Evidence for Spring Loaded Inverted Pendulum Running in a Hexapod Robot

Although legged locomotion is better at tackling complicated terrains compared with wheeled locomotion, legged robots are rare, in part, because of the lack of simple design tools. The dynamics governing legged locomotion are generally nonlinear and hybrid (piecewise-continuous) and so require numerical simulation for analysis and are not easily applied to robot designs. During the past decade, a few approximated analytical solutions of Spring-Loaded Inverted Pendulum (SLIP), a canonical model in legged locomotion, have been developed. However, SLIP is energy conserving and cannot predict the dynamical stability of real-world legged locomotion. To develop new analytical tools for legged robot designs, we first analytically solved SLIP in a new way. Then based on SLIP solution, we developed an analytical solution of a hip-actuated Spring-Loaded Inverted Pendulum (hip-actuated-SLIP) model, which is more biologically relevant and stable than the canonical energy conserving SLIP model. The analytical approximations offered here for SLIP and the hip actuated-SLIP solutions compare well with the numerical simulations of each. The analytical solutions presented here are simpler in form than those resulting from existing analytical approximations. The analytical solutions of SLIP and the hip actuated-SLIP can be used as tools for robot design or for generating biological hypotheses.

Download Full-text

Comparison of Hip Torque and Radial Forcing Effects on Locomotion Stability and Energetics

Volume 6B: 37th Mechanisms and Robotics Conference ◽

10.1115/detc2013-13516 ◽

2013 ◽

Cited By ~ 1

Author(s):

Zhuohua Shen ◽

Peter Larson ◽

Justin Seipel

Keyword(s):

Inverted Pendulum ◽

Legged Robots ◽

Asymptotically Stable ◽

Alternative Strategies ◽

Advantages And Disadvantages ◽

Potential Alternative ◽

Spring Loaded Inverted Pendulum

Hip torque and radial forcing along the leg are two common actuation methods for legged robots. However, hip torque and radial forcing have not been compared as potential alternative strategies of actuation. The respective advantages and disadvantages of hip torque and radial forcing are not well known. In this paper, we compare hip torque and radial forcing actuation through the simulation of two models: a Rotary-forced Spring-Loaded Inverted Pendulum and a Radially Forced Spring-Loaded Inverted Pendulum. Both actuation methods can produce fully asymptotically stable locomotion. Interestingly, it is found that they improve locomotion stability in different ways: hip torque first destabilizes locomotion when initially introduced but greatly stabilizes locomotion when it keeps increasing; radial forcing always stabilizes locomotion, but in a moderate way.

Download Full-text

Design and optimization of an elastic linkage quadruped robot based on workspace and tracking error

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406217750186 ◽

2018 ◽

Vol 232 (22) ◽

pp. 4152-4166 ◽

Cited By ~ 2

Author(s):

Haoyu Ren ◽

Qimin Li ◽

Bing Liu ◽

Zhenhuan Dou

Keyword(s):

Inverted Pendulum ◽

Tracking Error ◽

Design Procedure ◽

Design Parameters ◽

Linkage Mechanism ◽

Inverted Pendulum Model ◽

Pendulum Model ◽

Extreme Load ◽

Cable Drive ◽

Spring Loaded Inverted Pendulum

High acceleration and extreme load are frequently appeared on high-speed locomotion of legged robot’s legs, imposing a challenging trade-off between weight and torque in leg design. This paper proposes a new design paradigm based on cable-drive and elastic linkage to solve the problem. The details of the design procedure are given, including the construction of the single leg. With the optimum design of the linkage mechanism, a combined index of the workspace and tracking error are used as object function, and taking geometrical design parameters of the linkage as optimization parameters. Based on the target workspace and the spring-loaded inverted pendulum model, the best foot trajectory in obstacle climbing and trotting gait are analyzed and illustrated. This paper built linkage cable-drive spring robot based on the legged module integration. Simulations and experiments indicate that linkage cable-drive spring robot performs stable trotting with control of the spring-loaded inverted pendulum model. Linkage cable-drive spring robot prototype experiments results are provided to verify the validity of the new method.

Download Full-text

Gait Based on the Spring-Loaded Inverted Pendulum

Humanoid Robotics: A Reference ◽

10.1007/978-94-007-7194-9_43-1 ◽

2017 ◽

pp. 1-25

Author(s):

Hartmut Geyer ◽

Uluc Saranli

Keyword(s):

Inverted Pendulum ◽

Spring Loaded Inverted Pendulum

Download Full-text

Stabilized Walking of Humanoid NAO using Enhanced Spring-Loaded Inverted Pendulum Model on Uneven Terrain

International Journal of Social Ecology and Sustainable Development ◽

10.4018/ijsesd.293253 ◽

2022 ◽

Vol 13 (1) ◽

pp. 0-0

Keyword(s):

Path Length ◽

Inverted Pendulum ◽

Center Of Mass ◽

Humanoid Robots ◽

Slip Model ◽

Turning Angle ◽

Uneven Terrain ◽

Inverted Pendulum Model ◽

Pendulum Model ◽

Spring Loaded Inverted Pendulum

In the coming decades, humanoid robots will play a rising role in society. The present article discusses their walking control and obstacle avoidance on uneven terrain using enhanced spring-loaded inverted pendulum model (ESLIP). The SLIP model is enhanced by tuning it with an adaptive particle swarm optimization (APSO) approach. It helps the humanoid robot to reach closer to the obstacles in order to optimize the turning angle to optimize the path length. The desired trajectory, along with the sensory data, is provided to the SLIP model, which creates compatible COM (center of mass) dynamics for stable walking. This output is fed to APSO as input, which adjusts the placement of the foot during interaction with uneven surfaces and obstacles. It provides an optimum turning angle for shunning the obstacles and ensures the shortest path length. Simulation has been carried out in a 3D simulator based on the proposed controller and SLIP controller in uneven terrain.

Download Full-text

Towards Robustly Stable Musculo-Skeletal Simulation of Human Gait: Merging Lumped and Component-Based Modeling Approaches

Volume 3: 38th Design Automation Conference, Parts A and B ◽

10.1115/detc2012-71473 ◽

2012 ◽

Author(s):

Justin Seipel

Keyword(s):

Inverted Pendulum ◽

Dynamic Models ◽

Sagittal Plane ◽

Center Of Mass ◽

Human Model ◽

Whole Body ◽

Human Gait ◽

Slip Model ◽

Spring Loaded Inverted Pendulum ◽

Low Dimensional

The objective of work presented in this paper is to increase the center-of-mass stability of human walking and running in musculo-skeletal simulation. The approach taken is to approximate the whole-body dynamics of the low-dimensional Spring-Loaded Inverted Pendulum (SLIP) model of locomotion in the OpenSim environment using existing OpenSim tools. To more directly relate low-dimensional dynamic models to human simulation, an existing OpenSim human model is first modified to more closely represent bilateral above-knee amputee locomotion with passive prostheses. To increase stability further beyond the energy-conserving SLIP model, an OpenSim model based upon the Clock-Torqued Spring-Loaded-Inverted-Pendulum (CT-SLIP) model of locomotion is also created. The result of this work is that a multi-body musculo-skeletal simulation in Open-Sim can approximate the whole-body sagittal-plane dynamics of the passive SLIP model. By adding a plugin controller to the OpenSim environment, the Clock-Torqued-SLIP dynamics can be approximated in OpenSim. To change between walking and running, only one parameter representing the preferred period of a stride is changed. The result is a robustly stable simulation of the center-of-mass locomotion for both walking and running that could serve as a first step toward increasingly anatomically accurate and robustly stable musculo-skeletal simulations.

Download Full-text