## Part Pose Statistics: Estimators and Experiments (1999)

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Venue: | IEEE TRANS. ON ROBOTICS AND AUTOMATION |

Citations: | 14 - 2 self |

### BibTeX

@ARTICLE{Goldberg99partpose,

author = {Ken Goldberg and Brian Mirtich and Yan Zhuang and John Craig and Brian Carlisle and John Canny},

title = {Part Pose Statistics: Estimators and Experiments},

journal = {IEEE TRANS. ON ROBOTICS AND AUTOMATION},

year = {1999},

volume = {15}

}

### OpenURL

### Abstract

Many of the most fundamental examples in probability involve the pose statistics of coins and dice as they are dropped on a flat surface. For these parts, the probability assigned to each stable face is justified based on part symmetry, although most gamblers are familiar with the possibility of loaded dice. Our goal is to develop a science base for part feeding, where parts arrive in random orientations. We consider the following problem: given part geometry and parameters such as center of mass, estimate the probability of encountering each stable pose of the part. We describe

### Citations

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Citation Context ... of the biggest obstacles to automated manufacturing. One of the earliest systematic efforts to model part feeding was Erdmann and Mason’s analysis of the mechanics of a part moving in a tilting tray =-=[14]-=-. This was followed by a number of efforts to rigorously model mechanics and uncertainty [2], [7], [8], [15], [21]. A closely related example is Peshkin and Sanderson’s study of feeding parts on a con... |

164 |
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Citation Context ...cumulative normal distribution function. For example, to pinpoint the probability of a particular final pose to within 5%, with 90% certainty, 0.05 and 0.10. From (17), 385 trials are sufficient. See =-=[13]-=- for more information. The perturbed quasistatic estimator’s predictions are consistently more accurate than those of the quasistatic estimator, and the added computation time is negligible. Hence, th... |

142 | Impulse-based Simulation of Rigid Bodies - Mirtich, Canny - 1995 |

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Citation Context ...static estimator that incorporates a model of dynamic stability. We then introduce a third estimator based on repeated Monte Carlo simulation experiments using Impulse, a mechanics simulation package =-=[26]-=-–[28]. We discuss impulsebased simulation, a paradigm for efficient simulation, and present its model for frictional collisions. To evaluate these estimators, we used the robot and computer vision sys... |

110 |
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Citation Context ...ems prohibitive for two reasons. First, the interaction between the part and environment is very collision intensive, and it is notoriously difficult to model the dynamics of collisions with friction =-=[22]-=-. Second, dynamic simulation is much slower than the previous described estimators, and so obtaining a statistically significant number of trials may take too long. Mirtich and Canny have studied impu... |

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Citation Context ...l mechanics and uncertainty [2], [7], [8], [15], [21]. A closely related example is Peshkin and Sanderson’s study of feeding parts on a conveyor belt as they move against a sequence of passive fences =-=[31]-=-; this model was extended in a sequence of papers [1], [4], [37]. A variety of sensor-based (robotic) alternatives to mechanical bowl feeders have been proposed. For example, [23] propose an optical s... |

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Citation Context ...uires significantly more computation time. This paper is a revised and updated version of [25]. II. RELATED WORK An excellent introduction to mechanical parts feeders can be found in Boothroyd’s book =-=[6]-=-, which describes vibratory bowl feeders in detail as well as nonvibratory feeders such as the magnetic and revolving hook feeders. Sony introduced a novel approach using random motion of parts over p... |

75 | A complete algorithm for designing passive fences to orient parts
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Citation Context ... related example is Peshkin and Sanderson’s study of feeding parts on a conveyor belt as they move against a sequence of passive fences [31]; this model was extended in a sequence of papers [1], [4], =-=[37]-=-. A variety of sensor-based (robotic) alternatives to mechanical bowl feeders have been proposed. For example, [23] propose an optical silhouette sensor with air nozzle to reject all but the desired p... |

