Randy C. Brost

A complete algorithm for designing planar fixtures using modular components

We present an implemented algorithm that accepts a polygonal description of a parts silhouette, and efficiently constructs the set of all feasible fixture designs that kinematically constrain the part in the plane. Each fixture is composed of three locators rigidly attached to the lattice and one sliding clamp, and constrains the part without relying on friction. The algorithm is based on an efficient enumeration of admissible designs that exploits part geometry and graphical force analysis. The algorithm run time is linear in the number of designs found, which is bounded by a polynomial in the number of part edges and the parts maximal diameter in lattice units. Our review of the literature suggests that this is the first fixturing algorithm that is complete in the sense that it is guaranteed to find all admissible fixture designs for an arbitrary polygonal silhouette and to identify the optimal fixture relative to an arbitrary quality metric. The algorithm does not consider out-of-plane forces or motions; however, we view this planar result as an essential component of a larger algorithm that solves the 3D fixture design problem by treating the planar and out-of-plane constraint problems separately. This approach is analogous to the widely used 3-2-1 fixture design heuristic.

A complete algorithm for synthesizing modular fixtures for polygonal parts

Commercially-available modular fixturing systems typically include a square lattice of tapped and bushed holes with precise spacing and an assortment of precision locating and clamping elements that can be rigidly attached to the lattice using dowel pins or expanding mandrels. Currently, human expertise is required to synthesize a suitable arrangement of these elements to hold a given part. Besides being time consuming, if the set of alternatives is not systematically explored, the designer may fail to find an acceptable fixture or may settle upon a suboptimal fixture. The authors consider a class of modular fixtures that prevent a part from translating or rotating in the plane using four point contacts on the parts boundary. These fixtures are based on three round locators, each centered on a lattice point, and one translating clamp. The authors present an algorithm that accepts a polygonal part shape as input and synthesizes the set of all fixture designs that achieve form closure for the given part. The algorithm also allows the user to specify geometric access constraints on fixtures. If the part has n edges and its maximal diameter is d lattice units, the asymptotic running time of the algorithm is O(n/sup 5/d/sup 5/). The authors have implemented the algorithm and present example fixtures that it has synthesized. This implementation includes a metric to rank fixtures based on their ability to resist applied forces. The authors believe this is the first fixture synthesis algorithm that is complete in the sense that it is guaranteed to find an admissible fixture if one exists. Furthermore, the algorithm is guaranteed to find the optimal fixture, relative to any well-defined quality metric.<<ETX>>

Dynamic analysis of planar manipulation tasks

The author presents two algorithms that construct a set of initial configurations from which a given action will reliably accomplish a planar manipulation task. The first algorithm applies energy arguments to construct a conservative set of successful initial configurations, while the second algorithm performs numerical integration to construct a set that is much less conservative. The algorithms may be applied to a variety of tasks, including pushing, placing-by-dropping, and force-controlled assembly tasks. Both algorithms consider the task geometry and mechanics, and allow uncertainty in every task parameter except for the object shapes. Experimental results which demonstrate the validity of the algorithms output for two example manipulation tasks are presented.<<ETX>>

A 3-D modular gripper design tool

Modular fixturing kits are sets of components used for flexible, rapid construction of fixtures. A modular vise is a parallel-jaw vise, each jaw of which is a modular fixture plate with a regular grid of precisely positioned holes. To fixture a part, one places pins in some of the holes so that when the vise is closed, the part is reliably located and completely constrained. The modular vise concept can be adapted easily to the design of modular parallel-jaw grippers for robots. By attaching a grid-plate to each jaw of a parallel-jaw gripper we gain the ability to easily construct high-quality grasps for a wide variety of parts from a standard set of hardware. Wallack and Canny (1994) developed an algorithm for planning planar grasp configurations for the modular vise. We expand this work to produce a 3D fixture/gripper design tool. We describe several analyses we have added to the planar algorithm, including a 3D grasp quality metric based on force information, 3D geometric loading analysis, and inter-gripper interference analysis. Finally, we describe two applications of our code. One of these is an internal application at Sandia, while the other shows a potential use of our code for designing part of an agile assembly line.

Automatic design of 3-d fixtures and assembly pallets

This paper presents an implemented algorithm that automatically designs fixtures and assembly pallets to hold three-dimensional parts. The designed fixtures rigidly constrain and locate the part, obey task constraints, are robust to part shape variations, are easy to load, and are economical to produce. The algorithm is guaranteed to find the global optimum solution that satisfies these and other pragmatic conditions. We present the results of the algorithm applied to several practical manufacturing problems. For these complex problems the algorithm typically returns initial high-quality fixture designs in less than two minutes, and identifies the global optimum design in just over an hour.

Probabilistic analysis of manipulation tasks: a conceptual framework

This article addresses the problem of manipulation planning in the presence of uncertainty. We begin by reviewing the worst-case planning techniques introduced by Lozano-Pérez et al. (1984) and show that these methods are limited by an information gap inherent to worst-case analysis techniques. As the task uncertainty increases, these methods fail to produce useful information, even though a high-quality plan may exist. To fill this gap, we present the notion of a probabilistic back projection, which describes the likelihood that a given action will achieve the task goal from a given initial state. We provide a constructive definition of the probabilistic backprojection and related probabilistic models of manipulation task mechanics and show how these models unify and enhance several past results in manipulation planning. These models capture the fundamental nature of the task behavior but appear to be very complex. We present the results of laboratory experiments, comprising over 100,000 grasping trials, that measured the probabilistic backprojection of a grasping task under varying conditions. The resulting data support the probabilistic back projection model and illustrate a task in which probabilistic analysis is required. We sketch methods for computing these models and using them to construct multiple-step plans.

Probabilistic analysis of manipulation tasks: a research agenda

The problem of manipulation planning in the presence of uncertainty is addressed. The worst-case planning techniques introduced in Lozano-Perez, Mason, and Taylor (1984) are reviewed. It is shown that these methods are limited by an information gap inherent to worst-case analysis techniques. As the task uncertainty increases, these methods fail to produce useful information even though a high-quality plan may exist. To fill this gap, the probabilistic backprojection, which describes the likelihood that a given action will achieve the task goal from a given initial state is presented. A constructive definition of the probabilistic backprojection and related probabilistic models of manipulation task mechanics is provided. It is shown how these models unify several past results in manipulation planning. These models capture the fundamental nature of the task behavior, but appear to be very complex. Methods for computing these models are sketched. Efficient computational methods remain unknown.<<ETX>>

Computing the possible rest configurations of two interacting polygons

An algorithm that constructs the set of all possible equilibrium configurations for two interacting polygonal objects is described. Given two polygons, associated friction properties, and an applied force, the algorithm constructs the set of all configurations where the contact reaction force can balance the applied force, obeying friction constraints. The algorithm explicitly includes uncertainty in friction, applied force, and mass properties of the polygons. The algorithm has been implemented, and physical experiments have been performed to test the validity of the algorithms predictions. The algorithm may be applied to a variety of physical systems to determine the possible rest states: examples include a part falling into a fixture and an object being pushed by a robot end-effector.<<ETX>>

Empirical verification of fine-motoion planning theories

Successful robot systems must employ actions that are robust in the face of task uncertainty. Toward this end, Lozano-Perez, Mason, and Taylor developed a model of manipulation tasks that explicitly considers task uncertainty. In this paper we study the utility of this model applied to real-world tasks. We report the results of two experiments that highlight the strengths and weaknesses of the LMT approach. The first experiment showed that the LMT formalism can successfully plan solutions for a complex real-world task. The second experiment showed a task that the formalism is fundamentally incapable of solving.