scholarly journals Feasible speeds for two optimal periodic walking gaits of a planar biped robot

Robotica ◽  
2021 ◽  
pp. 1-26
Author(s):  
Mathieu Hobon ◽  
Víctor De-León-Gómez ◽  
Gabriel Abba ◽  
Yannick Aoustin ◽  
Christine Chevallereau
Keyword(s):  
Optimization Algorithm ◽  
Finite Time ◽  
Parametric Optimization ◽  
Biped Robot ◽  
Double Support ◽  
Walking Velocity ◽  
Definition Of

Abstract The purpose is to define the range of feasible speeds for two walking motions for a particular planar biped robot, which differ in the definition of their finite-time double support phases. For each speed, these two walking motions are numerically obtained by using a parametric optimization algorithm, regarding a sthenic criterion. Results allow us to define the range of allowable speeds for each walking. One result is that the first gait is less consuming in energy for moderate to fast velocity with respect to the second one, while the second gait is more efficient for low walking velocity.

scholarly journals Modeling and Finite-Time Walking Control of a Biped Robot with Feet

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Juan E. Machado ◽  
Héctor M. Becerra ◽  
Mónica Moreno Rocha
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Biped Robot ◽  
Robot Dynamics ◽  
Local Diffeomorphism ◽  
Double Support ◽  
Finite Time Convergence ◽  
Mode Control ◽  
Support Phase

This paper addresses the problem of modeling and controlling a planar biped robot with six degrees of freedom, which are generated by the interaction of seven links including feet. The biped is modeled as a hybrid dynamical system with a fully actuated single-support phase and an instantaneous double-support phase. The mathematical modeling is detailed in the first part of the paper. In the second part, we present the synthesis of a controller based on virtual constraints, which are codified in an output function that allows defining a local diffeomorphism to linearize the robot dynamics. Finite-time convergence of the output to the origin ensures a collision between the swing foot and the ground with an appropriate configuration for the robot to give a step forward. The components of the output track adequate references that encode a walking pattern. Finite-time convergence of the tracking errors is enforced by using second-order sliding mode control. The main contribution of the paper is an evaluation and comparison of discontinuous and continuous sliding mode control in the presence of parametric uncertainty and external disturbances. The robot model and the synthesized controller are evaluated through numerical simulations.

scholarly journals Effects of Torso Pitch Motion on Energy Efficiency of Biped Robot Walking

2021 ◽  
Vol 11 (5) ◽  
pp. 2342
Author(s):  
Long Li ◽  
Zhongqu Xie ◽  
Xiang Luo ◽  
Juanjuan Li
Keyword(s):  
Energy Efficiency ◽  
Energy Consumption ◽  
Biped Robot ◽  
Gait Pattern ◽  
Pattern Generation ◽  
Biped Robots ◽  
Pitch Motion ◽  
Double Support ◽  
Gait Parameters ◽  
Support Phase

Gait pattern generation has an important influence on the walking quality of biped robots. In most gait pattern generation methods, it is usually assumed that the torso keeps vertical during walking. It is very intuitive and simple. However, it may not be the most efficient. In this paper, we propose a gait pattern with torso pitch motion (TPM) during walking. We also present a gait pattern with torso keeping vertical (TKV) to study the effects of TPM on energy efficiency of biped robots. We define the cyclic gait of a five-link biped robot with several gait parameters. The gait parameters are determined by optimization. The optimization criterion is chosen to minimize the energy consumption per unit distance of the biped robot. Under this criterion, the optimal gait performances of TPM and TKV are compared over different step lengths and different gait periods. It is observed that (1) TPM saves more than 12% energy on average compared with TKV, and the main factor of energy-saving in TPM is the reduction of energy consumption of the swing knee in the double support phase and (2) the overall trend of torso motion is leaning forward in double support phase and leaning backward in single support phase, and the amplitude of the torso pitch motion increases as gait period or step length increases.

On the Calculation of Directional Scale Elasticity in Data Envelopment Analysis

2016 ◽  
Vol 33 (04) ◽  
pp. 1650026
Author(s):  
Mahdi Mirjaberi ◽  
Reza Kazemi Matin
Keyword(s):  
Data Envelopment Analysis ◽  
Decision Maker ◽  
Cross Sections ◽  
Optimization Algorithm ◽  
Parametric Optimization ◽  
Geometric Interpretation ◽  
Data Envelopment ◽  
Scale Elasticity

In recent years, the notion of scale elasticity—the relative changes of outputs with respect to relative changes of inputs—has received a lot of ink in the literature. However, all prior studies, except a few of them, assume that changes are equi-proportional. This simplifying assumption makes scale elasticity measure to preserve the throughput mix and implicitly ignores both input independencies and decision-maker preferences. This paper seeks to investigate two main objectives. It initially proposes the notion of directional scale elasticity to allow evaluation of elasticity in any direction which may naturally alter the mix. Subsequently, by providing a tangible geometric interpretation, it attempts to clarify the measure. Relevant computations are used to construct cross sections of frontier in a given direction by enlisting the advantages of parametric optimization algorithm.

