J. Luntz, W. Messner, and H Choset. Velocity field design on the modular distributed manipulator system. In Proceedings, Workshop on the Algorithmic Foundations of Robotics, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to physically create a vector field (a closed loop feedback law) which will configure parts which are placed upon them. These ideas have been implemented in a variety of forms including longitudinally vibrating plates [6] MEMS devices [7] and platforms with arrays of wheeled actuators on them [8]. Although there has been a significant amount of work done on what type of control laws can and cannot be used to orient parts, little work has been done on obstacle avoidance using such systems. Presumably, if the long term goal of these systems will be to sort parts and perform assembly tasks, ....

J. Luntz, W. Messner, and H. Choset, "Velocity field design for the modular distributed manipulator system (mdms)," Workshop on the Algorithmic Foundations of Robotics, vol. 3, pp. 35--48, 1998.

....force is applied to the parts the deviations are caused by ill conditioning in the linear system. 62 Chapter 5 Building a Universal Planar Manipulator Distributed manipulation devices make use of a large number of actuators, organized in array fashion, to manipulate a small number of parts [25, 19, 10]. Inspired by minimalism in robotics [12] in our own research we have looked at a complementary question: can a device with few degrees of actuation freedom be used to independently manipulate a large number of parts The well known bowl feeder [11] achieves just that at the expense of ....

J. Luntz, W. Messner, and H. Choset. Velocity field design for the modular distributed manipulator system (MDMS). In P. Agarwal, L. Kavraki, and M. Mason, editors, 3rd Workshop on Algorithmic Foundations of Robotics: Robotics: the algorithmic perspective. A. K. Peters, Natick, MA, 1998.

....the cells and the specific interaction between each wheel and the object. That work was extended into two dimensions (plus rotation) in a following paper[7] which is a precursor to the work presented here. Much of the modeling in its final form presented here is presented in another precursor paper[9]. The authors presented work on modeling nonlinear friction modes, including mixed stick slip friction modes in another paper[8] along with a rudimentary simulator. The simulator presented here is much more efficient since it takes advantage of the piecewise nature of the dynamics. In addition to ....

....classes of fields on regular square lattice arrays. The first is an elliptic field, defined by the following equation. V = k sxx 0 0 k syy X (29) This field has the special property that the translational constants of motion, k s and f o are invariant with respect to the set of supports[9]. In particular k s is diagonal (with elements k sxx and k syy ) and f o is everywhere zero. Therefore, the object acts as a simple mass spring damper system centered at the origin over the entire array. This field also tends to orient a rectangular object such that its major axis aligns with ....

J. Luntz, W. Messner, and H. Choset. Velocity field design on the modular distributed manipulator system. In Proceedings. Workshop on the Algorithmic Foundations of Robotics., 1998.

....n c b a 3 7 7 7 7 7 7 7 7 7 5 z N T abc = 2 6 6 6 6 6 6 6 6 6 4 0 . 0 W Wx c Wy c 3 7 7 7 7 7 7 7 7 7 5 z W (2) A can be inverted to solve for N abc . A 1 exists if B has rank 3 (which is true as long as all the cells do not lie on a line) After computing A 1 (Luntz et al. 1998), N as a function of object position is N T = WB T BB T 1 0 2 4 1 0 0 3 5 2 4 0 0 1 0 0 1 3 5 X cm 1 A (3) Luntz et al. Discreteness Issues in Actuator Arrays X cm V N i f i Figure 2 Interaction between wheel and object. 3.2 PLANAR DYNAMICS The planar dynamics ....

.... # = V 1x : V nx V 1y : V ny = h V 1 : V n i (5) Summing vectorially, the net horizontal force is f = V N T X cm W (6) Observe that the net horizontal force is not a function of the object s rotation speed the terms multiplying are identically zero (Luntz et al. 1998). Furthermore, the second term in this equation is a dissipative linear damping term. Substituting N from Equation 3 yields f = WVB T BB T 1 2 4 0 0 1 0 0 1 3 5 z ks X cm WVB T BB T 1 2 4 1 0 0 3 5 z fo X cm W (7) DISTRIBUTED ....

