Design and Dynamic Analysis of a Compliant Leg Configuration towards the Biped Robot’s Spring-Like Walking

Luo, Guifu; Du, Rong-Gui; Zhu, Shiqiang; Song, Sumian; Yuan, Haihui; Hua, Zhou; Zhao, Mingguo; Gu, Jason

doi:10.1007/s10846-022-01614-3

Cited by 10 publications

(7 citation statements)

References 37 publications

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“…As shown in Fig. 8, the desired oscillation period should be measured after 1.5 s, and this period is around 0.16 s. This period can also be estimated by evaluating the vertical stiffness through (20) and substituting it into a simple mass-spring harmonic oscillator model. Specifically for this test, according to (20), the equivalent leg stiffness along the vertical direction is 5569 N/m.…”

Section: Dropping Testmentioning

confidence: 99%

“…8, the desired oscillation period should be measured after 1.5 s, and this period is around 0.16 s. This period can also be estimated by evaluating the vertical stiffness through (20) and substituting it into a simple mass-spring harmonic oscillator model. Specifically for this test, according to (20), the equivalent leg stiffness along the vertical direction is 5569 N/m. Given the leg mass is around 3 kg, the oscillation period should be 2π √ m/k, which is 0.146 s. The estimated oscillation period of 0.146 s is close to the measured one of 0.16 s, indicating that the actual leg stiffness fits the predicted one.…”

Section: Dropping Testmentioning

confidence: 99%

“…For these leaf springs, as external forces act on their end, deflections as well as resisting torques will be generated. Relation between resisting torques and deflections can be modeled as [20]: where denotes the stiffness and denotes the deflection angle of a leaf spring. As a linear approximation, (1) usually works well for small deflection angles.…”

Section: Robot Leg With Leaf Springsmentioning

confidence: 99%

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A compliant leg design combining pantograph structure with leaf springs

Wang,

Zhang,

et al. 2023

Robotica

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We proposed a compliant leg configuration that enhances the conventional pantograph design with leaf springs. The following facts characterize the proposed configuration: (1) Due to the use of the pantograph structure, the mass is centralized around the hip joint, reducing the lower leg inertia; (2) Leaf springs are chosen as elastic parts to increase energy efficiency and estimate foot-end contact forces. Compared with coil springs, leaf springs require no guide rails to deploy, and their stiffness can be easily adjusted through shape cutting. Analytical models are introduced to analyze the leg’s stiffness and estimate the contact forces only with the deflections of leaf springs. A one-leg robot based on the proposed design is built, and various experiments are conducted. Experiments regarding the stiffness calibration and the contact forces estimation showed an acceptable agreement with the analytical model. Experiments of dropping demonstrate the feasibility of the leg to perform spring-like behaviors. Experiments of periodic hopping demonstrate the feasibility of using spring deflections to detect touch-down events. For energy efficiency, it is also observed that the elastic leg has a 20% increment concerning the jumping height in the flight phase, compared with the one where leaf springs are replaced with rigid materials.

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Section: Dropping Testmentioning

confidence: 99%

Section: Dropping Testmentioning

confidence: 99%

Section: Robot Leg With Leaf Springsmentioning

confidence: 99%

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A compliant leg design combining pantograph structure with leaf springs

Wang,

Zhang,

et al. 2023

Robotica

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“…To simplify the modeling of the leg, the leg was divided into two parts: a rigid part that refers to the part from the hip joint to the leg CoM, whose length would not change, and a spring part that refers to the part from the leg CoM to the pointed foot, whose length would change concerning ground reaction force. Table 1 displays some design parameters of the simplified robot model shown in Figure 3, and for more details on the robot design, one can refer to our previously published work [26,27].…”

Section: Brief Description Of the Planar Compliant One-legged Robotmentioning

confidence: 99%

Stable and Fast Planar Jumping Control Design for a Compliant One-Legged Robot

Luo

Song

et al. 2022

Micromachines

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Compliant bipedal robots demonstrate a potential for impact resistance and high energy efficiency through the introduction of compliant elements. However, it also adds to the difficulty of stable control of the robot. To motivate the control strategies of compliant bipedal robots, this work presents an improved control strategy for the stable and fast planar jumping of a compliant one-legged robot designed by the authors, which utilizes the concept of the virtual pendulum. The robot was modeled as an extended spring-loaded inverted pendulum (SLIP) model with non-negligible torso inertia, leg inertia, and leg damping. To enable the robot to jump forward stably, a foot placement method was adopted, where due to the asymmetric feature of the extended SLIP model, a variable time coefficient and an integral term with respect to the forward speed tracking error were introduced to the method to accurately track a given forward speed. An energy-based leg rest length regulation method was used to compensate for the energy dissipation due to leg damping, where an integral term, regarding jumping height tracking error, was introduced to accurately track a given jumping height. Numerical simulations were conducted to validate the effectiveness of the proposed control strategy. Results show that stable and fast jumping of compliant one-legged robots could be achieved, and the desired forward speed and jumping height could also be accurately tracked. In addition to that, using the proposed control strategy, the robust jumping performance of the robot could be observed in the presence of disturbances from state variables or uneven terrain.

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“…The robot's movement was directed using a control system that works in a rotating frame, and a feedback controller based on estimating and compensating for disturbances was developed to decouple the motion in the Cartesian coordinates. A robot that has the ability to walk with a flexible leg design, similar to a spring, was introduced [23]. It was made up of two sequential motors and a compliant mechanism with six bars to achieve the requirements of the SLIP model.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Modeling and Hybrid Compliant Control for a 2-DOF Compliant Robotic Leg With a New Biarticular Actuation

Kalibala

Mohamed

Umezu

et al. 2023

Preprint

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It is well recognized that biarticular muscles cross over two joints instead of just one, granting them the ability to generate substantial forces across both joints. This type of muscle plays a crucial role in human movement, since it produces large forces. In literature, there have been numerous designs of mono- and biarticular actuations applied for a two- or three-link robotic leg, aimed at studying human locomotion. A novel biarticular actuation configuration for a two-link compliant robotic leg is proposed in this research. It features mono-articular rotational actuation for the proximal link and biarticular linear actuation for the distal link. The distal link is actuated by a linear Series Elastic Actuator (SEA) that is suitable for compliant ground interaction, while the proximal link is driven by a stiff rotary actuator. This biarticular actuation is bio-inspired by the biarticular muscles in humans, especially the hamstring muscle, which span two joints instead of one to provide high torque at both joints. This new configuration for the two-link robotic leg realizes the Spring-loaded Inverted Pendulum (SLIP) dynamics, making human locomotion during the compliant ground interaction simpler. In the biarticular coordinates, complete kinematic and dynamic analyses are developed for this new configuration. The approach also involves using a rotating task space to represent the swing and stance phases of human gait. The dynamic model is transformed into this rotating task space and a hybrid impedance and position controller is developed with optimized gains to minimize the tracking errors and prevent any disturbance. A disturbance observer controller is developed and integrated with the hybrid impedance control for the proposed linear SEA in order to improve the force control precision and the resilience against external disturbances. The simulation results show the feasibility of this new approach.

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Design and Dynamic Analysis of a Compliant Leg Configuration towards the Biped Robot’s Spring-Like Walking

Cited by 10 publications

References 37 publications

A compliant leg design combining pantograph structure with leaf springs

A compliant leg design combining pantograph structure with leaf springs

Stable and Fast Planar Jumping Control Design for a Compliant One-Legged Robot

Dynamic Modeling and Hybrid Compliant Control for a 2-DOF Compliant Robotic Leg With a New Biarticular Actuation

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