On Rosen's gradient projection methods

1990 ◽  
Vol 24 (1) ◽  
pp. 9-28 ◽  
Author(s):  
D. -Z. Du ◽  
F. Wu ◽  
X. -S. Zhang
Keyword(s):  
Projection Methods ◽  
Gradient Projection ◽  
Gradient Projection Methods

Redundancy Resolution of Kinematically Redundant Parallel Manipulators Via Differential Dynamic Programing

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
João Cavacanti Santos ◽  
Maíra Martins da Silva
Keyword(s):  
Parallel Manipulators ◽  
Projection Methods ◽  
Inverse Kinematic ◽  
Gradient Projection ◽  
Redundancy Resolution ◽  
Inverse Kinematic Problem ◽  
Serial Manipulators ◽  
Optimal Inputs ◽  
Dynamic Programing ◽  
Gradient Projection Methods

Kinematic redundancy may be an efficient way to improve the performance of parallel manipulators. Nevertheless, the inverse kinematic problem of this kind of manipulator presents infinite solutions. The selection of a single kinematic configuration among a set of many possible ones is denoted as redundancy resolution. While several redundancy resolution strategies have been proposed for planning the motion of redundant serial manipulators, suitable proposals for parallel manipulators are seldom. Redundancy resolution can be treated as an optimization problem that can be solved locally or globally. Gradient projection methods have been successfully employed to solve it locally. For global strategies, these methods may be computationally demanding and mathematically complex. The main objective of this work is to exploit the use of differential dynamic programing (DDP) for decreasing the computational demand and mathematical complexity of a global optimization based on the gradient projection method for redundancy resolution. The outcome of the proposed method is the optimal inputs for the active joints for a given trajectory of the end-effector considering the input limitations and different cost functions. Using the proposed method, the performance of a redundant 3PRRR manipulator is investigated numerically and experimentally. The results demonstrate the capability and versatility of the strategy.

scholarly journals Variant Gradient Projection Methods for the Minimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yonghong Yao ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen
Keyword(s):  
Strong Convergence ◽  
Projection Methods ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Projection Algorithms ◽  
Infinite Dimensional ◽  
Minimization Problems ◽  
Gradient Projection Algorithm ◽  
Convex Minimization Problems ◽  
Gradient Projection Methods

The gradient projection algorithm plays an important role in solving constrained convex minimization problems. In general, the gradient projection algorithm has only weak convergence in infinite-dimensional Hilbert spaces. Recently, H. K. Xu (2011) provided two modified gradient projection algorithms which have strong convergence. Motivated by Xu’s work, in the present paper, we suggest three more simpler variant gradient projection methods so that strong convergence is guaranteed.

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