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Luntz, J., Messner, W., and Choset, H. (1998). Velocity Field Design on the Modular Distributed Manipulator System. In Proceedings, Workshop on the Algorithmic Foundations of Robotics.

....The Modular Distributed Manipulator System (MDMS) is a macroscopic actuator array which transfers, as well as manipulates, objects in the plane, enhancing applications such as flexible manufacturing and package handling systems. This system has been described in detail in previous work [4, 6] 1 . Essentially, the MDMS comprises an fixed array of actuators (cells) each of which is an orthogonally mounted pair or roller wheels whose combined motion provides a directable traction force to an object resting on top. In this system, several cells support a single object that can be made ....

.... velocity matrix V as V = V 1x V 2x : Vnx V 1y V 2y : Vny : 12) Summing vectorially, the net horizontal force is f = V N T Gamma X cmW: 13) Observe that the net horizontal force is not a function of the object s rotation speed the terms multiplying are identically zero[6]. Furthermore, the second term in this equation is a dissipative linear damping term. The substitution of N from Equation 10 into Equation 13 yields f = WVB T Gamma BB T Delta Gamma1 2 4 0 0 1 0 0 1 3 5 z k s Xcm WVB T Gamma BB T Delta Gamma1 2 4 1 0 ....

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J. Luntz, W. Messner, and H. Choset. Velocity Field Design on the Modular Distributed Manipulator System. In Proceedings of Workshop on the Algorithmic Foundations of Robotics., 1998.

....a finite number of orientations. Kavraki [4] supplied further analysis of continuous field microactuator arrays using elliptical potential fields to bring any object to a single orientation. She used potential functions to predict stable configurations of objects. In previous papers, the authors [5, 6, 7] examined the dynamics of an object carried by a macroscopic discrete actuator array called the Modular Distributed Manipulator System (MDMS) or Virtual Vehicle) Each cell in this array contains an orthogonally mounted pair of motorized roller wheels whose combined motion provides a directable ....

....the quadrant nature and symmetry of the field. In general, the x axis has a natural position, but the y axis may have somewhat arbitrary placement (see Figure 1) Discretized versions of Bohringer s squeeze field[2] and Kavraki s elliptical potential field[4] as well as Luntz s computed field[7] are all squeeze like, as are many other fields. In general, squeeze like fields transport objects to the origin (except for a pure squeeze field which has an arbitrary origin) After the object is brought to the origin, rotational equilibrium is reached when the object rotates to cover symmetric ....

J. Luntz, W. Messner, and H. Choset. Velocity Field Design on the Modular Distributed Manipulator System. In Proceedings. Workshop on the Algorithmic Foundations of Robotics., 1998.

....analysis of microactuated systems using elliptical potential fields to orient an object to symmetry without sensors. These microactuated systems differ from the authors work in that on such a small scale, mass, friction, and array resolution may be ignored. In previous papers by the authors [7, 8, 9] motions of objects on the MDMS both in 1 D and in 2 D with rotation were analyzed, and a velocity field was designed which can position and orient certain symmetric objects within cell resolution and symmetry. This analysis assumed full sliding friction between the wheels and the object without ....

....determine the normal forces supporting the object. Using vertical and rotational equilibrium Figure 5: Flexible cells support a flat object. along with the assumptions that each cell provides a linear spring support and that the bottom of the object is flat (as shown in Figure 5) it was shown in [9] that the collection of normal forces exerted by each contact written as a vector N= N 1 : Nn ] T is equal to N T = B T Gamma BB T Delta Gamma1 W Wx c (1) where W is the weight of the object, x c is the location of the object s center of mass, and B = 1 : 1 x 1 : ....

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J. Luntz, W. Messner, and H. Choset. Velocity Field Design on the Modular Distributed Manipulator System. In Proceedings. Workshop on the Algorithmic Foundations of Robotics., 1998.

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J. Luntz, W. Messner, and H Choset. Velocity field design on the modular distributed manipulator system. In Proceedings, Workshop on the Algorithmic Foundations of Robotics, 1998.

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