Trinkle, J.C., Farahat, A.O., and Stiller, P.F. Second order stability cells of a frictionless rigid body grasped by rigid fingers. Proc. IEEE Int. Conf. on Robotics and Automation, pp. 2815-- 2821, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....If second order effects are examined, it is necessary to incorporate a model of the curvature of the contacting surfaces. Now even if a grasp is not form (force) closed, second order effects may guarantee the closure of the grasp. The formulation of such second order effects is discussed in [27, 76, 77, 92]) Higher order kinematic effects require the derivatives of the curvature and Christoffel symbols characterizing the contacting surfaces [81] While third and higher order closure properties have not been formally defined, we now have a roadmap in this direction. We can now claim that such ....

....plays a strong role in determining the contact grasp stability of non force closed grasps. He showed (through examples) that two grasps could have differing contact stability, even though they were identical except for the curvature of the contacting surfaces. Trinkle, Farahat, and Stiller [90, 92] were the first to look at a general formulation for the stability of non force closed grasps. Their work, which is limited to polygons with vertex contacts, explores a linear programming approach to determining what they term first and second order stability cells. They defined a first order ....

Trinkle, J.C., Farahat, A.O., and Stiller, P.F.: Second order stability cells of a frictionless rigid body grasped by rigid fingers. Proc. IEEE Int. Conf. on Robotics and Automation, pp. 2815--2821, 1994.

....much of the work on pushing may be considered passive manipulation, in contrast to the more active manipulation explored in the work of Paljug, et.al. and in much research on grasping. Examples of passive manipulation include the manipulation techniques of Trinkle, et.al. 90] 36] 85] [86]) Their analysis and planning uses the idea of contact formations originally presented by Desai, and incorporated into a planner for dextrous manipulation by Trinkle and Hunter [88] The work described in this dissertation follows a similar method to Trinkle, et.al. However, the paths through ....

....correspond to a particular side of the object in edge contact with a particular palm equivalent configurations. For example, see Figure 3.5) all stable configurations where rectangle side a rests on the left palm are equivalent. Define contact formations (Desai, as cited in [88] 84] 85] [86]) as the set of contact configurations where the same vertices of the object are making contact with the same edges of the cone. Note that the definition of equivalent configurations forms a superset of the sets of stable contact formations corresponding to side a against the left palm, since for ....

J. C. Trinkle, A. O. Farahat, and P. F. Stiller, P. F. "Second Order Stability Cells of Frictionless Rigid Body Systems", Proceedings of the 1994 IEEE International Conference on Robotics and Automation, 1994.

....elsewhere. Figure 1: A two fingered (4 degrees of freedom) gripper with curling fingers grasping an object. Figure 2: Robust hold of an object by means of an enveloping, whole arm grasp. A growing attention on kinematically defective systems is witnessed by a number of recent papers. Trinkle et al. 1994) investigated the problem of planning joint motions to reposition and reorient the object within whole arm grasps. The grasp robustness by kinematically defective devices has been studied in (Zhang et al. 1994) and (Prattichizzo et al. 1995) Howard and Kumar (1995) analyzed the stability of ....

Trinkle, J.C., Farahat, A.O., and Stiller, P.F., 1994, "Second--Order Stability Cells of a Frictionless Rigid Body Grasp by Rigid Body Fingers," Proceedings IEEE Int. Conf. Robotics Automat.. pp. 2815--2821.

....the exception of Trinkle s work mentioned below, all of these analyzes consider a single rigid object lying on a flat plane. In contrast, in our analysis the points of contact can lie anywhere, and the contacts may assume any curvature. In the context of whole arm manipulation, Trinkle et al. [15, 16] have also extensively studied the gravitational stability of multiply contacted objects. However, Trinkle et. al were chiefly concerned with movable supporting bodies (representing the links of a robot arm) They investigated the allowable configurations of the supporting bodies which hold a ....

J. C. Trinkle, A. O. Farahat, and P. F. Stiller. Second-order stability cells of a frictionless rigid body grasped by rigid fingers. In IEEE International Conference on Robotics and Automation, pages 2815--2821, San Diego, CA, May 1994.

