Kavraki Lab

The Problem

Part manipulation is an important but also time-consuming operation in industrial automation. Parts arrive at manufacturing sites in boxes and they need to be sorted and oriented before assembly. Traditionally part orientation has been performed with vibratory bowl feeders. These devices are customly designed for the orientation of a single part and rely on mechanical filters to reject parts in unwanted orientations. However, vibratory bowl feeders have several disadvantages: they have to be redesigned when the geometry of the part changes, may damage parts, etc.

The Methods

Recent work investigates alternative ways for feeding parts in assembly workcells. Parts feeders that are programmed, rather than mechanically modified, offer an attractive solution since they can be used for a wide variety of parts. Practical considerations favor feeding methods that require little or no sensing, employ simple devices, and are as robust as possible.

One of the proposed alternatives is the use of programmable force fields. The basic idea is the following: the field is realized on an horizontal planar surface. A part placed on such a field is subjected to resultant force and torque and moves toward a stable equilibrium configuration. Orienting a part consists then in finding a force field giving rise to few or possibly a unique stable equilibrium for the given part.

Current technology permits the implementation of certain vector fields in the microscale with MEMS actuator arrays and in the macroscale with transversely vibrating plates or arrays of mechanical actuators.

We are investigating the capabilities of vector fields in parts handling including tasks such as positioning and orientation, separation and assembly of parts. Our most impressive results so far are in parts positioning and orientation.

Our Results

  • Two stable equilibrium configurations
    Consider the following linear force field:

    F(x,y)=(-ax,-by)

    F derives from a quadratic potential function that we call an elliptic potential field. If the principal moments of inertia of a part are different, we proved that the part has two stable equilibrium configurations under the elliptic field. If the two principal moments of inertia are equal, the center of mass of the part moves toward the center of the field and the orientation of the part remains unconstrained.

  • One stable equilibrium configuration
    Now consider a unit radial field ur(x,y) oriented toward the origin O. A part posed in such a field moves to an equilibrium position where a point of the part is at O and the orientation is unconstrained. The point of the part located at the origin is called pivot point. We proved that if the pivot point and the center of mass are different, the combination of the above radial field with a small constant field orients uniquely the part.

  • An algorithm for computing all stable equilibrium orientations
    For the combination of unit-radial and constant field we give an algorithm to compute all equilibrium orientations for any part. The analysis is based on a treatment of the problem through the use of potential fields. A drawback of this analysis is that the work cannot address how to compute a finite magnitude of the small constant field that satisfies our proofs. Therefore it is impossible to explicitly specify the field for a given part. Instead, the determination of the value of the constant field value is done experimentally using a standard search procedure.

  • A field based on the geometry of a part
    We show that it is possible to produce (a) a field that positions and orients most parts into a single equilibrium configuration and (a) an algorithm that computes the parameters of the field together with the corresponding stable equilibrium configuration of the part. Unlike most previous works, the analysis presented throughout this paper is based on geometric reasoning. Our novel field is a combination of a linear-radial force field and a constant force field. We accentuate the geometric relationship between the proposed field and the inducing force and torque. Our approach derives an intuitive insight about the effect of the new field on a given part and also leads to an efficient algorithm for computing the `pivot’ point of a part, a topic which is of interest to the robotics and vision community.

  • A single field to position and orient multiple parts
    Our geometric analysis above us to reach an even more interesting new result, that is, the computation of a single field (and its parameters) that can uniquely position and orient parts that may be in any shape listed in a given set of possible part’s shapes. According to our knowledge, it is the first time that a field with such a capabilities has been proposed.