Output error MISO system identification using fractional models

2021 ◽  
Vol 24 (5) ◽  
pp. 1601-1618
Author(s):  
Abir Mayoufi ◽  
Stéphane Victor ◽  
Manel Chetoui ◽  
Rachid Malti ◽  
Mohamed Aoun
Keyword(s):  
System Identification ◽  
Optimization Algorithm ◽  
Simulation Analysis ◽  
Good Efficiency ◽  
Output Error ◽  
Single Output ◽  
Multiple Input ◽  
Fractional Models ◽  
Definition Of ◽  
Initialization Procedure

Abstract This paper deals with system identification for continuous-time multiple-input single-output (MISO) fractional differentiation models. An output error optimization algorithm is proposed for estimating all parameters, namely the coefficients and the differentiation orders. Given the high number of parameters to be estimated, the output error method can converge to a local minimum. Therefore, an initialization procedure is proposed to help the convergence to the optimum by using three variants of the algorithm. Moreover, a new definition of structured-commensurability (or S-commensurability) has been introduced to cope with the differentiation order estimation. First, a global S-commensurate order is estimated for all subsystems. Then, local S-commensurate orders are estimated (one for each subsystem). Finally the S-commensurability constraint being released, all differentiation orders are further adjusted. Estimating a global S-commensurate order greatly reduces the number of parameters and helps initializing the second variant, where local S-commensurate orders are estimated which, in turn, are used as a good initial hit for the last variant. It is known that such an initialization procedure progressively increases the number of parameters and provides good efficiency of the optimization algorithm. Monte Carlo simulation analysis are provided to evaluate the performances of this algorithm.

Biped robot stability based on an A–C parametric Whale Optimization Algorithm

2019 ◽  
Vol 31 ◽  
pp. 17-32 ◽  
Author(s):  
Mostafa A. Elhosseini ◽  
Amira Y. Haikal ◽  
Mahmoud Badawy ◽  
Nour Khashan
Keyword(s):  
Optimization Algorithm ◽  
Biped Robot ◽  
Whale Optimization Algorithm ◽  
Whale Optimization

Step-exchange strategy for balance control of a walking biped under a lateral impact

2014 ◽  
Vol 41 (5) ◽  
pp. 456-464
Author(s):  
Yeoun-Jae Kim ◽  
Joon-Yong Lee ◽  
Ju-Jang Lee
Keyword(s):  
External Force ◽  
Balance Control ◽  
Biped Robot ◽  
Conservation Equation ◽  
Hill Climbing ◽  
Lateral Impact ◽  
Content Type ◽  
Double Support ◽  
The Right ◽  
The Impact

Purpose – This paper aims to present a step-exchange strategy for balance control of a walking biped robot when a lateral impact acts suddenly. A step-out strategy has been recently proposed for balance control when an unknown lateral force acts to a biped robot during walking. This step-out strategy causes a robot to absorb the impact kinetic energy and efficiently maintain balance without falling down. Nevertheless, it was found that the previous strategies have drawbacks that the two foots should always be on the ground (double-support mode) after being balanced and the authors think it is difficult to continue walking after being balanced. Unlike the existing balance strategies, the proposed step-exchange strategy is to not only maintain balance but also to lift one leg in the air (single-support mode) after being balanced so that it is easy for a biped robot to keep walking after being balanced. Design/methodology/approach – In the proposed step-exchange strategy, forward Newton–Euler equation, angular momentum and energy conservation equation were derived. Hill-climbing algorithm is utilized for numerically finding a solution. To verify the proposed strategy, a biped robot by Open Dynamics Engine was stimulated, and experiments with a real biped robot (LRH-1) were also conducted. Findings – The proposed step-exchange strategy enables a walking biped robot under a lateral impact to keep balance and to keep a single-support mode after exchanging a leg. It is helpful for a biped robot to continue walking without any stop. It is found that the proposed step-exchange strategy can be applicable for maintaining balance even if a biped robot is moving. Even though this proposal seems immature yet, it is the first attempt to exchange the supporting foot itself. This strategy is very straightforward and intuitive because humans are also likely to exchange their supporting foot onto the opposite side when an unexpected force is acting. Research limitations/implications – The proposed step-exchange strategy described in this paper can be applicable in the situation when the external force is applied in the +Y direction, the left leg is the swing leg and the right leg is the stance leg, or it can also be applicable in the situation when the external force is applied in −Y direction, the right leg is the swing leg and the left leg is the stance leg (Figure 2 for ±Y force direction). If an impact force acts to the side of the swing leg, the other step-exchange strategy is needed. The authors are studying this issue as a future work. Originality/value – The authors have originated the proposed step-exchange strategy for balance control of a walking biped robot under lateral impact. The strategy is genuine and superior in comparison with the state-of-the-art strategy because not only can a biped robot be balanced but it can also easily continue walking by using the step-exchange strategy.

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