A least-square semismooth Newton method for the second-order cone complementarity problem

2011 ◽  
Vol 26 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Shaohua Pan ◽  
Jein-Shan Chen
Keyword(s):  
Newton Method ◽  
Complementarity Problem ◽  
Second Order ◽  
Least Square ◽  
Semismooth Newton Method ◽  
Second Order Cone ◽  
Semismooth Newton

scholarly journals A smoothing Newton method for the second-order cone complementarity problem

2013 ◽  
Vol 58 (2) ◽  
pp. 223-247 ◽  
Author(s):  
Jingyong Tang ◽  
Guoping He ◽  
Li Dong ◽  
Liang Fang ◽  
Jinchuan Zhou
Keyword(s):  
Newton Method ◽  
Complementarity Problem ◽  
Second Order ◽  
Smoothing Newton Method ◽  
Second Order Cone

scholarly journals Optimal Grasping Manipulation for Multifingered Robots Using Semismooth Newton Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Chun-Hsu Ko ◽  
Jein-Shan Chen
Keyword(s):  
Newton Method ◽  
Complementarity Problems ◽  
Minimum Principle ◽  
Rigid Body Dynamics ◽  
Motion Path ◽  
Semismooth Newton Method ◽  
Generalized Jacobian ◽  
Grasping Forces ◽  
Second Order Cone ◽  
Semismooth Newton

Multifingered robots play an important role in manipulation applications. They can grasp various shaped objects to perform point-to-point movement. It is important to plan the motion path of the object and appropriately control the grasping forces for multifingered robot manipulation. In this paper, we perform the optimal grasping control to find both optimal motion path of the object and minimum grasping forces in the manipulation. The rigid body dynamics of the object and the grasping forces subjected to the second-order cone (SOC) constraints are considered in optimal control problem. The minimum principle is applied to obtain the system equalities and the SOC complementarity problems. The SOC complementarity problems are further recast as the equations with the Fischer-Burmeister (FB) function. Since the FB function is semismooth, the semismooth Newton method with the generalized Jacobian of FB function is used to solve the nonlinear equations. The 2D and 3D simulations of grasping manipulation are performed to demonstrate the effectiveness of the proposed approach.

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