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Citation Context ...or Impulse has the fastest execution times reported in the literature [28]. A. Computing Frictional Collisions Details about Impulse, and a comparison of constraintand impulse-based simulation are in =-=[27]-=-, [28]. In the latter paradigm, all interactions between simulated bodies are affected through frictional collisions, thus a good collision model is crucial to physical accuracy. Our model is similar ... |

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Citation Context ...del part feeding was Erdmann and Mason’s analysis of the mechanics of a part moving in a tilting tray [14]. This was followed by a number of efforts to rigorously model mechanics and uncertainty [2], =-=[7]-=-, [8], [15], [21]. A closely related example is Peshkin and Sanderson’s study of feeding parts on a conveyor belt as they move against a sequence of passive fences [31]; this model was extended in a s... |

45 | Designing parts feeders using dynamic simulation
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Citation Context ...d arm cycle time. Similar feeder designs are described in [10], [39]. To facilitate the design of parts feeders, researchers have considered configuration space models [2], [7], [8], [14], simulation =-=[3]-=-, [17], [24], heuristics [20], and genetic algorithms [11]. The latter paper made use of our preliminary results in estimating pose statistics. III. THE QUASI-STATIC ESTIMATOR In our first model, we i... |

41 | The mechanics of fine manipulation by pushing
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Citation Context ... was Erdmann and Mason’s analysis of the mechanics of a part moving in a tilting tray [14]. This was followed by a number of efforts to rigorously model mechanics and uncertainty [2], [7], [8], [15], =-=[21]-=-. A closely related example is Peshkin and Sanderson’s study of feeding parts on a conveyor belt as they move against a sequence of passive fences [31]; this model was extended in a sequence of papers... |

34 |
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Citation Context ...art feeding was Erdmann and Mason’s analysis of the mechanics of a part moving in a tilting tray [14]. This was followed by a number of efforts to rigorously model mechanics and uncertainty [2], [7], =-=[8]-=-, [15], [21]. A closely related example is Peshkin and Sanderson’s study of feeding parts on a conveyor belt as they move against a sequence of passive fences [31]; this model was extended in a sequen... |

34 | Stochastic Plans for Robotic Manipulation
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Citation Context ...eeding was Erdmann and Mason’s analysis of the mechanics of a part moving in a tilting tray [14]. This was followed by a number of efforts to rigorously model mechanics and uncertainty [2], [7], [8], =-=[15]-=-, [21]. A closely related example is Peshkin and Sanderson’s study of feeding parts on a conveyor belt as they move against a sequence of passive fences [31]; this model was extended in a sequence of ... |

31 |
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Citation Context ...el is crucial to physical accuracy. Our model is similar to that of Routh [33], although we derive equations which are more amenable to numerical integration. Keller also gives an excellent treatment =-=[18]-=-, and Bhatt and Koechling give a classification of frictional collisions, based on the flow patterns of tangential contact velocity [5]. Finally, Wang and Mason have studied two-dimensional (2-D) impa... |

24 |
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Citation Context ...llisions, based on the flow patterns of tangential contact velocity [5]. Finally, Wang and Mason have studied two-dimensional (2-D) impact dynamics for robotic applications, based on Routh’s approach =-=[36]-=-. Consider two rigid bodies coming into contact as shown in Fig. 6. Each body has a known mass inertia tensor linear center of mass velocity and an angular velocity If is the offset vector of the cont... |

23 | Estimating pose statistics for robotic part feeders
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(Show Context)
Citation Context ...ulation system described in [12]). We find that dynamic simulation provides the most accurate results, but requires significantly more computation time. This paper is a revised and updated version of =-=[25]-=-. II. RELATED WORK An excellent introduction to mechanical parts feeders can be found in Boothroyd’s book [6], which describes vibratory bowl feeders in detail as well as nonvibratory feeders such as ... |

