On The Closure Properties, Optimal Planning, And Dynamic Force Distribution In Multifingered Grasping

Being an important research direction in robotics, multifingered grasping has been ardently investigated for over two decades because of the attractive potential in dexterous manipulation of various objects. Many excellent results have been deduced on closure analysis, grasp quality evaluation, optimal grasp planning (OGP), and dynamic force distribution (DFD). However, some closure analysis approaches can still be enhanced or generalized. Various grasp quality criteria need to be analyzed and perfected. OGP techniques deserve further exploration. The existing DFD algorithms do not achieve the best solution quality and the highest computational efficiency simultaneously. Therefore, this thesis aims to make new advances in these aspects.The main contributions of this thesis are summarized as follows:1 Linearizes the soft finger contact constraint[1] (Note: The references in this abstract are listed on page 154)Currently, most efficient algorithms for force-closure analysis, OGP, and DFD utilize linear programming, but friction models are nonlinear. Substituting polyhedral cones for circular cones of Coulomb friction realizes the linearization of the frictional point contact constraint. So far, however, there is no approach to soft finger contact. This thesis fills this void. The linear and elliptical friction models of soft finger contact can be regarded as different 4D convex cones. We linearize them by linearizing their sections in certain hyperplanes, which are a 3D bicone and an ellipsoid, respectively. By doing this, any linearization-based algorithms for force-closure test, OGP, and DFD can be generalized to soft finger contact.2 Enhances the ray-shooting approach to force-closure analysis[3], [6]Liu proposed the ray-shooting approach to force-closure test, which compares two distances to determine whether the origin of the wrench space lies in the interior of the convex hull of primitive contact wrenches. It is highly efficient and has no limitation on the number of contacts. Till now 3 SCI papers have been published on this approach and its applications. This thesis first completes its exactness by considering the dimension of the convex hull, then increases its efficiency by directly calculating the ratio of the two distances instead of their difference, and finally reveals the positive correlation between the ratio and the inclination angle of the contact force so as to apply the ratio as a grasp stability index to force-closure grasp synthesis.3 Generalizes the infinitesimal motion approach to force-closure analysis[2]The infinitesimal motion approach was used only in form-closure analysis, while the duality between the consistent infinitesimal motion and the feasible resultant wrench was discussed only in the frictionless case. This thesis generalizes this approach to cover point contact with friction and soft finger contact. The sets of feasible contact forces, feasible resultant wrenches, consistent infinitesimal motions, and consistent functional movements are defined. Their properties and relationships are clarified with distinct figures. By the duality between them, the force-closure test is formulated as a nonlinear programming problem. The optimal objective value is proved to be the separation or penetration distance from the origin of the wrench space to the convex hull of the primitive contact wrenches, which represents the minimal virtual work that can be generated by the contact forces having unit sum of normal components with respect to the infinitesimal motion. Its negativity means force-closure.4 Discusses the influence of grasping uncertainties on force-closure[2]Friction uncertainty and contact position uncertainty may have a disastrous effect on grasping. This thesis investigates their influence on the force-closure property for the first time. By means of the generalized infinitesimal motion approach, the tolerance of a force-closure grasp to them is computed.5 Presents a new method for grasp quality evaluation[9]In general, the grasp quality is evaluated by the scale factor of a required wrench set such that the scaled set just fits within a grasp wrench set, which indicates the maximum among the minimal contact forces for generating all required wrenches. The grasp wrench set may adopt the convex hull or Minkowski sum of the primitive contact wrenches for minimizing the sum or maximum of normal force components. In the presence of unknown required wrenches, the required wrench set was taken to be the unit ball centered at the origin of the wrench space. This thesis presents a new method for computing the factors in this case. The computation is precise, efficient, and unified for any grasps with any types of contacts without linearizing the friction cones. The results are independent of the choice of unit and reference frame. The effect of the object geometry is also taken into account.6 Indicates that the maximum of normal force components should be minimized rather than their sum[5]Since the convex hull of the primitive contact wrenches has a much simpler formation than their Minkowski sum, the mainstream of both OGP and DFD adopts the former as the grasp wrench set to facilitate the computation; that