Grasping and Assembling with Modular Robots

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)

Mobility of bodies in contact. II. How forces are generated bycurvature effects

For part I, see ibid., p.696-708. The paper considers how forces are produced by compliance and surface curvature effects in systems where an object a is kinematically immobilized to second-order by finger bodies Al,...,Ak. A class of configuration-space based elastic deformation models is introduced. Using these elastic deformation models, it is shown that any object which is kinematically immobilized to first or second-order is also dynamically locally asymptotically stable with respect to perturbations. Moreover, it is shown that for preloaded grasps kinematic immobility implies that the stiffness matrix of the grasp is positive definite. The stability result provides physical justification for using second-order effects for purposes of immobilization in practical applications. Simulations illustrate the concepts

Constructing minimum deflection fixture arrangements using frame invariant norms

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

Fast and flexible determination of force-closure independent regions to grasp polygonal objects

Force-closure independent regions are parts of the object edges such that a grasp with a finger in each region ensures a force-closure grasp. These regions are useful to provide some robustness to the grasp in the presence of uncertainty as well as in grasp planning. Most of the approaches to the computation of these regions for N fingers work on the contact space, implying a N-dimensional problem. This paper presents a new approach to determinate independent regions on polygonal objects considering N friction or frictionless contact. The approach works on the object space, implying that it is always a two-dimensional problem and, since it is not necessary to compute all the force-closure space, it becomes a very fast approach. Besides, the approach is also flexible since constraints on the fingers placement can be easily introduced. Some graphical examples are includes in this paper showing the simplicity of the methodology

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

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

Flexible Object Manipulation

Flexible objects are a challenge to manipulate. Their motions are hard to predict, and the high number of degrees of freedom makes sensing, control, and planning difficult. Additionally, they have more complex friction and contact issues than rigid bodies, and they may stretch and compress. In this thesis, I explore two major types of flexible materials: cloth and string. For rigid bodies, one of the most basic problems in manipulation is the development of immobilizing grasps. The same problem exists for flexible objects. I have shown that a simple polygonal piece of cloth can be fully immobilized by grasping all convex vertices and no more than one third of the concave vertices. I also explored simple manipulation methods that make use of gravity to reduce the number of fingers necessary for grasping. I have built a system for folding a T-shirt using a 4 DOF arm and a fixed-length iron bar which simulates two fingers. The main goal with string manipulation has been to tie knots without the use of any sensing. I have developed single-piece fixtures capable of tying knots in fishing line, solder, and wire, along with a more complex track-based system for autonomously tying a knot in steel wire. I have also developed a series of different fixtures that use compressed air to tie knots in string. Additionally, I have designed four-piece fixtures, which demonstrate a way to fully enclose a knot during the insertion process, while guaranteeing that extraction will always succeed

Synthesis of 4-frictionless optimal grasp of polygonal objects

The paper proposes a new approach to the problem of determining optimal form-closure grasps of polygonal objects using four frictionless contacts. A new set of grasp parameters is determined based only on the directions of the applied forces. These parameters are used to obtain a new formulation of the necessary and sufficient condition for the existence of four-finger frictionless form-closure grasps, as well as 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 fins a root of a non-linear equation). This procedure is the used for an efficient determination of the optimal grasp on the whole object. The algorithms have been implemented and numerical examples are show

Interlocking structure design and assembly

Many objects in our life are not manufactured as whole rigid pieces. Instead, smaller components are made to be later assembled into larger structures. Chairs are assembled from wooden pieces, cabins are made of logs, and buildings are constructed from bricks. These components are commonly designed by many iterations of human thinking. In this report, we will look at a few problems related to interlocking components design and assembly. Given an atomic object, how can we design a package that holds the object firmly without a gap in-between? How many pieces should the package be partitioned into? How can we assemble/extract each piece? We will attack this problem by first looking at the lower bound on the number of pieces, then at the upper bound. Afterwards, we will propose a practical algorithm for designing these packages. We also explore a special kind of interlocking structure which has only one or a small number of movable pieces. For example, a burr puzzle. We will design a few blocks with joints whose combination can be assembled into almost any voxelized 3D model. Our blocks require very simple motions to be assembled, enabling robotic assembly. As proof of concept, we also develop a robot system to assemble the blocks. In some extreme conditions where construction components are small, controlling each component individually is impossible. We will discuss an option using global controls. These global controls can be from gravity or magnetic fields. We show that in some special cases where the small units form a rectangular matrix, rearrangement can be done in a small space following a technique similar to bubble sort algorithm