In manufacturing, it is often necessary to orient parts prior to packing or assembly. We say that a planar part is polygonal if its convex hull is a polygon. We consider the following problem: given a list of n vertices describing a polygonal part whose initial orientation is unknown, find the shortest sequence of mechanical gripper actions that is guaranteed to orient the part up to symmetry in its convex hull. We show that such a sequence exists for any polygonal part by giving an O#n log n# algorithm for finding the sequence. Since the gripper actions do not require feedback, this result implies that any polygonal part can be oriented without sensors.

In which order can a product be assembled or disassembled? How many hands are required? How many degrees of freedom? What parts should be withdrawn to allow the removal of a specified subassembly? To answer such questions automatically, important theoretical issues in geometric reasoning must be addressed. This paper investigates the planning of assembly algorithms specifying (dis)assembly operations on the components of a product and the ordering of these operations. It also presents measures to evaluate the complexity of these algorithms and techniques to estimate the inherent complexity of a product. The central concept underlying these planning and complexity evaluation techniques is that of a "non-directional blocking graph," a qualitative representation of the internal structure of an assembly product. This representation describes the combinatorial set of parts interactions in polynomial space. It is obtained by identifying physical criticalities where geometric int...

This paper presents a method for determining the possible instantaneous motions of a sliding object during multiple contact pushing. The approach consists of two components: a kinematic analysis considering kinematic motion constraints, and a force analysis considering force constraints on the motion. A new representation of the support friction of a sliding object is presented, and the results of the force analysis are independent of the exact support distribution of the object. The analysis results in a new manipulation primitive: stable rotational pushing. This primitive may be used for precise placement operations by pushing. 1.

Planning the motion of bodies in contact requires a model of contact mechanics in order to predict sliding, rolling, and jamming. Such a model typically assumes that the bodies are rigid and that tangential forces at the contacts obey Coulomb's law. Though, usually assumed to be constant, the static and dynamic coefficients of friction vary in space and time and are difficult to measure accurately. In this paper, we study a quasistatic, multi-rigid-body model for planar systems, in which the coefficients of friction are treated as independent variables. Our analysis yields inequalities defining regions in the space of friction coefficients for which a particular contact mode (i.e., a particular combination of sliding, rolling, or separating at the contacts) is feasible. The geometrical interpretation of these inequalities leads to a simple graphical technique to test contact mode feasibility. This technique is then used to generate a nontrivial example in which several contact modes ar...

We present a framework for analyzing and computing motion plans for a robot that operates in an environment that both varies over time and is not completely predictable. We first classify sources of uncertainty in motion planning into four categories, and argue that the problems addressed in this paper belong to a fundamental category that has received little attention. We treat the changing environment in a flexible manner by combining traditional configuration space concepts with a Markov process that models the environment. For this context, we then propose the use of a motion strategy, which provides a motion command for the robot for each contingency that it could be confronted with. We allow the specification of a desired performance criterion, such as time or distance, and determine a motion strategy that is optimal with respect to that criterion. We demonstrate the breadth of our framework by applying it to a variety of motion planning problems. Examples are computed...

We consider the problem of grasping an unknown polygonal flat object using a parallel jaw gripper. Here we propose to equip a standard gripper with several light-beam sensors (close to each jaw) and describe a reactive grasping algorithm. This is done by probing the object to locate a good grasp position, and then grasping, without moving the object significantly. The goal is to do as little motion as possible to find a grasp. This algorithm can be viewed in a competitive framework, where our algorithm is competing against any algorithm which already knows the object. 1 Introduction In the past, the usual approach to grasping has been to assume an accurate model of the object to be grasped and from such a model, an offline geometric algorithm determines a set of grip points, where the fingers are then placed. (See Mishra, Schwartz and Sharir [MSS87]). Once the grip points have been determined, the geometry of the object is deemed irrelevant and the grasp is determined and maintained ...

Many of the most fundamental examples in probability involve the pose statistics of coins and dice as they are dropped on a flat surface. For these parts, the probability assigned to each stable face is justified based on part symmetry, although most gamblers are familiar with the possibility of loaded dice. Our goal is to develop a science base for part feeding, where parts arrive in random orientations. We consider the following problem: given part geometry and parameters such as center of mass, estimate the probability of encountering each stable pose of the part. We describe

This paper is about sensing and manipulation strategies using simple, modular robot hardware. RISC robotics is an attempt to fuse automation and robotic technologies. It uses traditional automation hardware such as parallel-jaw grippers and optical beam sensors, together with geometric planning and sensing algorithms. RISC systems should be cost-effective and reliable, and easy to setup and reconfigure. They should also be flexible enough to support small batch sizes and rapid changes in part design needed in forthcoming flexible-agile manufacturing systems. The RISC acronym, borrowed from computer architecture, suggests the parallels between the two technologies. RISC robots perform complex operations by composing simple elements. The elements may be individual light beam sensors, grouped together to form an array for recognition. Or a complex manipulation task may be performed via a sequence of grasp steps by different grippers specialized for acquisition and placement. This paper emphasizes three areas: (i) RISC sensing, primarily optical beam sensing (ii) RISC manipulation using simple parallel-jaw grippers or minimal configurations of fingers (iii) Computer-aided design of RISC workcells.

In order to plan manipulation of an object by pushing, a robot must have a model of the geometry and the friction properties of the object. This paper presents an approach to estimating the relevant friction parameters by performing experimental pushes and observing the resultant motion. Recognition of objects based on their friction parameters is also explored. 1.

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