Results 1  10
of
16
Grasp Analysis as Linear Matrix Inequality Problems
"... 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 th ..."
Abstract

Cited by 33 (2 self)
 Add to MetaCart
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 ngers 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 available for their solutions. We perform simulation studies to show the simplicity and efficiency of the LMI formulation to the three problems.
Grasping the Dice by Dicing the Grasp
 in Proc. IROS
, 2003
"... Many methods for generating and analyzing grasps have been developed in the recent years. They gave insight and comprehension of grasping with robot hands but many of them are rather complicated to implement and of high computational complexity. ..."
Abstract

Cited by 18 (0 self)
 Add to MetaCart
Many methods for generating and analyzing grasps have been developed in the recent years. They gave insight and comprehension of grasping with robot hands but many of them are rather complicated to implement and of high computational complexity.
Grasp Planning: How to Choose a Suitable Task Wrench Space
, 2004
"... For the evaluation of grasp quality, different measures have been proposed that are based on wrench spaces. Almost all of them have drawbacks that derive from the nonuniformity of the wrench space, composed of force and torque dimensions. Moreover, many of these approaches are computationally expens ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
For the evaluation of grasp quality, different measures have been proposed that are based on wrench spaces. Almost all of them have drawbacks that derive from the nonuniformity of the wrench space, composed of force and torque dimensions. Moreover, many of these approaches are computationally expensive.
Fast computation of optimal contact forces
 IEEE Transactions on Robotics
, 2007
"... Abstract — We consider the problem of computing the smallest contact forces, with pointcontact friction model, that can hold an object in equilibrium against a known external applied force and torque. It is known that the force optimization problem (FOP) can be formulated as a semidefinite programm ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
Abstract — We consider the problem of computing the smallest contact forces, with pointcontact friction model, that can hold an object in equilibrium against a known external applied force and torque. It is known that the force optimization problem (FOP) can be formulated as a semidefinite programming problem (SDP), or a secondorder cone problem (SOCP), and so can be solved using several standard algorithms for these problem classes. In this paper we describe a custom interiorpoint algorithm for solving the FOP that exploits the specific structure of the problem, and is much faster than these standard methods. Our method has a complexity that is linear in the number of contact forces, whereas methods based on generic SDP or SOCP algorithms have complexity that is cubic in the number of forces. Our method is also much faster for smaller problems. We derive a compact dual problem for the FOP, which allows us to rapidly compute lower bounds on the minimum contact force, and to certify infeasibility of a FOP. We use this dual problem to terminate our optimization method with a guaranteed accuracy. Finally, we consider the problem of solving a family of FOPs that are related. This occurs, for example, in determining whether force closure occurs, in analyzing the worstcase contact force required over a set of external forces and torques, and in the problem of choosing contact points on an object so as to minimize the required contact force. Using dual bounds, and a warmstart version of our FOP method, we show how such families of FOPs can be solved very efficiently.
Grasp Evaluation Based on Unilateral Force Closure
, 1999
"... In this paper we present an algorithm which allows qualitative and quantitative analysis of the general force closure property of a grasp when fingertip contact forces are limited by unilateral friction constraints. It is applied to grasp synthesis during regrasping sequences. Contact points for mov ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
In this paper we present an algorithm which allows qualitative and quantitative analysis of the general force closure property of a grasp when fingertip contact forces are limited by unilateral friction constraints. It is applied to grasp synthesis during regrasping sequences. Contact points for moving fingers which result in structurally stable grasps are calculated. The proposed method is suitable for two and three dimensional grasps with an arbitrary number of fingers. The approach is validated by nu,merical examples and in dynamical simulations. ngers. The approach is validated by numerical examples and in dynamical simulations.
