# Optimal grasping manipulation for multifingered robots using semismooth newton method

Chun Hsu Ko, Jein Shan Chen

Research output: Contribution to journalArticle

13 Citations (Scopus)

### Abstract

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.

Original language English 681710 Mathematical Problems in Engineering 2013 https://doi.org/10.1155/2013/681710 Published - 2013 Dec 9

### Fingerprint

Semismooth Newton Method
Grasping
Newton-Raphson method
Cones
Manipulation
Second-order Cone
Robot
Robots
Complementarity Problem
Nonlinear equations
Generalized Jacobian
Cone Constraints
Rigid Body Dynamics
Minimum Principle
Path
Motion
Optimal Control Problem
Equality
Nonlinear Equations
Object

### ASJC Scopus subject areas

• Mathematics(all)
• Engineering(all)

### Cite this

In: Mathematical Problems in Engineering, Vol. 2013, 681710, 09.12.2013.

Research output: Contribution to journalArticle

title = "Optimal grasping manipulation for multifingered robots using semismooth newton method",
abstract = "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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AB - 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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