Optimization of Gait Trajectory of Bipedal Walking on Inclined Plane With Pitch and Roll Using Genetic Algorithm

2012 ◽  
Author(s):  
H. F. Yu ◽  
E. H. K. Fung ◽  
X. J. Jing
Keyword(s):  
Genetic Algorithm ◽  
Fourier Series ◽  
Kinematic Model ◽  
Step Length ◽  
Bipedal Walking ◽  
Inclined Plane ◽  
Inverse Dynamic ◽  
Dynamic Algorithm ◽  
Truncated Fourier Series ◽  
Single Support Phase

This paper adopts Genetic Algorithm Optimized Fourier Series Formulation (GAOFSF) [1] to achieve stable walking on inclined plane with pitch and roll angle. The first section presents the physical configuration of bipedal robot. Also, kinematic model and inverse dynamic model are derived by Denavit-Hartenberg notation and iterative Newton-Euler dynamic algorithm respectively. Both of them consider the period of single support phase (SSP) only. Then, the formulae of the proposed trajectories which are represented by Truncated Fourier Series (TFS) are given. Moreover, the control objectives of genetic algorithm (GA) which are ZMP trajectories, strike velocity, desired step length and desired average trunk velocity are shown in the third section. Besides, the objective functions and constraints are clearly stated. In the final section, the performance of the proposed trajectories is analyzed based on the preset requirements. The optimized trajectory is found to be satisfactory since it can fulfill all the preset requirements.

A uniform biped gait generator with offline optimization and online adjustable parameters

Robotica ◽  
2007 ◽  
Vol 25 (5) ◽  
pp. 549-565 ◽  
Author(s):  
Lin Yang ◽  
Chee-Meng Chew ◽  
Teresa Zielinska ◽  
Aun-Neow Poo
Keyword(s):  
Genetic Algorithm ◽  
Fourier Series ◽  
Step Length ◽  
Stride Frequency ◽  
Bipedal Locomotion ◽  
Dynamic Simulations ◽  
External Perturbations ◽  
Stable Gait ◽  
Truncated Fourier Series ◽  
Two Parameters

SUMMARYThis paper presents the Genetic Algorithm Optimized Fourier Series Formulation (GAOFSF) method for stable gait generation in bipedal locomotion. It uses a Truncated Fourier Series (TFS) formulation with its coefficients determined and optimized by Genetic Algorithm. The GAOFSF method can generate human-like stable gaits for walking on flat terrains as well as on slopes in a uniform way. Through the adjustment of only a single or two parameters, the step length and stride-frequency can easily be adjusted online, and slopes of different gradients are accommodated. Dynamic simulations show the robustness of the GAOFSF, with stable gaits achieved even if the step length and stride frequency are adjusted by significant amounts. With its ease of adjustments to accommodate different gait requirements, the approach lends itself readily for control of walking on a rough terrain and in the presence of external perturbations.

REAL-TIME BIPEDAL WALKING GAIT ADJUSTMENT MODES BASED ON A TRUNCATED FOURIER SERIES MODEL

2010 ◽  
Vol 07 (01) ◽  
pp. 95-126 ◽  
Author(s):  
LIN YANG ◽  
CHEE-MENG CHEW ◽  
AUN-NEOW POO ◽  
TERESA ZIELINSKA
Keyword(s):  
Fourier Series ◽  
Real Time ◽  
Step Length ◽  
Pattern Generator ◽  
Bipedal Walking ◽  
Step Frequency ◽  
Dynamic Simulations ◽  
Walking Gait ◽  
Walking Pattern ◽  
Truncated Fourier Series

This paper presents three basic bipedal walking gait adjustment modes: step-frequency, step-length and biped lower extremities' pattern adjustments. All the adjustment modes are based on a simple Fourier Series formulation named the Truncated Fourier Series (TFS) model which is newly proposed as a walking pattern generator. Making use of these three gait adjustment modes, bipedal walking can be modified in real-time according to the environment changes. In this paper, the developed gait adjustment modes have been studied by dynamic simulations. The results obtained show that stable walking on uneven terrains as well as human-like walking behaviors can be achieved.

Truncated Fourier series formulation for bipedal walking balance control

Robotica ◽  
2009 ◽  
Vol 28 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Lin Yang ◽  
Chee-Meng Chew ◽  
Yu Zheng ◽  
Aun-Neow Poo
Keyword(s):  
Fourier Series ◽  
Control Method ◽  
Balance Control ◽  
Bipedal Walking ◽  
Reference Trajectory ◽  
Dynamic Feedback ◽  
Long Distance ◽  
Time Dynamic ◽  
Truncated Fourier Series ◽  
Walking Balance

SUMMARYThis paper studies the parameters contained in the truncated Fourier series (TFS) formulation for bipedal walking balance control. Using the TFS generated lateral motion reference, 3D bipedal walking can be directly achieved without any parameter adjustment. Furthermore, the potential of this TFS formulation for motion balance control has also been investigated. One more motion balance strategy is developed through the reinforcement learning, which adjusts the motion's reference trajectory according to the selected dynamic feedback in real time. Dynamic simulation results of the presented balance control method show that the resulting motion can be constrained periodical and long-distance 3D bipedal walking motions are achievable.

