The problem of computing zeros of a system of polynomial equations has been well studied in the computational literature.A n umber of algorithms have been proposed and many computer algebra and public domain packages provide the capability of computing the roots of polynomial equations.Most of these implementations are based on Gr obner bases which can be slow for even small problems.In this paper, we present a new system, MARS, to compute the roots of a zero dimensional polynomial system.It is based on computing the resultant of a system of polynomial equations followed by eigendecomposition of a generalized companion matrix.MARS includes a robust library of Maple functions for constructing resultant matrices, an ecient library of Matlab routines for numerically solving the eigenproblem, and C code generation routines and a C library for incorporating the numerical solver into applications.We illustrate the usage of MARS on various examples and utilize dierent resultant formulations.

Fixturing, i.e. the process of immobilizing a workpiece for manufacturing or assembly operations, is a fundamental task in manufacturing. Fixtures can either be fabricated from scratch or assembled from a toolkit of modular components; the latter approach is termed modular fixturing. Recently, many researchers have proposed generate and test fixture design algorithms for minimal modular fixture toolkits where minimal fixture toolkits incorporate a single degree of freedom and constrain fixture elements to a finite number of locations. Generate and test strategies have succeeded because minimal fixture toolkits can only fixture generic workpieces in a finite number of ways. In this paper, we present alternative minimal toolkits and two generic fixture design algorithms: a complete enumeration algorithm based upon the generate and test paradigm, and an efficacious heuristic hill climbing algorithm. Our generate and test design algorithm is based upon a duality we observed between fixture design and object recognition from sparse probe data. In particular, we reduce the task of completely enumerating fixtures to the task of constructing complete indexing tables.

The term fixturing refers to the task of immobilizing a workpiece for the purpose of performing operations such as assembly and machining. As such, fixturing is of fundamental importance to industrial manufacturing. Fixtures can either be fabricated from scratch, or assembled from a toolkit of modular components, the latter approach is termed modular fixturing. In this paper, we present a complete algorithm to automatically design fixtures for the fixture vice toolkit. The algorithm enumerates fixture configurations, consisting of peg positions, workpiece pose, and jaw separation, for a given generalized polyhedral workpiece. A generalized polyhedral prismatic workpiece is defined to have a generalized polygonal silhouette, with a boundary composed of linear edges and circular area.

Many industrial applications are well suited to nonanthropomorphic pick and place robots. Robotworld is adept at performing vertical assembly operations, which may constitute 60% of all manufacturing operations. Furthermore, nonanthropomorphic robots can achieve higher accuracy than anthropomorphic (six degree of freedom) robots because they can be calibrated to higher precision. In this report we describe calibration techniques for Robotworld modules, simple four degree of freedom (x, y, z, /spl theta/) manipulators. Robotworld modules consist of base which is actuated in (x, y) via Sawyer motors, and a servo-controlled rotating and translating end effector arm, which extends downward from the base. Robotworld modules are implicitly coordinated in x and y (to 0.025 mm) because all the Sawyer motors are actuated with respect to the same platen; therefore, only the axes of rotation and translation of the end effector arm, need to be calibrated. We estimated these axes by localizing a calibration peg using multiple crossbeam sensors. We analyzed the performance of our calibration technique via self validation methods and found that as few as 40 observations provided reasonably high precision (0.025 mm root mean squared error).

Model based object recognition and object localization are fundamental problems in industrial automation. The authors present techniques which use a scanner composed of binary light beam sensors to quickly recognize objects (as fast as 5 microseconds) and to accurately localize objects (0.025 millimeters), and they describe localization and recognition experiments and present results. Binary sensors only sense whether the part is present or absent at a particular location, and their high performance is due to their simple specification. Fast recognition is achieved by using indexing to solve the correspondence problem, the problem of interpreting the sensed data as model features; indexing involves using the sensed data to directly look up the correspondence information using a precomputed indexing table. Since each experiment only produces a single indexing vector, indexing tables need to be complete; in this paper the authors detail a complete indexing construction method for flat polygonal and polyhedral objects.

Indexing is a model-based recognition technique, in which unknown objects are identified using lookup tables. Indexing coordinates are extracted from sensed features, and the indexing coordinates specify a table entry containing the object's identity. Usually, only a small fraction of the possible indexing coordinates correspond to modeled objects, and hash tables are often used to save space. In this paper, we present a new indexing data structure called a tree grid which has two advantages over hash tables. (i) The tree grid preserves spatial ordering, so that nearby indexing entries can be retrieved efficiently (ii) The tree grid compacts the storage size of the table by a factor of as much as two orders of magnitude. k coordinates index an ordering of the interpretations, and 1 coordinate determines the consistent interpretations for objects with k degrees of freedom. We also show that for almost all model sets, 2k+1 indexing coordinates care sufficient to discriminate between two generic models, implying that 2k+1 indexing coordinates specify a unique in interpretation. We have implemented an indexing algorithm for recognizing 3D objects from pairs of image rays using the tree grid technique, and the results are reported.>

Fixturing is a fundamental problem in mechanical assembly. Usually, two and a half dimensional objects can be fixtured in many different ways using a fixture vice, especially if pegs of different radii are available. The authors present an algorithm which enumerates all force closure fixture vice configurations and corresponding object poses. Automatic fixture design algorithms are essential for planning because optimal fixturing selections for multiple operations requires examining all of the valid configurations. The algorithm runs in O(A) time, where A is the number of configurations which simultaneously contact the object.>