....also used SMT to analyze the stable poses of piecewise smooth bodies lying on a plane. In some sense, our work can be considered as an extension of some of Kriegman s results to the case of multiple nonplanar and nonflat contacts. In the context of whole arm manipulation, Trinkle and coworkers [10] have also extensively studied the stability of a multiply contacted body under the influence of gravity. Our SMT approach formalizes and extends many of their results, generalizing to non uniform force fields and to non polyhedral objects. We also introduce an integer measure of grasp quality, ....

J.C. Trinkle, A.O. Farahat, and P.F. Stiller. Secondorder stability cells of a frictionless rigid body grasped by rigid fingers. In Proc. IEEE Int. Conf. on Robotics and Automation, San Diego, CA, May 1994.

....model, which is based on a simple linear spring idealization, can be used to assess the stability of a given grasp. In comparison, Rimon and Burdick [11] have shown that kinematic immobility automatically implies dynamic stability for a large class of nonlinear compliance models. Trinkle et. al [18] have also considered 2 nd terms in the stability analysis of frictionless grasps of polygonal objects. While Ref.s [2] and [18] both give means to determine the stability of a given grasp (under the assumptions of their models) neither work addresses the more general issue of how to develop a ....

....Rimon and Burdick [11] have shown that kinematic immobility automatically implies dynamic stability for a large class of nonlinear compliance models. Trinkle et. al [18] have also considered 2 nd terms in the stability analysis of frictionless grasps of polygonal objects. While Ref.s [2] and [18] both give means to determine the stability of a given grasp (under the assumptions of their models) neither work addresses the more general issue of how to develop a unifying viewpoint on the issues of force and form closure. A 1 A 2 A 3 B Figure 1: A 3 finger immobilizing grasp Although the ....

J. C. Trinkle, A. O. Farahat, and P. F. Stiller. Second-order stability cells of frictionless rigid body systems. In IEEE Int. Conference on Robotics and Automation, San Diego, CA, May 1994.

....work on pushing may be considered passive manipulation, in contrast to the more active manipulation explored in [35] 25] and in much research on grasping. Examples of passive manipulation appear in the wholearm manipulation techniques of Trinkle, Ram, Farahat and Stiller ( 33] 13] 30] [31]) Their analysis and planning use the idea of contact formations originally presented by Desai, and incorporated into a planner for dextrous manipulation by Trinkle and Hunter [32] The work described in the present paper follows a similar method to Trinkle, et al. However, the paths through ....

Trinkle, J. C; Farahat, A. O.; Stiller, P. F.; "Second Order Stability Cells of Frictionless Rigid Body Systems", Proceedings, ICRA, 1994.

....has been investigated by many authors, beginning with Hanafusa and Asada [1982] Cutkosky and Kao [1989] discussed how to compute the aggregated compliance matrix of a hand object system, while [Sinha and Abel, 1992] reported on contact stress models for manipulation. Montana [1991 and 1992] Trinkle et al. 1994] and Howard and Kumar [1994 and 1995] considered relations of compliant (and rolling) contacts with the stability of the grasp. Compliant manipulation was also considered by Michelmann and Allen [1993] Bicchi and Prattichizzo [1995] considered the dynamic structure of general (including ....

Trinkle, J.C., Farahat, A.O., and Stiller, P.F.: "Second order stability cells of a frictionless rigid body grasped by rigid fingers;;, Proc. IEEE Int. Conf. on Robotics and Automation, pp. 2815-- 2821, 1994.

.... n . Note that we do not consider cases for which there are more than n q n contacts, because such cases only occur under special geometric circumstances [17] Also, because of space limitations, we will only consider the first case here. Details of the second and third cases can be found in [18]. 5.1 Case 1 SS cells Since Wn is full rank, we can write the workpiece equilibrium equation as follows: W I (q ; W III (q ; cn = Gammag I Gammag III (18) where the matrix, W I 2 R n c Thetan c is nonsingular, W III 2 R (nq Gamman c ) Thetan c contains the rows of Wn ....