23 |
Automated design of parts feeders using a genetic algorithm
- Christiansen, Edwards, et al.
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(Show Context)
Citation Context ... [10], [39]. To facilitate the design of parts feeders, researchers have considered configuration space models [2], [7], [8], [14], simulation [3], [17], [24], heuristics [20], and genetic algorithms =-=[11]-=-. The latter paper made use of our preliminary results in estimating pose statistics. III. THE QUASI-STATIC ESTIMATOR In our first model, we ignore part inertia and velocity, treating part motion as q... |

21 |
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Citation Context ...ratory bowl feeders in detail as well as nonvibratory feeders such as the magnetic and revolving hook feeders. Sony introduced a novel approach using random motion of parts over part-specific pallets =-=[29]-=-, [35]. Although there is a substantial body of research in feeder design, practitioners still rely on instinct and rules-of-thumb [20]. Part feeders are responsible for up to 30% of the cost 1042–296... |

19 | Computing a statistical distribution of stable poses for a polyhedron
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Citation Context ...of poses, onto a flat worksurface. Estimate We consider three estimators for solving this problem for polyhedral parts. We start with an estimate based on a quasistatic motion model first reported in =-=[38]-=-. Next we describe a perturbed quasistatic estimator that incorporates a model of dynamic stability. We then introduce a third estimator based on repeated Monte Carlo simulation experiments using Impu... |

18 | Complete algorithms for feeding polyhedral parts using pivot grasps
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Citation Context ... ON ROBOTICS AND AUTOMATION, VOL. 15, NO. 5, OCTOBER 1999 flexible feeder; assuming part pose is known, they give an algorithm to generate pivot grasps for a part with faces and stable configurations =-=[32]-=-. The perturbed quasistatic estimator described in this paper has been incorporated into a commercial simulation package where it is used to predict part behavior for rapid design of modular workcells... |

17 |
Planar manipulation on a conveyor by a one joint robot with and without sensing
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(Show Context)
Citation Context ... A closely related example is Peshkin and Sanderson’s study of feeding parts on a conveyor belt as they move against a sequence of passive fences [31]; this model was extended in a sequence of papers =-=[1]-=-, [4], [37]. A variety of sensor-based (robotic) alternatives to mechanical bowl feeders have been proposed. For example, [23] propose an optical silhouette sensor with air nozzle to reject all but th... |

16 | A pivoting gripper for feeding industrial parts
- Carlisle, Goldberg, et al.
- 1994
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Citation Context ...ternatives to mechanical bowl feeders have been proposed. For example, [23] propose an optical silhouette sensor with air nozzle to reject all but the desired pose on a feeder track. Carlisle et. al. =-=[9]-=- proposed a flexible part feeding system that combines machine vision with a high-speed robot arm. In contrast to customdesigned hardware such as the bowl feeder, only software is changed when a new p... |

15 |
Models and algorithms for the collision of rigid and deformable bodies
- Deguet, Joukhadar, et al.
- 1998
(Show Context)
Citation Context ...n each trial the system determined the part’s final orientation. We compare this data to the results from each estimator. (Our data was also used as a benchmark for the simulation system described in =-=[12]-=-). We find that dynamic simulation provides the most accurate results, but requires significantly more computation time. This paper is a revised and updated version of [25]. II. RELATED WORK An excell... |

14 |
Elementary Rigid Dynamics
- Routh
- 1905
(Show Context)
Citation Context ...tter paradigm, all interactions between simulated bodies are affected through frictional collisions, thus a good collision model is crucial to physical accuracy. Our model is similar to that of Routh =-=[33]-=-, although we derive equations which are more amenable to numerical integration. Keller also gives an excellent treatment [18], and Bhatt and Koechling give a classification of frictional collisions, ... |

