The form--closure and force--closure properties of robotic grasping are investigated. Loosely speaking, these properties are related to the capability of the robot to inhibit motions of the workpiece in spite of externally applied forces. In this paper, form--closure is considered as a purely geometric property of a set of unilateral (contact) constraints, such as those applied on a workpiece by a mechanical fixture, while force--closure is related with the capability of the particular robotic device being considered to apply forces through contacts. The concepts of partial form-- and force--closure properties are introduced and discussed, and an algorithm is proposed to obtain a synthetic geometric description of partial form--closure constraints. While the literature abounds with form--closure tests, proposed algorithms for testing force--closure are either approximate or computationally expensive. This paper proves the equivalence of force--closure analysis with the study of the equ...

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.

We investigate manipulation and active sensingby a pushing control system using only tactile feedback. The equations of motion of a pushed object are derived using a model of the object's limit surface, and we design a control system to translate and orient objects. The effectiveness of the proposed controller is confirmed through simulation and experiments. Active sensing of the object's center of mass is described. I. INTRODUCTION Pushing is a useful robotic capability for positioning and orienting parts. Several researchers have demonstrated the utility of pushing operations by planning open-loop pushing sequences to position and orient polygonal objects despite the presence of uncertainty in the initial state [1, 2, 3, 4, 5, 6, 7]. These operations typically plan for a known object shape and center of mass (CM) and a flat pushing fence or specially designed pusher geometry to exploit the mechanics of pushing. Others have proposed pushing control systems based on visual feedback [8,...

This paper presents models and algorithms that can be used to simulate contact between one or more fingertips and a virtual object. First, the paper presents various models for rotational friction obtained from in-vivo fingertip models previously proposed in the robotics and biomechanics community. Then the paper describes two sets of experiments that were performed on in-vivo fingertips in order to understand which of the models presented fits best with the real rotational friction properties of the human fingertips. Finally an extension of the god object/proxy algorithm which allows the simulation of soft finger contact, i.e. a point-contact with friction capable of supporting moments (up to a torsional friction limit) about the contact normal, is proposed. The resulting algorithm is computationally efficient, being point-based, while retaining a good level of realism. 1. Introduction and

In this paper we propose a novel approach to reference behavior specification for multiple robotic mechanisms using hybrid system models. Hybrid automata can specify discrete states (operational modes) and continuous variable reference values in one unified framework. An example mechanism with 3 degrees-offreedom and a 6-legged walking machine with a combination of several hybrid automata for reference generation and synchronization are discussed. Simulation results show that a hybrid system model is an effective method for robotic behavior specification. Using a model verification tool we show that behavior correctness verification and parametric analysis are possible. 1 Introduction Multiple robotic mechanisms have been investigated to realize more flexible and complex behavior otherwise not achievable with single robots. Active research areas are cooperating robot manipulators which may carry heavy loads [1], dextrous multifingered hands which are used for complex manipulation tas...

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.

This paper describes a gripper for manipulation in natural, unstructured environments. The specific manipulation task is to pick up surface material such as pebbles, or small rocks, in a natural terrain. The application is to give autonomous sampling capabilities to an autonomous vehicle for planetary exploration. We describe the task analysis process that led to the selection of a configuration with three "soft" fingers. We carry out a complete Analysis of the stability of a grasp for this gripper including an analysis of the deformation of the fingers at the points of contact. Finally. we describe the implementation of a grasp selection algorithm and present results on three-dimensional representations of objects computed from range data

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