focused stage and deduces the algorithm. Based on the obtained algorithm, a realizing Matlab program is written to calculate all possible lengths of front and rear legs at every moment during the process. Finally, the calculation results are presented to precisely describe the track of movement, the length deformations during the whole process, and different contributions of structural variables. This article provides the design and the control of an in-pipe robot with an algorithm to calculate the lengths of its legs at every moment and to what extent the deformations of elastic legs are required.

高性能希土類磁石を利用し扁平化した摩擦駆動型電磁マイクロモータの基礎特性

An electromagnetic micromotor based upon a friction drive features relatively high torque at low speeds without reduction gears. In this paper, we have redesigned the motor structure to reduce the thickness below 3 mm and examined its basic characteristics. The motor has a single-phase, two-pole axial gap structure. The stator is a thin excitation coil with a ferrite core. The rotor consists of a NdFeB magnet, 5 mm in diameter and 1 mm in thickness, with three inclined elastic legs, and is magnetically fixed on the stator. When an alternating current is applied to the coil, the rotor oscillates axially according to the change in the attractive force and hops on the stator. Thus the axial oscillation of the rotor is converted into the rotary movement through the friction of the legs. We constructed the motors using a commercial NdFeB magnet and a surface-modified one. As a result, the torque of the motor using the surface-modified NdFeB magnet was much larger than that of the commercial motor. The maximum starting torque obtained here reached approximately 0.11 mNm, which is several times as large as those of commercial DC motors of this volume.

Mechanical models for insect locomotion: dynamics and stability in the horizontal plane I. Theory.

We study the dynamics and stability of legged locomotion in the horizontal plane. Motivated by experimental studies of insects, we develop two- and three-degree-of freedom rigid body models with pairs of 'virtual' elastic legs in intermittent contact with the ground. We focus on conservative compliant-legged models, but we also consider prescribed forces, prescribed leg displacements, and combined strategies. The resulting mechanical systems exhibit periodic gaits whose stability characteristics are due to intermittent foot contact, and are largely determined by geometrical criteria. Most strikingly, we show that mechanics alone can confer asymptotic stability in heading and body orientation. In a companion paper, we apply our results to rapidly running cockroaches.

Stability and Postbuckling of a Platform with Flexible Legs Resting on a Slippery Surface*

ABSTRACT A rigid platform is supported by thin elastic legs. The legs are able to slide on the ground as they deform. The governing equations for large deformations are formulated and solved numerically by homotopy and quasi Newton methods. Nonlinear phenomena such as nonuniqueness are found. A global critical load for nonlinear stability is presented.

Omnidirectional Walking Mechanism. 2nd Report. Inclination Control while Walking on Rough Terrain.

This paper proposes an inclination control algorithm of the Omnidirectional Walking Mechanism, which consists of a parallel link mechanism connecting two frames with three linear actuators and six elastic legs. The relative position and angle of the frames are selected arbitrarily by three actuators. Walking motion is produced by combining them with extendable legs. The ground is not always flat, and many different levels and obstacles exist, so posture control is essential for robot-labor. Posture of the robot can be controlled by changing the lengths of the legs referring data from inclination sensors. We constructed an experimental prototype model, and used the above method to control the inclination of the upper surface of the prototype model. The performance was investigated in terms of motion in every direction and over steps, and as a result of the experiments, it is confirmed that this robot can walk in all directions and can walk on a gentle slope by controlling the inclination of the upper surface.