22 research outputs found

    Grasping and Assembling with Modular Robots

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    A wide variety of problems, from manufacturing to disaster response and space exploration, can benefit from robotic systems that can firmly grasp objects or assemble various structures, particularly in difficult, dangerous environments. In this thesis, we study the two problems, robotic grasping and assembly, with a modular robotic approach that can facilitate the problems with versatility and robustness. First, this thesis develops a theoretical framework for grasping objects with customized effectors that have curved contact surfaces, with applications to modular robots. We present a collection of grasps and cages that can effectively restrain the mobility of a wide range of objects including polyhedra. Each of the grasps or cages is formed by at most three effectors. A stable grasp is obtained by simple motion planning and control. Based on the theory, we create a robotic system comprised of a modular manipulator equipped with customized end-effectors and a software suite for planning and control of the manipulator. Second, this thesis presents efficient assembly planning algorithms for constructing planar target structures collectively with a collection of homogeneous mobile modular robots. The algorithms are provably correct and address arbitrary target structures that may include internal holes. The resultant assembly plan supports parallel assembly and guarantees easy accessibility in the sense that a robot does not have to pass through a narrow gap while approaching its target position. Finally, we extend the algorithms to address various symmetric patterns formed by a collection of congruent rectangles on the plane. The basic ideas in this thesis have broad applications to manufacturing (restraint), humanitarian missions (forming airfields on the high seas), and service robotics (grasping and manipulation)

    New bounds on the number of frictionless fingers required to immobilize 2D objects

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    This paper develops new lower bounds on the number of frictionless fingers or fixtures which are required to immobilize planar objects. We study in detail the case of objects with smooth boundaries and polygonal objects. Analogous results for the case of piecewise smooth objects follow directly from the analysis presented herein. These results have obvious applications to fixture planning and grasp planning, as we show that it is possible to immobilize objects with fewer fingers than was previously thought possible

    Constructing minimum deflection fixture arrangements using frame invariant norms

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    This paper describes a fixture planning method that minimizes object deflection under external loads. The method takes into account the natural compliance of the contacting bodies and applies to two-dimensional and three-dimensional quasirigid bodies. The fixturing method is based on a quality measure that characterizes the deflection of a fixtured object in response to unit magnitude wrenches. The object deflection measure is defined in terms of frame-invariant rigid body velocity and wrench norms and is therefore frame invariant. The object deflection measure is applied to the planning of optimal fixture arrangements of polygonal objects. We describe minimum-deflection fixturing algorithms for these objects, and make qualitative observations on the optimal arrangements generated by the algorithms. Concrete examples illustrate the minimum deflection fixturing method. Note to Practitioners-During fixturing, a workpiece needs to not only be stable against external perturbations, but must also stay within a specified tolerance in response to machining or assembly forces. This paper describes a fixture planning approach that minimizes object deflection under applied work loads. The paper describes how to take local material deformation effects into account, using a generic quasirigid contact model. Practical algorithms that compute the optimal fixturing arrangements of polygonal workpieces are described and examples are then presented

    Efficient determination of four-point form-closure optimal constraints of polygonal objects

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    This paper proposes a new and more efficient solution to the problem of determining optimal form-closure constraints of polygonal objects using four contacts. New grasp parameters are determined based only on the directions of the applied forces, which are then used to determine the optimal grasp. Given a set of contact edges, using an analytical procedure a solution that is either the optimal one or is very close to it is obtained (only in this second case an iterative procedure is needed to find a root of a nonlinear equation). This procedure is used for an efficient determination of the optimal grasp on the whole object. The algorithms have been implemented and numerical examples are shown. Note to Practitioners—This paper presents an algorithm that improves previous approaches in terms of efficiency in the determination of the optimal object constraint maximizing the minimum wrench that the object can support in any direction. The problem can always be solved using numerical optimization techniques but when time is relevant an efficient algorithm becomes of interest. Practical applications include optimal determination of fixtures and object grasps.Peer ReviewedPostprint (published version

    New bounds on the number of frictionless fingers required to immobilize 2D objects

    Get PDF
    This paper develops new lower bounds on the number of frictionless fingers or fixtures which are required to immobilize planar objects. We study in detail the case of objects with smooth boundaries and polygonal objects. Analogous results for the case of piecewise smooth objects follow directly from the analysis presented herein. These results have obvious applications to fixture planning and grasp planning, as we show that it is possible to immobilize objects with fewer fingers than was previously thought possible

    Computation and analysis of natural compliance in fixturing and grasping arrangements

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    This paper computes and analyzes the natural compliance of fixturing and grasping arrangements. Traditionally, linear-spring contact models have been used to determine the natural compliance of multiple contact arrangements. However, these models are not supported by experiments or elasticity theory. We derive a closed-form formula for the stiffness matrix of multiple contact arrangements that admits a variety of nonlinear contact models, including the well-justified Hertz model. The stiffness matrix formula depends on the geometrical and material properties of the contacting bodies and on the initial loading at the contacts. We use the formula to analyze the relative influence of first- and second-order geometrical effects on the stability of multiple contact arrangements. Second-order effects, i.e., curvature effects, are often practically beneficial and sometimes lead to significant grasp stabilization. However, in some contact arrangements, curvature has a dominant destabilizing influence. Such contact arrangements are deemed stable under an all-rigid body model but, in fact, are unstable when the natural compliance of the contacting bodies is taken into account. We also consider the combined influence of curvature and contact preloading on stability. Contrary to conventional wisdom, under certain curvature conditions, higher preloading can increase rather than decrease grasp stability. Finally, we use the stiffness matrix formula to investigate the impact of different choices of contact model on the assessment of the stability of multiple contact arrangements. While the linear-spring model and the more realistic Hertz model usually lead to the same stability conclusions, in some cases, the two models lead to different stability results

    Computation Reuse in Statics and Dynamics Problems for Assemblies of Rigid Bodies

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    The problem of determining the forces among contacting rigid bodies is fundamental to many areas of robotics, including manipulation planning, control, and dynamic simulation. For example, consider the question of how to unstack an assembly, or how to find stable regions of a rubble pile. In considering problems of this type over discrete or continuous time, we often encounter a sequence of problems with similar substructure. The primary contribution of our work is the observation that in many cases, common physical structure can be exploited to solve a sequence of related problems more efficiently than if each problem were considered in isolation. We examine three general problems concerning rigid-body assemblies: dynamic simulation, assembly planning, and assembly stability given limited knowledge of the structure\u27s geometry. To approach the dynamic simulation and assembly planning applications, we have optimized a known method for solving the system dynamics. The accelerations of and forces among contacting rigid bodies may be computed by formulating the dynamics equations and contact constraints as a complementarity problem. Dantzig\u27s algorithm, when applicable, takes n or fewer major cycles to find a solution to the linear complementarity problem corresponding to an assembly with n contacts. We show that Dantzig\u27s algorithm will find a solution in n - k or fewer major cycles if the algorithm is initialized with a solution to the dynamics problem for a subassembly with k internal contacts. Finally, we show that if we have limited knowledge of a structure\u27s geometry, we can still learn about stable regions of its surface by physically pressing on it. We present an approach for finding stable regions of planar assemblies: sample presses on the surface to identify a stable cone in wrench space, partition the space of applicable wrenches into stable and unstable regions, and map these back to the surface of the structure

    対象物体と指配置のコンフィグレーション空間を用いた不確かさを扱える効率的なケージング計画

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    学位の種別:課程博士University of Tokyo(東京大学
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