Investigation of discontinuous periodic signals using the measuring labview complex

2020 ◽  
pp. 72-79
Author(s):  
E.B. Solovyeva ◽  
◽  
Yu.M. Inshakov ◽  
Keyword(s):  
Fourier Series ◽  
Laboratory Experiment ◽  
Gibbs Phenomenon ◽  
Electrical Signals ◽  
Measuring Complex ◽  
Universal Measuring ◽  
Depth Study ◽  
Periodic Signals ◽  
Truncated Fourier Series

General approaches to the analysis of the Gibbs phenomenon for discontinuous periodic signals approximated by the truncated Fourier series are considered. Methods for smoothing the truncated Fourier series and improving its convergence are discussed. The software means for modeling is a universal measuring complex LabVIEW, which possesses a convenient environment for analyzing electrical signals, on the basis of this complex a laboratory experiment is carried out. The advantages of the measuring LabVIEW complex and its capabilities for in-depth study of discontinuous periodic signals are noted.

scholarly journals Dynamics of Fourier Modes in Torus Generative Adversarial Networks

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 325
Author(s):  
Ángel González-Prieto ◽  
Alberto Mozo ◽  
Edgar Talavera ◽  
Sandra Gómez-Canaval
Keyword(s):  
Fourier Series ◽  
Generative Adversarial Networks ◽  
Learning Models ◽  
Training Process ◽  
Small Perturbations ◽  
Adversarial Networks ◽  
Novel Method ◽  
Truncated Fourier Series ◽  
Real Flow ◽  
Machine Learning Models

Generative Adversarial Networks (GANs) are powerful machine learning models capable of generating fully synthetic samples of a desired phenomenon with a high resolution. Despite their success, the training process of a GAN is highly unstable, and typically, it is necessary to implement several accessory heuristics to the networks to reach acceptable convergence of the model. In this paper, we introduce a novel method to analyze the convergence and stability in the training of generative adversarial networks. For this purpose, we propose to decompose the objective function of the adversary min–max game defining a periodic GAN into its Fourier series. By studying the dynamics of the truncated Fourier series for the continuous alternating gradient descend algorithm, we are able to approximate the real flow and to identify the main features of the convergence of GAN. This approach is confirmed empirically by studying the training flow in a 2-parametric GAN, aiming to generate an unknown exponential distribution. As a by-product, we show that convergent orbits in GANs are small perturbations of periodic orbits so the Nash equillibria are spiral attractors. This theoretically justifies the slow and unstable training observed in GANs.

Kinetic and Dynamic Modeling of Single ActuatorWave-Like Robot

Robotica ◽  
2019 ◽  
Vol 37 (11) ◽  
pp. 1971-1986
Author(s):  
Ruoyu Feng ◽  
Peng Zhang ◽  
Junfeng Li ◽  
Hexi Baoyin
Keyword(s):  
Power Consumption ◽  
Dynamic Analysis ◽  
Dynamic Modeling ◽  
Dynamic Equation ◽  
Kinematic Model ◽  
Theoretical Models ◽  
Equation Of Motion ◽  
Kinematics And Dynamics ◽  
Inverse Dynamic ◽  
Inverse Dynamic Analysis

SummaryIn this study, the kinematics and dynamics of a single actuator wave (SAW)-like robot are explored. Comprising a helical spine and links, SAW has the potential for miniaturization. A kinematic model for SAW is firstly established, and the dynamic equation of motion is derived based on Kane’s method. For validation, the motion of SAW is simulated using both MATLAB and ADAMS, and the comparison of results demonstrates the effectiveness of the theoretical models. Then the inverse dynamic analysis is performed to reveal the power consumption. Finally, robot prototypes are developed and tested to confirm the robot velocity predicted by simulations.

scholarly journals Calibration of Kinematic Parameters of Robot Arm Using Laser Tracking System: Compensation for Non-Geometric Errors by Neural Networks and Selection of Optimal Measuring Points by Genetic Algorithm

2012 ◽  
Vol 6 (1) ◽  
pp. 29-37 ◽  
Author(s):  
Seiji Aoyagi ◽  
◽  
Masato Suzuki ◽  
Tomokazu Takahashi ◽  
Jun Fujioka ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Neural Networks ◽  
Tracking System ◽  
Kinematic Model ◽  
Three Dimensional ◽  
Geometric Parameters ◽  
Geometric Errors ◽  
Robot Arm ◽  
Positioning Accuracy ◽  
Laser Tracking

Offline teaching based on high positioning accuracy of a robot arm is desired to take the place of manual teaching. In offline teaching, joint angles are calculated using a kinematic model of the robot arm. However, a nominal kinematic model does not consider the errors arising in manufacturing or assembly, not to mention the non-geometric errors arising in gear transmission, arm compliance, etc. Therefore, a method of precisely calibrating the parameters in a kinematic model is required. For this purpose, it is necessary to measure the three-dimensional (3-D) absolute position of the tip of a robot arm. In this paper, a laser tracking system is employed as the measurement apparatus. The geometric parameters in the robot kinematic model are calibrated by minimizing errors between the measured positions and the predicted ones based on the model. The residual errors caused by non-geometric parameters are further reduced by using neural networks, realizing high positioning accuracy of sub-millimeter order. To speed up the calibration process, a smaller number of measuring points is preferable. Optimal measuring points, which realize high positioning accuracy while remaining small in number, are selected using Genetic Algorithm (GA).

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