Robert-Paul Berretty

Trap Design for Vibratory Bowl Feeders

The vibratory bowl feeder is the oldest and still most common approach to the automated feeding (orienting) of industrial parts. In this paper, the authors consider a class of vibratory bowl filters that can be described by removing polygonal sections from the track; this class of filters is referred to as traps. For an n-sided polygonal part and an m-sided polygonal trap, an O(n2m log n) algorithm is given to decide whether the part in a specific orientation will safely move across the trap or will fall through the trap and thus be filtered out. For an n-sided convex polygonal part and m-sided convex polygonal trap, this bound is improved to O((n+m) log n). Furthermore, the authors show how to design various trap shapes, ranging from simple traps to general polygons, which will filter out all but one of the different stable orientations of a given part. Although the runtimes of the design algorithms are exponential in the number of trap parameters, many industrial part feeders use few-parameter traps (balconies, canyons, slots); in these cases, the running times of the algorithms range from linear to low-degree polynomial.

Computing fence designs for orienting parts

A common task in automated manufacturing processes is to orient parts prior to assembly. We consider sensorless orientation of a polygonal part by a sequence of fences. We show that any polygonal part can be oriented by a sequence of fences placed along a conveyor belt, thereby settling a conjecture by Wiegley et al. (1997), and present the first polynomial-time algorithm to compute the shortest such sequence. The algorithm is easy to implement and runs in time O(n3 logn), where n is the number of vertices of the part.

Orienting polyhedral parts by pushing

A common task in automated manufacturing processes is to orient parts prior to assembly. We consider sensorless orientation of an asymmetric polyhedral part by a sequence of push actions, and show that is it possible to move any such part from an unknown initial orientation into a known final orientation if these actions are performed by a jaw consisting of two orthogonal planes. We also show how to compute an orienting sequence of push actions.We propose a three-dimensional generalization of conveyor belts with fences consisting of a sequence of tilted plates with curved tips; each of the plates contains a sequence of fences. We show that it is possible to compute a set-up of plates and fences for any given asymmetric polyhedral part such that the part gets oriented on its descent along plates and fences.

Geometry and Part Feeding

Many automated manufacturing processes require parts to be oriented prior to assembly. A part feeder takes in a stream of identical parts in arbitrary orientations and outputs them in uniform orientation. We consider part feeders that do not use sensing information to accomplish the task of orienting a part; these feeders include vibratory bowls, parallel jaw grippers, and conveyor belts and tilted plates with so-called fences. The input of the problem of sensorless manipulation is a description of the part shape and the output is a sequence of actions that moves the part from its unknown initial pose into a unique final pose. For each part feeder we consider, we determine classes of orientable parts, give algorithms for synthesizing sequences of actions, and derive upper bounds on the length of these sequences.

Trap design for vibratory bowl feeders

The vibratory bowl feeder is the oldest and still most common approach to the automated feeding (orienting) of industrial parts. We consider a class of vibratory bowl filters that can be described by removing polygonal sections from the track; we refer to this class of filters as traps. For an n-sided convex polygonal part and m-sided convex polygonal trap, we give an O((n+m)log(n+m)) algorithm to decide if the part will be rejected by the trap, and an O((nm(n+m))/sup 1+/spl epsiv//) algorithm which deals with non-convex parts and traps. We then consider the problem of designing traps for a given part, and consider two rectilinear subclasses, balconies and gaps. We give linear and O(n/sup 2/) algorithms for designing feeders and have tested the results with physical experiments using a commercial inline vibratory feeder.

On fence design and the complexity of push plans for orienting parts

A common task in automated manufacturing processes is to orient parts prior to assembly. We consider sensorless orientation of a polygonal part by a sequence of push actions. We show that any polygonaJ part can be oriented by a sequence of fences placed along a conveyor belt, thereby settling a conjecture by Wiegley et al. [25], and present the first polynomial-time algorithm to compute the shortest such sequence. The algorithm is simple and runs in time 0(n3 log n), where n is the number of vertices of the part. Even though pathological parts can be constructed that require Q(n) push actions, it turns out that almost all parts can be oriented using a small number of pushes. We deduce a new bound on the length of the shortest push plan that depends on the thinness – or eccentricity – of the part. The bound shows that only O(1) pushes are required for the large class of parts with non-square minimum-width bounding boxes.

Orienting parts by inside-out pulling

A common task in automated manufacturing processes is that of orienting (or feeding) parts prior to assembly. We propose a new type of feeder. We consider sensorless orientation of polygonal parts with elevated edges by pull actions with an overhead finger. We show that any asymmetric convex polygonal part can be oriented by a sequence of pull operations. We give an O(n/sup 3/) algorithm to compute the shortest sequence of pull operations to orient a convex polygonal part with n vertices, if such a sequence exists. We also show that there exist non-convex parts that cannot be fed by a sequence of pull operations.

Dynamic motion planning in low obstacle density environments

A fundamental task for an autonomous robot is to plan its own motions. Exact approaches to the solution of this motion planning problem suffer from high worst-case running times. The weak and realistic low obstacle density (L.O.D.) assumption results in linear complexity in the number of obstacles of the free space [1l]. In this paper we consider the dynamic version of the motion planning problem in which a robot moves among moving polygonal obstacles. The obstacles move along constant complexity polylines, but respect the low density property at any given time. We will show that in this situation a cell decomposition of the free space of size O(n2α(n) log2n) can be computed in O(n2α(n) log2n) time. The dynamic motion planning problem is then solved in O(n2α(n) log3n) time. We also show that these results are close to optimal.

Geometric algorithms for trap design

Geometric algorithms have successfully been applied to solve or give insight into problems in robotic manipulation. In this paper, we present a framework to filter polygonal parts on a track. The filter consists of a polygonal hole in the track; we refer to the filters as trap’s. For an n-sided polygonal part and an m-sided polygonal trap, we give an O((nm.(n + m))‘+‘) algorithm to. decide whether the part in a specific orientation will safely move across the trap or will fall through the trap and thus be filtered out. Furthermore, we show how to design various parameterized traps, ranging from simple gaps to arbitrary polygons which will filter out all but one of the different stable orientations of a given part.

Geometric Trap Design for Automatic Part Feeders

Geometric algorithms have been applied successfully to solve or give insight into problems in robotic manipulation. In this paper, we present a framework to filter polygonal parts on a track. The filter consists of a polygonal hole in the track; we refer to the filters as traps.