13 |
Designing Assemblies
- Whitney
- 1999
(Show Context)
Citation Context ...s was reported in [19] but tested only with rectangular parts. Fig. 1. Flexible parts feeding workcell using machine vision, a high-speed robot arm, and pivoting gripper. and 50% of workcell failures =-=[30]-=-, [6]. Thus systematic feeder design remains one of the biggest obstacles to automated manufacturing. One of the earliest systematic efforts to model part feeding was Erdmann and Mason’s analysis of t... |

12 | Parts entropy methods for robotic assembly system design
- Sanderson
- 1984
(Show Context)
Citation Context ...a parts feeder is based on pose statistics [6]. He gave a quasistatic estimator for rectangular and cylindrical parts. Sanderson showed that robot assembly can be analyzed in terms of pose statistics =-=[34]-=-. Reference [38] improved on the Boothroyd estimator by treating the convex hull of any polyhedral part and propagating probability from unstable faces. The resulting estimate is a good first approxim... |

11 | Coello Coello. Automated design of parts feeders using a genetic algorithm - Christiansen, Edwards, et al. - 1996 |

11 |
A computer-aided framework for the selection and sequencing of orientating devices for the vibratory bowl feeder,” Int
- Lim, Ngoi, et al.
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(Show Context)
Citation Context ...approach using random motion of parts over part-specific pallets [29], [35]. Although there is a substantial body of research in feeder design, practitioners still rely on instinct and rules-of-thumb =-=[20]-=-. Part feeders are responsible for up to 30% of the cost 1042–296X/99$10.00 © 1999 IEEE850 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 15, NO. 5, OCTOBER 1999 Boothroyd noted that the feedrate... |

11 |
A systems model and simulation of the vibratory bowl feeder
- Maul, Thomas
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Citation Context ... time. Similar feeder designs are described in [10], [39]. To facilitate the design of parts feeders, researchers have considered configuration space models [2], [7], [8], [14], simulation [3], [17], =-=[24]-=-, heuristics [20], and genetic algorithms [11]. The latter paper made use of our preliminary results in estimating pose statistics. III. THE QUASI-STATIC ESTIMATOR In our first model, we ignore part i... |

10 |
Computer simulation of vibratory parts feeding and assembly
- Jakiela, Krishnasamy
- 1993
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Citation Context ... cycle time. Similar feeder designs are described in [10], [39]. To facilitate the design of parts feeders, researchers have considered configuration space models [2], [7], [8], [14], simulation [3], =-=[17]-=-, [24], heuristics [20], and genetic algorithms [11]. The latter paper made use of our preliminary results in estimating pose statistics. III. THE QUASI-STATIC ESTIMATOR In our first model, we ignore ... |

7 |
An open-loop planner for posing polygonal objects in the plane by pushing
- Akella, Mason
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(Show Context)
Citation Context ...to model part feeding was Erdmann and Mason’s analysis of the mechanics of a part moving in a tilting tray [14]. This was followed by a number of efforts to rigorously model mechanics and uncertainty =-=[2]-=-, [7], [8], [15], [21]. A closely related example is Peshkin and Sanderson’s study of feeding parts on a conveyor belt as they move against a sequence of passive fences [31]; this model was extended i... |

7 |
Design of a flexible parts feeding system
- Causey, Quinn
- 1997
(Show Context)
Citation Context ...rated in Fig. 1. A recent paper [16] outlines how feeder throughput can be estimated based on estimates of pose statistics, conveyor speed, and arm cycle time. Similar feeder designs are described in =-=[10]-=-, [39]. To facilitate the design of parts feeders, researchers have considered configuration space models [2], [7], [8], [14], simulation [3], [17], [24], heuristics [20], and genetic algorithms [11].... |

5 |
Classifying dynamic behavior during threedimensional frictional rigid body impact
- Bhatt, Koechling
- 1994
(Show Context)
Citation Context ...numerical integration. Keller also gives an excellent treatment [18], and Bhatt and Koechling give a classification of frictional collisions, based on the flow patterns of tangential contact velocity =-=[5]-=-. Finally, Wang and Mason have studied two-dimensional (2-D) impact dynamics for robotic applications, based on Routh’s approach [36]. Consider two rigid bodies coming into contact as shown in Fig. 6.... |

