## Grasp Analysis as Linear Matrix Inequality Problems (1998)

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Venue: | IEEE Transactions on Robotics and Automation |

Citations: | 37 - 2 self |

### BibTeX

@ARTICLE{Han98graspanalysis,

author = {Li Han and Jeffrey C. Trinkle and Zexiang Li},

title = {Grasp Analysis as Linear Matrix Inequality Problems},

journal = {IEEE Transactions on Robotics and Automation},

year = {1998},

volume = {16},

pages = {1261--1268}

}

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### Abstract

Three important problems in the study of grasping and manipulation by multifingered robotic hands are: (a) Given a grasp characterized by a set of contact points and the associated contact models, determine if the grasp has force closure; (b) If the grasp does not have force closure, determine if the fingers are able to apply a specified resultant wrench on the object; and (c) Compute "optimal" contact forces if the answer to problem (b) is affirmative. In this paper, based on an early result by Buss, Hashimoto and Moore, which transforms the nonlinear friction cone constraints into positive definiteness of certain symmetric matrices, we further cast the friction cone constraints into linear matrix inequalities (LMIs) and formulate all three of the problems stated above as a set of convex optimization problems involving LMIs. The latter problems have been extensively studied in optimization and control community and highly efficient algorithms with polynomial time complexity are now av...

### Citations

809 | Semidefinite programming
- Vandenverghe, Boyd
- 1996
(Show Context)
Citation Context ...en the whole friction cone P (x)s0 will be used in the optimization. Such a linear objective function will lead the grasping force optimization problem to a standard semi-definite programming problem =-=[22]-=- or a standard second order cone programming problem [11], depending on the friction cone constraints being cast into LMIs(7, 8, 9) or the conventional cone constraints (2,3, 4). Paper[11] includes a ... |

668 | A Mathematical Introduction to Robotic Manipulation
- Murray, Li, et al.
- 1994
(Show Context)
Citation Context ...ncy of the LMI formulation to the three problems. 1 Introduction Grasping and manipulation by multifingered robotic hands have been active areas of research in robotics over the last two decades, see =-=[8, 9, 12, 13, 14, 17, 18, 19, 20, 21]-=- and references therein for further details. Three important problems in the study of grasping and multifingered manipulation are: (a) Given a grasp which is characterized by a set of contact This wor... |

180 | Determinant maximization with linear matrix inequality constraints
- Vandenberghe, Boyd, et al.
- 1998
(Show Context)
Citation Context ...spectively. Problems (31) and (32) are thus shown to be convex optimization problems involving LMIs. Problem (32) is also in the standard form of determinant maximization problem with LMI constraints =-=[23]-=- and can be efficiently solved using existing software package. Remark 1. The barrier term ln detP \Gamma1 (x) in the objective function (30), in fact, requires P (x) ? 0. Another way to define a conv... |

167 |
Robot Hands and the Mechanics of Manipulation
- Mason, Salisbury
- 1985
(Show Context)
Citation Context ...ncy of the LMI formulation to the three problems. 1 Introduction Grasping and manipulation by multifingered robotic hands have been active areas of research in robotics over the last two decades, see =-=[8, 9, 12, 13, 14, 17, 18, 19, 20, 21]-=- and references therein for further details. Three important problems in the study of grasping and multifingered manipulation are: (a) Given a grasp which is characterized by a set of contact This wor... |

157 | Applications of second-order cone programming - Lobo, Vandenberghe, et al. - 1998 |

135 | On the existence and synthesis of multifinger positive grips
- Mishra, Schwartz, et al.
- 1987
(Show Context)
Citation Context ...ncy of the LMI formulation to the three problems. 1 Introduction Grasping and manipulation by multifingered robotic hands have been active areas of research in robotics over the last two decades, see =-=[8, 9, 12, 13, 14, 17, 18, 19, 20, 21]-=- and references therein for further details. Three important problems in the study of grasping and multifingered manipulation are: (a) Given a grasp which is characterized by a set of contact This wor... |

127 |
Application of second-order cone programming, Linear Algebra and its
- Lobo, Vandenberghe, et al.
- 1998
(Show Context)
Citation Context ...timization. Such a linear objective function will lead the grasping force optimization problem to a standard semi-definite programming problem [22] or a standard second order cone programming problem =-=[11]-=-, depending on the friction cone constraints being cast into LMIs(7, 8, 9) or the conventional cone constraints (2,3, 4). Paper[11] includes a brief discussion on the grasping force optimization probl... |

123 | A Mathematical Introduction to Robot Manipulation. Boca - Murray, Li, et al. - 1993 |

115 | Kinematic and Force Analysis of Articulated Hands - Salisbury - 1982 |

114 |
Analysis of multifingered hands
- Roth
- 1986
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104 |
Constructing force-closure grasps
- Nguyen
- 1988
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98 | Lagrange multipliers and optimality - Rockafellar - 1993 |

64 | On Computing Four-Finger Equilibrium and Force-Closure Grasps of Polyhedral Objects
- Ponce, Sullivan, et al.
- 1997
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61 | Introduction to Convex Optimization with Engineering Applications - Boyd, Vandenberghe - 2003 |

55 | On the closure properties of robotic grasping - Bicchi - 1995 |

51 | An Introduction to Dierentiable Manifolds and Riemannian Geometry - Boothby - 1975 |