....definition of SS 1 , because they are used in the definition of CF [17] Since SS cells are defined in the (n q n ) dimensional C space, X , we see that the dimension of Case 1 SScells is n Gamma l. Interestingly, the dimensions of typical Case 2 and Case 3 SS cells are also n Gamma l [18]. The most important implication of SS cells normally having dimension n (recall that l is usually zero) is that when position controlling the manipulator, the motion of the workpiece can be determined unquely even though the kinematic constraints alone are insufficient to predict the motion. ....

J.C. Trinkle, A.O. Farahat, and P.F. Stiller. Second-order stability cells for frictionless rigid body systems. Technical Report TAMU-CS TR 93-020, Texas A&M University Department of Computer Science, April 1993.

....unchanged. When such a situation occurs, the stability tests presented below cannot resolve the stability question, but they do provide an indication that second or higher order information is needed. A method for determining stability or instability using second order information is presented in[15]. Following the approach used in [14] let q be the generalized velocity vector of the bodies in the assembly. In two dimensional assemblies, this is defined as: q = x 1 ; y 1 ; 1 ; x 2 ; y 2 ; 2 ; xn b ; yn b ; n b ] T where x i , y i and i are the linear and ....

J.C. Trinkle, A.O. Farahat, and P.F. Stiller. Second-order stability cells for frictionless rigid body systems. Technical Report TAMU-CS TR 93-020, Texas A&M University Department of Computer Science, April 1993.

.... of c n ; second and or high order effects become important [35] Also, in this case, the equations f geo = 0 and f phy1 = 0 define a cell that represents part of the boundary between the FS cell in question and portions of C space for which the object is either higher order stable or unstable [41]. 4.2 Active Frictionless FS cells When the number of contacts, n c , is greater than 6, then the elements of the wrench intensity vector, c n , are linearly dependent on the joint efforts, see equation (12) As discussed earlier, maintaining the current contact formation requires active ....

J.C. Trinkle, A.O. Farahat, and P.F. Stiller. Second-order stability cells for frictionless rigid body systems. Technical Report TAMU-CS TR 93-020, Texas A&M University Department of Computer Science, April 1993.

....rare. If during manipulation in a passive FS cell, l becomes positive, the corresponding l contacts are about to break. In this case, the object may still be stable, but stability can no longer be determined by the signs of the elements of c n ; second and or high order effects become important [35]. Also, in this case, the equations f geo = 0 and f phy1 = 0 define a cell that represents part of the boundary between the FS cell in question and portions of C space for which the object is either higher order stable or unstable [41] 4.2 Active Frictionless FS cells When the number of ....

J. C. Trinkle, A.O. Farahat, and P.F. Stiller. Second-order stability cells of frictionless rigid body systems. In Proceedings, IEEE International Conference on Robotics and Automation, volume 4, pages 2815--2821, May 1994.

....and second, cell decomposition techniques lend themselves to parallel and distributed computation. In this paper, we present the geometric characterization and analytic representation of eight fundamental types of kinematic constraint surfaces in C space (called contact formation cells [30] [29]) These constraint surfaces are the most important ones that arise during the planar manipulation of a passive polygonal workpiece by a manipulator composed of up to three active polygons whose positions and orientations are independently controlled. Using simple techniques from algebraic ....

....parameters. 1 The term elemental contact [5] refers to either a type A or a type B contact. Brost represented the patches and edges of the C obstacle in parametric form and found the vertices by numerical solution. In the dexterous manipulation planning problem that we have been pursuing [27, 28, 30, 29], the vertices are extremely important, because during manipulation, the workpiece configuration commonly resides at a vertex or (when rolling is involved) at a fixed point on an edge of the deforming C obstacle. Actual manipulation of the workpiece corresponds to the deliberate deformation of the ....

J.C. Trinkle, A.O. Farahat, and P.F. Stiller. Second-order stability cells for frictionless rigid body systems. Technical Report TAMU-CS TR 93-020, Texas A&M University Department of Computer Science, April 1993.

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Trinkle, J.C., Farahat, A.O., and Stiller, P.F. Second order stability cells of a frictionless rigid body grasped by rigid fingers. Proc. IEEE Int. Conf. on Robotics and Automation, pp. 2815-- 2821, 1994.

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