1P1-S-045 A Gait Based on the Stability Mechanism of Passive Walking : Generation of Fixed Point and Local Stabilization Method(Biped Robot 2,Mega-Integration in Robotics and Mechatronics to Assist Our Daily Lives)

2005 ◽  
Vol 2005 (0) ◽  
pp. 85
Author(s):  
YOSHITO IKEMATA ◽  
AKIHITO SANO ◽  
HIDEO FUJIMOTO
Keyword(s):  
Fixed Point ◽  
Biped Robot ◽  
Stabilization Method ◽  
Daily Lives ◽  
Passive Walking ◽  
The Stability

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

scholarly journals On the stability of set-valued functional equations with the fixed point alternative

2012 ◽  
Vol 2012 (1) ◽  
pp. 81 ◽  
Author(s):  
Hassan Kenary ◽  
Hamid Rezaei ◽  
Yousof Gheisari ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
The Stability

An Operationally Optimized Seven Link Biped Robot Moving on Slopes

2013 ◽  
Author(s):  
Peiman Naseradinmousavi
Keyword(s):  
Simulated Annealing Algorithm ◽  
Nonlinear Modeling ◽  
Biped Robot ◽  
Gait Pattern ◽  
Critical Parameters ◽  
Modeling Process ◽  
Operational Optimization ◽  
Ankle Joints ◽  
Annealing Algorithm ◽  
The Stability

In this paper, we discuss operational optimization of a seven link biped robot using the well-known “Simulated Annealing” algorithm. Some critical parameters affecting the robot gait pattern are selected to be optimized reducing the total energy used. Nonlinear modeling process we published elsewhere is shown here for completeness. The trajectories of both the hip and ankle joints are used to plan the robot gait on slopes and undoubtedly those parameters would be the target ones for the optimization process. The results we obtained reveal considerable amounts of the energy saved for both the ascending and descending surfaces while keeping the robot stable. The stability criterion we utilized for both the modeling and then optimization is “Zero Moment Point”. A comparative study of human evolutionary gait and the operationally optimized robot is also presented.

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

Analyzing Bifurcation, Stability and Chaos for a Passive Walking Biped Model with a Sole Foot

2018 ◽  
Vol 28 (09) ◽  
pp. 1850113 ◽  
Author(s):  
Maysam Fathizadeh ◽  
Sajjad Taghvaei ◽  
Hossein Mohammadi
Keyword(s):  
Dynamic Models ◽  
Chaotic Behavior ◽  
Bifurcation Diagrams ◽  
Behavior Simulation ◽  
Passive Walking ◽  
Low Energy Consumption ◽  
Nonlinear Dynamic Models ◽  
Soles Of The Feet ◽  
The Stability ◽  
Intrinsic Characteristic

Human walking is an action with low energy consumption. Passive walking models (PWMs) can present this intrinsic characteristic. Simplicity in the biped helps to decrease the energy loss of the system. On the other hand, sufficient parts should be considered to increase the similarity of the model’s behavior to the original action. In this paper, the dynamic model for passive walking biped with unidirectional fixed flat soles of the feet is presented, which consists of two inverted pendulums with L-shaped bodies. This model can capture the effects of sole foot in walking. By adding the sole foot, the number of phases of a gait increases to two. The nonlinear dynamic models for each phase and the transition rules are determined, and the stable and unstable periodic motions are calculated. The stability situations are obtained for different conditions of walking. Finally, the bifurcation diagrams are presented for studying the effects of the sole foot. Poincaré section, Lyapunov exponents, and bifurcation diagrams are used to analyze stability and chaotic behavior. Simulation results indicate that the sole foot has such a significant impression on the dynamic behavior of the system that it should be considered in the simple PWMs.

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