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.

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.

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.

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.

Abstract — We consider the problem of computing the smallest contact forces, with point-contact 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 second-order cone problem (SOCP), and so can be solved using several standard algorithms for these problem classes. In this paper we describe a custom interior-point 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 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 warm-start version of our FOP method, we show how such families of FOPs can be solved very efficiently.

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

Abstract—This work proposes an evolutionary computation method to compute force-closure 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.

Abstract—We consider the problem of computing the smallest contact forces, with point-contact 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 second-order cone problem (SOCP), and thus, can be solved using several standard algorithms for these problem classes. In this paper, we describe a custom interior-point 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 warm-start 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, interior-point method, second-order cone program