scholarly journals Bipedal Walking Trajectory Generation Using Tchebychev Method

2011 ◽  
Vol 2-3 ◽  
pp. 414-418 ◽  
Author(s):  
Yeoun Jae Kim ◽  
Joon Yong Lee ◽  
Ju Jang Lee
Keyword(s):  
Quadratic Programming ◽  
Hip Joint ◽  
Sequential Quadratic Programming ◽  
Trajectory Generation ◽  
Biped Robot ◽  
Bipedal Walking ◽  
Cost Functions ◽  
The Given

It is still important and difficult for a biped robot to optimally generate the stable walking trajectory, because the mechanical limitations of the given biped robot should be also considered carefully. In this paper, we assume that different walking trajectories enable to be generated according to various set of weights of torques loaded in each partial joint (e.g., ankle, knee, and hip joint). We present a method for generating various bipedal walking trajectories corresponding to a set of weighted torques. For this purpose, Tchebychev method and sequential quadratic programming are employed to optimize single cost functions consisting in a set of weight torques. Some notations and constraints introduced in [1] are used and modified in this paper.

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.

GA Based Trajectory Generation for a 7-DOF Biped Robot by Considering Feet Rotation during Double Support Phase

2012 ◽  
Vol 463-464 ◽  
pp. 1252-1255 ◽  
Author(s):  
Farsam Farzadpour ◽  
Mohammad Danesh
Keyword(s):  
High Speed ◽  
Trajectory Generation ◽  
Biped Robot ◽  
Bipedal Walking ◽  
Double Support ◽  
Straight Line ◽  
Zero Moment ◽  
The Stability ◽  
Support Phase ◽  
Double Support Phase

This paper presents a trajectory generation approach for a 7-DOF biped robot on level ground. Simultaneously rotation of feet in double support phase is considered which leads to high-speed and more similar to human being walking. The zero moment point (ZMP) stability criterion is used to ensure the stability of the bipedal walking robot. Since ZMP trajectory in human walking does not stay fixed, it needs to be a straight line shaped forward ZMP trajectory to have a natural walk. A genetic algorithm based method is proposed to obtain key parameters in trajectory generation such that the ZMP follows a predefined trajectory while minimizing power consumption. Simulation results demonstrate the effectiveness of the proposed method.

Trajectory generation and control for a biped robot walking upstairs

2010 ◽  
Vol 8 (2) ◽  
pp. 339-351 ◽  
Author(s):  
Chan-Soo Park ◽  
Taesin Ha ◽  
Joohyung Kim ◽  
Chong-Ho Choi
Keyword(s):  
Trajectory Generation ◽  
Biped Robot ◽  
And Control

Design of evolutionary cubic spline intelligent solver for nonlinear Painlevé-I transcendent

2021 ◽  
Author(s):  
Sharafat Ali ◽  
Iftikhar Ahmad ◽  
Muhammad Asif Zahoor Raja ◽  
Siraj ul Islam Ahmad ◽  
Muhammad Shoaib
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Genetic Algorithms ◽  
Statistical Analysis ◽  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Process Variation ◽  
Nonlinear Ordinary Differential Equation ◽  
Second Derivative ◽  
Search Technique

In this research paper, an innovative bio-inspired algorithm based on evolutionary cubic splines method (CSM) has been utilized to estimate the numerical results of nonlinear ordinary differential equation Painlevé-I. The computational mechanism is used to support the proposed technique CSM and optimize the obtained results with global search technique genetic algorithms (GAs) hybridized with sequential quadratic programming (SQP) for quick refinement. Painlevé-I is solved by the proposed technique CSM-GASQP. In this process, variation of splines is implemented for various scenarios. The CSM-GASQP produces an interpolated function that is continuous upto its second derivative. Also, splines proved to be stable than a single polynomial fitted to all points, and reduce wiggles between the tabulated points. This method provides a reliable and excellent procedure for adaptation of unknown coefficients of splines by searching globally exploiting the performance of GA-SQP algorithms. The convergence, exactness and accuracy of the proposed scheme are examined through the statistical analysis for the several independent runs.

Co-Optimization of Output and Reserve with Significant Penetration of Renewables

2013 ◽  
Vol 427-429 ◽  
pp. 341-345
Author(s):  
Xue Fei Chang ◽  
Zhe Yong Piao ◽  
Xiang Yu Lv ◽  
De Xin Li
Keyword(s):  
Quadratic Programming ◽  
Wind Power ◽  
Sequential Quadratic Programming ◽  
Renewable Generation ◽  
Renewable Sources ◽  
Reliability Level ◽  
Maximum Benefit ◽  
Proposed Model ◽  
Programming Techniques

Co-optimization of output and reserve is necessary in order to provide maximum benefit to both consumers and producers. Once renewable generation sources like wind or solar begin to make up a large proportion of the generation mix, this co-optimization becomes much more difficult since the output of renewable sources is not well-known in advance. In this paper, a uniform reliability level is used as a constraint in the process of output and reserve. The proposed model is tested on the modified 5-bus PJM system. The co-optimization is performed by sequential quadratic programming techniques. The results show that the co-optimization results are strongly related to the uncertainties of wind power, the reliability level of the system, and the reliability of generators when wind makes up a significant portion of the generation mix.

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