A polyhedral bound on the indeterminate contact forces in 2D fixturing and grasping arrangements

This paper considers 2D contact arrangements where several bodies grasp, fixture, or support an object via frictional point contacts. Within a strictly rigid body modelling paradigm, when an external wrench (i.e. force and torque) acts on the object, the reaction forces at the contacts are indeterminate and span an unbounded linear space. This paper analyzes the contact forces within a quasi-rigid body framework that keeps the desirable geometric properties of rigid body modelling, while also includes more realistic physical effects. Using two principles governing the mechanics of quasi-rigid contacts, we show that for any given external wrench acting on the object, the contact forces lie in a bounded polyhedral set. The polyhedral bound depends on the external wrench, the grasp's geometry, and the preload forces. But it does not depend on any detailed knowledge of the contact mechanics parameters. The bound is useful for "robust" grasp and fixture synthesis. Given a collection of external wrenches that may act on an object, the grasp's geometry and preload forces can be chosen such that all of these external wrenches would be automatically supported by the contacts

Determining force-closure grasps reachable by a given hand

The paper presents an approach to find contact points on an object surface that are reachable by a given hand and such that the resulting grasp satisfies the force-closure condition. This is a very common problem that still requires a practical solution. The proposed method is based on the computation of a set of independent contact regions on the object boundary such that a finger contact on each region produces a force-closure grasp, and then this set of regions is iteratively recomputed while looking for a set of contact points that are reachable by a given hand. The search is done guided by a cost function that indicates the proximity of the hand fingertips to a candidate set of grasping contact points. The approach has been implemented for the Schunk Anthropomorphic Hand and planar objects,and application examples are included to illustrate its performance.Postprint (published version

Planning dextrous robot hand grasps from range data, using preshapes and digit trajectories

Dextrous robot hands have many degrees of freedom. This enables the manipulation of objects between the digits of the dextrous hand but makes grasp planning substantially more complex than for parallel jaw grippers. Much of the work that addresses grasp planning for dextrous hands concentrates on the selection of contact sites to optimise stability criteria and ignores the kinematics of the hand. In more complete systems, the paradigm of preshaping has emerged as dominant. However, the criteria for the formation and placement of the preshapes have not been adequately examined, and the usefulness of the systems is therefore limited to grasping simple objects for which preshapes can be formed using coarse heuristics.In this thesis a grasp metric based on stability and kinematic feasibility is introduced. The preshaping paradigm is extended to include consideration of the trajectories that the digits take during closure from preshape to final grasp. The resulting grasp family is dependent upon task requirements and is designed for a set of "ideal" object-hand configurations. The grasp family couples the degrees of freedom of the dextrous hand in an anthropomorphic manner; the resulting reduction in freedom makes the grasp planning less complex. Grasp families are fitted to real objects by optimisation of the grasp metric; this corresponds to fitting the real object-hand configuration as close to the ideal as possible. First, the preshape aperture, which defines the positions of the fingertips in the preshape, is found by optimisation of an approximation to the grasp metric (which makes simplifying assumptions about the digit trajectories and hand kinematics). Second, the full preshape kinematics and digit closure trajectories are calculated to optimise the full grasp metric.Grasps are planned on object models built from laser striper range data from two viewpoints. A surface description of the object is used to prune the space of possible contact sites and to allow the accurate estimation of normals, which is required by the grasp metric to estimate the amount of friction required. A voxel description, built by ray-casting, is used to check for collisions between the object and the robot hand using an approximation to the Euclidean distance transform.Results are shown in simulation for a 3-digit hand model, designed to be like a simplified human hand in terms of its size and functionality. There are clear extensions of the method to any dextrous hand with a single thumb opposing multiple fingers and several different hand models that could be used are described. Grasps are planned on a wide variety of curved and polyhedral object