is, the sum of normal force components is to be minimized. However, not the former but the latter really reflects the capability of a grasp, and the latter is much larger than the former and has a completely different form. By theoretical analysis and numerical computation, this thesis reveals: the grasp wrench set should be the Minkowski sum and the maximum of normal force components should be minimized, so that the actual capability of a grasp can be sufficiently utilized.7 Solves the realistic optimal grasp planning[8]The working space of any grasping mechanism is limited. Even using the dexterous hand with multiple DOFs, the contact points cannot move freely on the object surface, as supposed by the previous approaches to OGP. The feasible contact regions must be figured out prior to OGP. This thesis sets up a general method for computing them, which can be applied to diverse grasp forms, such as fingertip grasp and power grasp. The computed regions are represented by discrete points, and then the globally optimal contact points are found among them by the efficient algorithms proposed in this thesis.8 Consummates the surface-element-based method of optimal grasp planning[10]Usually the object surface cannot be expressed by a unique parametric function but a number of functions which describe individual pieces composing the object surface. The previous OGP methods can hardly cope with such cases. Ding et al. used two kinds of surface elements (convex facet and discrete point) to characterize the object surface and then optimized the contact positions in the selected eligible elements. Thus the problem was solved primarily. Nevertheless, only frictionless point contact can be located on the facets, while soft finger contact is not considered at all. To perfect the element-based OGP method and expand its application scope, this thesis adds the line segment to the surface elements and derives eligibility conditions and criterion for any mixed use of three types of contacts and the three kinds of elements.9 Proposes a novel DFD algorithm without online iteration[4]The algorithm is called DPC (decomposition and positive combination). It elaborately selects the spanning set for the external wrench and computes a corresponding spanning set for the optimal contact forces in the offline phase. Then in the online phase the contact forces are obtained by decomposition of the external wrench into the former spanning set and a coefficient vector followed by positive combination of the latter spanning set with the vector. To simplify the online computation to the utmost extent, all iterative operations are executed offline and only arithmetic ones are employed online. This algorithm is much faster than the mainstream and turns out much better results than the previous without online iteration. Moreover, it can be applied to all the contact types.10 Put forward another DFD algorithm fastest so far[7]The previous DFD algorithms pursue either the optimal contact forces (often with minimal sum of normal components) possibly fast or the least online computation (even at the cost of some optimality of the contact forces). This thesis presents a new one for attaining both goals (the best result and the highest speed) simultaneously for the first time. By linearizing the friction cones, the computation of the contact forces with minimal sum of normal components can be transformed into a linear programming (LP) problem. Its objective function is the inner product of the external wrench and a vector, and the constraints on the vector, given by a set of linear inequalities, define a polytope. The above is already known, but we notice that the polytope is determined by the grasp configuration and the solution to the LP problem can always be found at its vertices. Along with the direction change of the external wrench, the solution sequentially shifts from a vertex to one of its adjacencies, whereas the polytope with all its vertices remains unchanged. Therefore the vertices and adjacencies of each vertex are computed in the offline phase. Then the online phase simply searches the adjacencies of the old solution vertex for the new one. Without lose of optimality, this algorithm runs much faster than solving the LP problem by the simplex method in real time. 11 Develops a high-functional 3D modular fixture using some theories of grasping[11]Since grasping and fixturing have many similarities, their researches can benefit from each other. Using some results of grasping research, this thesis systematically investigates 3D modular fixtures, particularly for complex objects. The new points lie in: 1) The fixture has a simple structure but can hold complex objects in arbitrary poses. 2) Referring to the realistic OGP, an efficient algorithm for computing optimal fixel locations w.r.t. a given object pose is brought forth, optimizing both localization accuracy and immobilization capability. 3) On account of the manufacturing errors, measuring and adjusting techniques are explored to improve the localization accuracy. 4) Complete experience of developing 3D modular fixtures is provided from principles to practice. 5) The relevant theories of grasping and the adjusting technique are verified with experiments, which were not reported in previous literature.