5 |
Sensor-based solution to contiguous and overlapping parts in vibratory bowl feeders
- Maul, Jaksic
- 1994
(Show Context)
Citation Context ...ce of passive fences [31]; this model was extended in a sequence of papers [1], [4], [37]. A variety of sensor-based (robotic) alternatives to mechanical bowl feeders have been proposed. For example, =-=[23]-=- propose an optical silhouette sensor with air nozzle to reject all but the desired pose on a feeder track. Carlisle et. al. [9] proposed a flexible part feeding system that combines machine vision wi... |

3 | Analyzing the probabilities of natural resting for a component with a virtual resting face - Ngoi, Lim, et al. - 1995 |

2 |
On fence design and the complexity of push plans for orienting parts
- Berrety, Overmars, et al.
- 1997
(Show Context)
Citation Context ...osely related example is Peshkin and Sanderson’s study of feeding parts on a conveyor belt as they move against a sequence of passive fences [31]; this model was extended in a sequence of papers [1], =-=[4]-=-, [37]. A variety of sensor-based (robotic) alternatives to mechanical bowl feeders have been proposed. For example, [23] propose an optical silhouette sensor with air nozzle to reject all but the des... |

2 |
Estimating and optimizing throughput of a robotic part feeder using queueing theory
- Gudmundsson, Goldberg
- 1998
(Show Context)
Citation Context ... system determines the position and orientation of each part. The robot arm then picks up each part and moves it into a desired final position and orientation as illustrated in Fig. 1. A recent paper =-=[16]-=- outlines how feeder throughput can be estimated based on estimates of pose statistics, conveyor speed, and arm cycle time. Similar feeder designs are described in [10], [39]. To facilitate the design... |

2 |
Designing a parts feeding system for maximum flexibility
- Wolfson, Gordon
- 1997
(Show Context)
Citation Context ...in Fig. 1. A recent paper [16] outlines how feeder throughput can be estimated based on estimates of pose statistics, conveyor speed, and arm cycle time. Similar feeder designs are described in [10], =-=[39]-=-. To facilitate the design of parts feeders, researchers have considered configuration space models [2], [7], [8], [14], simulation [3], [17], [24], heuristics [20], and genetic algorithms [11]. The l... |

2 |
simulation of rigid bodies
- “Impulse-based
- 1995
(Show Context)
Citation Context ...c estimator that incorporates a model of dynamic stability. We then introduce a third estimator based on repeated Monte Carlo simulation experiments using Impulse, a mechanics simulation package [26]–=-=[28]-=-. We discuss impulsebased simulation, a paradigm for efficient simulation, and present its model for frictional collisions. To evaluate these estimators, we used the robot and computer vision system s... |

1 |
Parts supply in sony’s general purpose assembly system
- Shirai, Saito
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(Show Context)
Citation Context ... bowl feeders in detail as well as nonvibratory feeders such as the magnetic and revolving hook feeders. Sony introduced a novel approach using random motion of parts over part-specific pallets [29], =-=[35]-=-. Although there is a substantial body of research in feeder design, practitioners still rely on instinct and rules-of-thumb [20]. Part feeders are responsible for up to 30% of the cost 1042–296X/99$1... |

1 |
Determining the probabilities of natural resting aspects of parts from their geometries
- Lee, Ngoi, et al.
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(Show Context)
Citation Context ...xperimental distributions but do not take into account effects such as bouncing, vibrations, collisions, and friction. An estimator based on face area and height of the center of mass was reported in =-=[19]-=- but tested only with rectangular parts. Fig. 1. Flexible parts feeding workcell using machine vision, a high-speed robot arm, and pivoting gripper. and 50% of workcell failures [30], [6]. Thus system... |