Amorphous Robotic Construction
Nils Napp
nnapp@buffalo.edu
November 11th 2014
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Robots Building Stuff
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Robotic Construction in Messy Environments
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Related Work
Petersen, Werfel, Nagpal 2011
Rus, Lipson, Yim
Khoshnevis 2004
Lindsey, Mellinger, Kumar 2010
D’Andrea 2010
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Biological Inspiration
K. Petersen, N. Napp, J. Chin-Lee, J. Werfel and R. Nagpal, 3D Tracking of Building Processes in
Macrotermes , Visual Observation and Analysis of Animal and Insect Behavior, Workshop (ICPR), 2012.
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Biological Inspiration
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Outline
• Algorithm Design
– Adaptive Ramp Building Problem
– World and Material Model
– Navigable Structures
– Ramp Building Algorithm(s)
• Experiments
– Working in 3D
– Deposition Experiments
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Adaptive Ramp Building
Develop algorithms and robots to build
in unstructured environments
N. Napp, J. M. Wu, O. R. Rappoli, and R. Nagpal, Materials and Mechanisms for Amorphous Robotic Construction. IROS 12
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Algorithmic Challenges
1. Modeling Amorphous Depositions
2. Planning with Amorphous Depositions
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Outline
• Algorithm Design
– Adaptive Ramp Building Problem
– World and Material Model
– Navigable Structures
– Ramp Building Algorithm(s)
• Experiments
– Working in 3D
– Deposition Experiments
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Modeling Structures
: finite building area
: robot position
: height function
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Modeling Structures
: finite building area
: robot position
: height function
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Modeling Amorphous Depositions
• Shape defined by the environment
• Conforming on bottom
• Top defined by shape function:
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Modeling Amorphous Depositions
Deposition operator
INPUT: shape function and height function
OUTPUT: new height function
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Outline
• Algorithm Design
– Adaptive Ramp Building Problem
– World and Material Model
– Navigable Structures
– Ramp Building Algorithm(s)
• Experiments
– Working in 3D
– Deposition Experiments
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Maximum Climbable Steepness
A function
is called K-Lipschitz iff
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Navigable: Almost, Locally, Lipschitz
A function
is called navigable iff
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Navigable: Almost, Locally, Lipschitz
A function
is called navigable iff
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Navigable: Almost, Locally, Lipschitz
A function
is called navigable iff
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Navigable: Almost, Locally, Lipschitz
A function
is called navigable iff
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Outline
• Algorithm Design
– Adaptive Ramp Building Problem
– World and Material Model
– Navigable Structures
– Ramp Building Algorithm(s)
• Experiments
– Working in 3D
– Deposition Experiments
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Local Reactive Algorithm for Making
Navigable Structures
Algorithm 1
1.
2.
3.
4.
5.
6.
7.
8.
Given
Set
While
violating the navigability condition
Set to be point with lower h value (wlog assume
)
Pick deposition height
Deposit at
:
Set
EndWhile
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Local Reactive Algorithm for Making
Navigable Structures
Algorithm 1
1.
2.
3.
4.
5.
6.
7.
8.
Given
Set
While
violating the navigability condition
Set to be point with lower h value (wlog assume
)
Pick deposition height
Deposit at
:
Set
EndWhile
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Stopping for Algorithm 1
Bounded above
Guaranteed progress
Depositions never add material
above
.
Each deposition has a minimum
Volume.
Proof based on point selection,
Proof based on point selection,
and the inequalities
and deposition steepness
continuity assumptions on
and
.
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Adaptive Ramp Building (Alg 2)
Algorithm 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
Given
and navigable terrain around v .
Set
While
Move until
are non-navigable or
If
Move to lower point and deposit according to Alg. 1
Move backward to
EndIf
EndWhile
Proof based on termination of Alg.1 and backing up from
depositions that might have altered previously navigable terrain.
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Adaptive Ramp Building
Start
426 Steps
N. Napp and R. Nagpal, Distributed Amorphous Ramp Construction in Unstructured Environments . DARS 2012
Goal
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Outline
• Algorithm Design
– Adaptive Ramp Building Problem
– World and Material Model
– Navigable Structures
– Ramp Building Algorithm(s)
• Experiments
– Working in 3D
– Deposition Experiments
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Using Algorithm 2 in 3D
Leveling Mechanism
Level Deposition with
Conical Cross Section
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Experiment: Messy Leveling
Translating Carriage
Mixing Nozzle
Distance Sensor
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Experiment: Messy Leveling
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Foam Depositing Robot
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Robot Depositing Foam
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Foam Ramp
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5
4
3
2
1
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Summary
• Amorphous building materials can enable
robust construction in irregular terrain
• Model terrain with continuous functions
• