Computing fence designs for orienting parts

Abstract

A common task in automated manufacturing processes is to orient parts prior to assembly. W e 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. 17 , and present the rst polynomial-time algorithm to compute the shortest such sequence. The algorithm is easy to implement and runs in time On 3 log n, where n is the numb e r o f v ertices of the part. 1 Introduction 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 a uniform orientation. Part feeders often use data obtained from some kind of sensing device to accomplish their task. We consider the problem of sensorless orientation of parts, in which the initial pose of the part is assumed to be unknown. In sensorless manipulation, parts are positioned and or oriented using passive mechanical compliance. The input is a description of the part shape and the output is a sequence of open-loop actions that moves a part from an unknown initial pose into a unique nal pose. Among the sensorless part feeders considered in literature are the parallel-jaw gripper 6, 9 , a single pushing jaw 2, 10, 11, 13 , a conveyor belt with a sequence of stationary fences placed along its sides 5, 14, 17 , a conveyor belt with a single rotational fence 1JOC 1 , a tilting tray 8, 12 , and vibratory plates and programmable vector elds 3, 4. The pushing jaw 2 , 1 0 , 11, 13 orients a part by an alternating sequence of pushes and jaw reorientations. The problem of sensorless orientation by a pushing jaw is to nd a sequence of push directions that will move the part from an arbitrary initial orientation into a single known nal orientation. Such a sequence is referred to as a push plan. Goldberg 9 showed that any polygonal part can be oriented by a sequence of pushes. Chen and Ierardi 6 proved that any polygonal part with n vertices can be oriented by On pushes. They showed that this bound is tight b y constructing pathological n-gons that require n pushes to be oriented. Goldberg gave an algorithm for computing the shortest push plan for a polygon. His algorithm runs in On 2 time.

Abstractions and Algorithms for Cooperative Multiple Robot Planar Manipulation

“…We consider the uncertainties in the three support points, robot velocity magnitude, and friction coefficients that are chosen from three bounded continuous sets. We first generate a finite set of three support point samples, [4]) and rotational ( [5], [6]) motion primitives velocity samples, and friction coefficient samples, and then use the procedure in (2) to check whether Φ is satisfied for all these samples. If true, the manipulation is identified as robust; otherwise, it is non robust.…”

“…5 [5][6]: The reachable set under this pushing is also bounded by analyzing the potential contact model switching patterns.…”

“…2) [13], and part-feeding [29] have shown that feedback controllers, behaviors or designs, which are specially designed to preserve a specific set of properties (e.g., convergence to sub manifolds or limit sets), are more robust to uncertainties than those that follow optimally-planned trajectories in the full state space. Indeed, this philosophy of designing components that each drive the system to a state that satisfies a specific property is used extensively in manufacturing operations, where designers carefully structure the environment to ensure that devices like bowl-feeders [14], conveyors [1], traps [5], and pick-andplace arms work in concert to accomplish the given task. Many paradigms in robotics such as caging [7], the onejoint-over-conveyor part positioning [1], and remote-centerof-compliance assembly [12] are also illustrative of this philosophy.…”

Trap design for vibratory bowl feeders

“…The input is a description of the part shape and the output is a sequence of open-loop actions that moves a part from an unknown initial orientation into a unique final orientation. Among the sensorless part feeders considered in literature are the parallel-jaw gripper [17,21], the single pushing jaw [2,27,28,32], the conveyor belt with a sequence of (stationary) fences placed along its sides [10,14,33,36], the conveyor belt with a single rotational fence [1], the tilting tray [20,31], vibratory plates and programmable vector fields [11].…”

Orienting parts by inside-out pulling

“…The input is a description of the part shape and the output is a sequence of openloop actions that moves a part from an unknown initial orientation into a unique final orientation. Among the sensorless part feeders considered in literature are the parallel-jaw gripper [8,11], the single pushing jaw [2,13,14,16], the conveyor belt with a sequence of (stationary) fences placed along its sides [4,17,19], the conveyor belt with a single rotational fence (1JOC) [1], the conveyor belt with pins at various heights above the surface [12,20], the tilting tray [10,15], bowl feeders [6], vibratory plates and programmable vector fields [5].…”