scholarly journals Biped Robot Walking using a Combination of Truncated Fourier Series and GALA (Genetic Algorithm parameters adaption using Learning Automata)

2012 ◽  
pp. 598-603
Author(s):  
Omid Mohamad Nezami ◽  
Mohammad Reza Meybodi
Keyword(s):  
Genetic Algorithm ◽  
Fourier Series ◽  
Learning Automata ◽  
Biped Robot ◽  
Truncated Fourier Series

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.

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.

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.

Optimizing Fourier Series Based Gaits for Modular Robots Using an Evolutionary Algorithm

2013 ◽  
Author(s):  
David Ko ◽  
Harry H. Cheng
Keyword(s):  
Genetic Algorithm ◽  
Fourier Series ◽  
Evolutionary Algorithm ◽  
Periodic Motion ◽  
Degrees Of Freedom ◽  
Series Representation ◽  
Robotic System ◽  
Experimental Results ◽  
New Method ◽  
Modular Robots

A new method of controlling and optimizing robotic gaits for a modular robotic system is presented in this paper. A robotic gait is implemented on a robotic system consisting of three Mobot modules for a total of twelve degrees of freedom using a Fourier series representation for the periodic motion of each joint. The gait implementation allows robotic modules to perform synchronized gaits with little or no communication with each other making it scalable to increasing numbers of modules. The coefficients of the Fourier series are optimized by a genetic algorithm to find gaits which move the robot cluster quickly and efficiently across flat terrain. Simulated and experimental results show that the optimized gaits can have over twice as much speed as randomly generated gaits.

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