scholarly journals Adaptation of energy methods to automated calculation of mobile machines frame constructions

2021 ◽  
Vol 22 (2) ◽  
pp. 284-291
Author(s):  
E. Ripetskyi ◽  
R. Ripetskyy ◽  
M. Pidgurskyi ◽  
I. Pidgurskyi ◽  
O. Korobkov
Keyword(s):  
Potential Energy ◽  
Local Minimum ◽  
Descent Method ◽  
Coordinate Descent ◽  
Energy Methods ◽  
Local Function ◽  
Coordinate Descent Method ◽  
Dead End ◽  
Discrete Grid ◽  
Grid Surface

The paper shows that the adaptation of energy methods to automated calculation of mobile machines frame constructions consists of developing a single algorithm applicable to different construction schemes. The calculation outset still remains the idea of getting a function of potential energy of deformation as a function with unknown inner power factors. Search for local function minimum of potential power of deformation has been based on the function’s discrete grid-surface. We managed to reach tactical flexibility of coordinate descent method in an attempt to continue approaching local minimum in cases of a dead end situation by changing the discrete course. The paper suggests extending the implemented algorithm from 3-D surface dealing only with two power factors, to n-D one with many unknown values.

Coordinate Descent Method for k-means

2021 ◽  
pp. 1-1
Author(s):  
Feiping Nie ◽  
Jingjing Xue ◽  
Danyang Wu ◽  
Rong Wang ◽  
Hui Li ◽  
...  
Keyword(s):  
Descent Method ◽  
Coordinate Descent ◽  
Coordinate Descent Method

scholarly journals A Randomized Coordinate Descent Method with Volume Sampling

2020 ◽  
Vol 30 (3) ◽  
pp. 1878-1904
Author(s):  
Anton Rodomanov ◽  
Dmitry Kropotov
Keyword(s):  
Descent Method ◽  
Coordinate Descent ◽  
Coordinate Descent Method

scholarly journals A General Approach Based on Newton’s Method and Cyclic Coordinate Descent Method for Solving the Inverse Kinematics

2019 ◽  
Vol 9 (24) ◽  
pp. 5461
Author(s):  
Yuhan Chen ◽  
Xiao Luo ◽  
Baoling Han ◽  
Yan Jia ◽  
Guanhao Liang ◽  
...  
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Inverse Kinematics ◽  
Optimization Problem ◽  
Robot Manipulators ◽  
Descent Method ◽  
Coordinate Descent ◽  
Coordinate Descent Method ◽  
Prismatic Joints ◽  
Cyclic Coordinate Descent

The inverse kinematics of robot manipulators is a crucial problem with respect to automatically controlling robots. In this work, a Newton-improved cyclic coordinate descent (NICCD) method is proposed, which is suitable for robots with revolute or prismatic joints with degrees of freedom of any arbitrary number. Firstly, the inverse kinematics problem is transformed into the objective function optimization problem, which is based on the least-squares form of the angle error and the position error expressed by the product-of-exponentials formula. Thereafter, the optimization problem is solved by combining Newton’s method with the improved cyclic coordinate descent (ICCD) method. The difference between the proposed ICCD method and the traditional cyclic coordinate descent method is that consecutive prismatic joints and consecutive parallel revolute joints are treated as a whole in the former for the purposes of optimization. The ICCD algorithm has a convenient iterative formula for these two cases. In order to illustrate the performance of the NICCD method, its simulation results are compared with the well-known Newton–Raphson method using six different robot manipulators. The results suggest that, overall, the NICCD method is effective, accurate, robust, and generalizable. Moreover, it has advantages for the inverse kinematics calculations of continuous trajectories.

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