46 | Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with coulomb friction
- Pang, Trinkle
- 1996
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40 |
Dextrous hand grasping force optimization
- Buss, Hashimoto, et al.
- 1996
(Show Context)
Citation Context ...optimization problem. However, current computing resources can only allow off-line analysis. One major progress in the study of grasping force optimization was made by Buss, Hashimoto and Moore (BHM) =-=[3]-=-. They made the important observation that the nonlinear friction cone constraints are equivalent to positive definiteness of certain symmetric matrices. Consequently, the grasping force optimization ... |

35 | Semide nite programming - Vandenberghe, Boyd - 1996 |

30 |
Dynamics and stability in coordination of multiple robotic systems,” Int
- Nakamura, Nagai, et al.
- 1989
(Show Context)
Citation Context ...mption of isotropic Coulomb friction), (3) increasing the accuracy of the linearized friction model increases the running time unacceptably for real-time applications. Nonlinear programming approaches=-=[15]-=- have also been proposed for the grasping force optimization problem. However, current computing resources can only allow off-line analysis. One major progress in the study of grasping force optimizat... |

28 |
MAXDET: software for determinant maximization problems. Software package. Available from http://www.stanford.edu/∼boyd/MAXDET.html
- Vandenberghe, Boyd, et al.
(Show Context)
Citation Context ...ng application of the second order cone progamming. 5 Simulation Results In this section, we discuss the simulation results obtained from applying software package maxdet by Wu, Vandenberghe and Boyd =-=[24]-=- to various grasp analysis problems. We downloaded the source code of maxdet (written in ANSI C) from http://www.stanford.edu/boyd/MAXDET.html and extended it to record the contact forces and objectiv... |

25 | Qualitative test and force optimization of 3d frictional forceclosure grasps using linear programming - Liu, Wang - 1998 |

25 | Dynamic anal- ysis of mobility and graspability of general manipulation - Prattichizzo, Bicchi |

23 | Optimal force distribution for the legs of a walking machine with friction cone constraints - Klein, Kittivatcharapong - 1990 |

21 |
Efficient algorithm for optimal force distribution -the compactdual lp method
- Cheng, Orin
(Show Context)
Citation Context ...three problems will collectively be referred to as grasp analysis problems. One may note that these problems also arise in the study of foot-step planning and force distribution by multilegged robots =-=[6]-=-. Other applications of these problems can be found in fixturing, cell manipulation by multiple laser probes, and the control of satellites with multiple unidirectional thrusters. One major difficulty... |

20 | On force and form closure for multiple finger grasps
- Rimon, Burdick
- 1996
(Show Context)
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17 | Sliding of robotic fingers under combined torsion and shear loading - Howe, Kao, et al. |

11 |
A complementarity approach to a quasistatic rigid body motion problem
- Pang, Trinkle, et al.
- 1996
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10 | Analysis of multi ngered hands - Kerr, Roth - 1986 |

9 | On the existence and synthesis of multi nger positive grips - Mishra, Schwartz, et al. - 1987 |

8 | Multi-fingered grasping experiments using real-time grasping force optimization - Buss, Kleinmann - 1996 |

6 |
Dikin-type algorithms for dextrous grasping force optimization
- Buss, Faybusovich, et al.
- 1998
(Show Context)
Citation Context ...nts of the grasping force x, for a PCWF contact w i =[0 0 d i ] T and for a SFC contact w i =[0 0 d i 0] T , d is0. This objective function (30) is very similar to the self-concordant one proposed in =-=[2]-=- and can be interpreted as follows: the first term grows with the magnitudes of the normal components of the contact forces; and the second term is a barrier term which tends to infinity as any contac... |

5 | On computing four-¯nger equilibrium and force-closure grasps of polyhedral objects. The Int - Ponce, Sullivan, et al. - 1997 |

5 | Grasp evaluation based on unilateral force closure - Haidacher, Schlegl, et al. - 1999 |

4 | Multi-fingered regrasping using on-line grasping force optimization - Buss, Schlegl - 1997 |

4 | The planning and control of robot dextrous manipulation - Han, Li, et al. |

3 | The sliding of robot ¯ngers under combined torsion and shear loading - Howe, Kao, et al. - 1988 |

3 | Automatic selection of xture points for frictionless assemblies - Wolter, Trinkle - 1994 |

2 |
Multi- regrasping using on-line grasping force optimization
- Buss, Schlegl
- 1997
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Citation Context ...d as an optimization problem on the Riemannian manifold of linearly constrained symmetric positive definite matrices and solved by projected gradient flow methods [3, 2]. Various experimental studies =-=[4, 5, 10]-=- showed the efficiency of this approach. The optimization algorithm, however, needs valid contact forces, which satisfy the friction cone constraints and generate the specified object wrench, as the s... |

2 | Multi ngered grasping experiments using real-time grasping force optimization - Buss, Kleinmann - 1996 |

2 | Multi- ngered regrasping using online grasping force optimization - Buss, Schlegl - 1997 |

2 | On force and form closure for multiple nger grasps - Rimon, Burdick - 1996 |

1 |
Cosam : A unified control system architecture for multifingered manipulation
- Li, Qin, et al.
- 1998
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Citation Context ...d as an optimization problem on the Riemannian manifold of linearly constrained symmetric positive definite matrices and solved by projected gradient flow methods [3, 2]. Various experimental studies =-=[4, 5, 10]-=- showed the efficiency of this approach. The optimization algorithm, however, needs valid contact forces, which satisfy the friction cone constraints and generate the specified object wrench, as the s... |

1 | Cosam 2 : A uni ed control system architecture for multi ngered manipulation - Li, Qin, et al. - 1998 |

1 | Dynamics and stability in coordination ofmultiple robotic mechanisms - Nakamura, Nagai, et al. - 1989 |