scholarly journals Analytic Solution for Stable Bipedal Walking Trajectory Generation Using Fourier Series

2009 ◽  
Vol 15 (12) ◽  
pp. 1216-1222 ◽  
Keyword(s):  
Fourier Series ◽  
Analytic Solution ◽  
Trajectory Generation ◽  
Bipedal Walking

ZMP-Based Trajectory Generation for Bipedal Robots Using Quadratic Programming

2020 ◽  
pp. 266-285
Author(s):  
Sergei Savin
Keyword(s):  
Numerical Simulation ◽  
Quadratic Programming ◽  
Center Of Mass ◽  
Trajectory Generation ◽  
Bipedal Walking ◽  
Walking Robots ◽  
Bipedal Robots ◽  
Change Of Variables ◽  
Viable Solution ◽  
Modern Optimization

In this chapter, the problem of trajectory generation for bipedal walking robots is considered. A number of modern techniques are discussed, and their limitations are shown. The chapter focuses on zero-moment point methods for trajectory generation, where the desired trajectory of that point can be used to allow the robot to keep vertical stability if followed, and presents an instrument to calculate the desired trajectory for the center of mass for the robot. The chapter presents an algorithm based on quadratic programming, with an introduction of a slack variable to make the problem feasible and a change of variables to improve the numeric properties of the resulting optimization problem. Modern optimization tools allow one to solve such problems in real time, making it a viable solution for trajectory planning for the walking robots. The chapter shows a few results from the numerical simulation made for the algorithm, demonstrating its properties.

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.

Adhesive Contacts for Graded-Elastic Coatings Using Fourier Series Decomposition

2011 ◽  
Author(s):  
S. J. Chidlow ◽  
W. W. F. Chong ◽  
M. Teodorescu ◽  
N. D. Vaughan
Keyword(s):  
Fourier Series ◽  
Analytic Solution ◽  
Adhesive Contact ◽  
Solution Technique ◽  
Control Case ◽  
Principal Stresses ◽  
Pressure Distributions ◽  
Surface Deflection ◽  
Elastic Layers ◽  
Adhesive Contacts

We propose a semi-analytic solution technique to determine the subsurface stresses and local deflections resulting in an adhesive contact of graded elastic layers. Identical pressure distributions, typical for a Maugis parameter λ = 1, were applied to a range of graded elastic coatings. The principal stresses and surface deflection in both regions (graded elastic layer and substrate) are computed in terms of Fourier series. This control case has the advantage that the response of different coatings can be easily monitored and compared.

scholarly journals Trajectory Generation for Adaptive Motion by Phase Feedback - Synchronization of Multicycle Human Movement -

2009 ◽  
Vol 21 (3) ◽  
pp. 342-352 ◽  
Author(s):  
Takayuki Ubukata ◽  
◽  
Shinya Kotosaka ◽  
Hideyuki Ohtaki
Keyword(s):  
Fourier Series ◽  
Wavelet Transformation ◽  
Phase Synchronization ◽  
Trajectory Generation ◽  
Human Movement ◽  
Synchronous Motion ◽  
Series Approximation ◽  
Cyclic Motion ◽  
Fourier Series Approximation ◽  
Key Techniques

Synchronous motion is one of the important ability for the co-operation work by human. The focus of our research is to develop a robust and adaptive synchronous trajectory generation method for the robot. To be able to follow the uncertain action by human co-worker, the trajectory generation method must be required adaptability to frequency and phase of movement of human co-worker. Key techniques for our method are PLL (Phase Locked Loop), Fourier series approximation, wavelet transformation for trajectory. PLL technique achieves the phase synchronization with an arbitrary cyclic motion, like as human walking. Fourier series approximation of target trajectory allows us description of wide variety cyclic motion for the robot. More over, we can select the synchronous frequency from human movement with multiple cycles by wavelet transformation. The experiment of synchronization with 3-DOF manipulator and human demonstrator are carried out. As a result, we confirm synchronous performance and the effectiveness of proposed method.

scholarly journals Waves in electric contact wires subjected to transversal impulses

2018 ◽  
Vol 178 ◽  
pp. 05004
Author(s):  
Răzvan Andrei Oprea ◽  
Gabriel Popa ◽  
Marius Alin Gheţi
Keyword(s):  
Fourier Series ◽  
Contact Line ◽  
Phenomenological Model ◽  
Analytic Solution ◽  
Wave Attenuation ◽  
Electric Contact ◽  
Mechanical Contact ◽  
Transverse Waves

It is a well-known fact that the raising of the pantograph is followed by an electric arch. The reasons for this phenomenon are the oscillations of the pantograph and the oscillations of the contact line. Initially, these oscillations are not coupled. In this case, the mechanical contact between the two subsystems may be lost, and may generate electric arch. In the present work, the pantograph rising is modelled through a Dirac impulse. An analytic solution of the transverse waves is obtained by means of Fourier series. A phenomenological model of the wave attenuation is taken into account.

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.

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