On Quality Functions for Grasp Synthesis, Fixture Planning, and Coordinated Manipulation
 IEEE Trans. on Aut. Sci. and Eng
, 2004
"... Abstract—Planning a proper set of contact points on a given object/workpiece so as to satisfy a certain optimality criterion is a common problem in grasp synthesis for multifingered robotic hands and in fixture planning for manufacturing automation. In this paper, we formulate the grasp planning pro ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Abstract—Planning a proper set of contact points on a given object/workpiece so as to satisfy a certain optimality criterion is a common problem in grasp synthesis for multifingered robotic hands and in fixture planning for manufacturing automation. In this paper, we formulate the grasp planning problem as optimization problems with respect to three grasp quality functions. The physical significance and properties of each quality function are explained, and computation of the corresponding gradient flows is provided. One noticeable property of some of these quality functions is that the optimal solutions are also forceclosure grasps if they do exist for the given object. Furthermore, when specialized to twofingered or threefingered grasps on a spherical object, the optimal solutions become the familiar antipodal grasp, or the symmetric grasp, respectively. Thus, by following the gradient flows with arbitrary initial conditions, the optimal grasp synthesis
A SimplexGenetic method for solving the KleeMinty cube
 WSEAS Transactions on Systems
"... Abstract: Although the Simplex Method (SM) developed for Dantzig is efficient for solving many linear programming problems (LPs), there are constructions of hard linear programs as the KleeMinty cubes and another deformed products, where this method has an exponential behavior. This work presents ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract: Although the Simplex Method (SM) developed for Dantzig is efficient for solving many linear programming problems (LPs), there are constructions of hard linear programs as the KleeMinty cubes and another deformed products, where this method has an exponential behavior. This work presents the integration of genetic algorithms (GA) and SM to fastly reach the optimum of this type of problems. This integration, called Simplex Genetic Method (SGM), applies first a GA to find a solution near the optimum and afterwards uses the SM to reach the optimum in a few steps. In the GA phase, the populations are constructed by only basic LP solutions codified as binary chromosomes and the crossover operator uses a tabu approach over infeasible solutions to produce the new offsprings. Based in this binary representation, a translation schema is used to transfer the GA solution as the initial solution of the Simplex search mechanism, avoiding that the SM realizes many iterations and reducing the optimum search time. In this work, several instances of the KleeMinty cube are evaluated and compared with the traditional SM and the results suggest that for hard linear problems the SGM has better behavior that the SM.
Positive Span of Force and Torque Components in Three Dimensional Four Finger Force Closure Grasps
"... Testing whether a given grasp achieves force closure is a fundamental problem in grasping. Unfortunately, most of the force closure testing methods avoid dealing with the true quadratic friction cones by resorting to some linear approximation which unavoidably sacrifices completeness and accuracy. T ..."
Abstract
 Add to MetaCart
Testing whether a given grasp achieves force closure is a fundamental problem in grasping. Unfortunately, most of the force closure testing methods avoid dealing with the true quadratic friction cones by resorting to some linear approximation which unavoidably sacrifices completeness and accuracy. This paper presents a method, considering the true nonlinear friction cone, that can be used as a filter that quickly reject non force closure grasps. The method is based on a necessary condition stating that a force closure grasp must be able to generate wrenches that positively span the force space and the torque space separately. The geometric relationship between the friction cones and the corresponding force space and torque space is analyzed to help construct an efficient test of the condition. Due to the superior speed of the test over a complete method, the overall performance improvement is paramount. In our experiment, speed up factor of 20 or greater can be achieved when testing a large number of grasps on various test objects. 1
4Fingered ForceClosure Grasps from surface Points Using Genetic Algorithm
"... Abstract—This work proposes an evolutionary computation method to compute forceclosure grasps from surface points. The object is presented as set of points. The proposed method searches for grasping configurations without prior knowledge of object’s geometry. The experiment is carried out to valida ..."
Abstract
 Add to MetaCart
Abstract—This work proposes an evolutionary computation method to compute forceclosure grasps from surface points. The object is presented as set of points. The proposed method searches for grasping configurations without prior knowledge of object’s geometry. The experiment is carried out to validate the proposed method. The result when compared with a random search method shows that the proposed method finds more and better grasping configurations. I.
Fast Computation of Optimal Contact
"... Abstract—We consider the problem of computing the smallest contact forces, with pointcontact friction model, that can hold an object in equilibrium against a known external applied force and torque. It is known that the force optimization problem (FOP) can be formulated as a semidefinite programmin ..."
Abstract
 Add to MetaCart
Abstract—We consider the problem of computing the smallest contact forces, with pointcontact friction model, that can hold an object in equilibrium against a known external applied force and torque. It is known that the force optimization problem (FOP) can be formulated as a semidefinite programming problem (SDP) or a secondorder cone problem (SOCP), and thus, can be solved using several standard algorithms for these problem classes. In this paper, we describe a custom interiorpoint algorithm for solving the FOP that exploits the specific structure of the problem, and is much faster than these standard methods. Our method has a complexity that is linear in the number of contact forces, whereas methods based on generic SDP or SOCP algorithms have complexity that is cubic in the number of forces. Our method is also much faster for smaller problems. We derive a compact dual problem for the FOP, which allows us to rapidly compute lower bounds on the minimum contact force and certify the infeasibility of a FOP. We use this dual problem to terminate our optimization method with a guaranteed accuracy. Finally, we consider the problem of solving a family of FOPs that are related. This occurs, for example, in determining whether force closure occurs, in analyzing the worst case contact force required over a set of external forces and torques, and in the problem of choosing contact points on an object so as to minimize the required contact force. Using dual bounds, and a warmstart version of our FOP method, we show how such families of FOPs can be solved very efficiently. Index Terms—Convex optimization, force closure, friction cone, grasp force, interiorpoint method, secondorder cone program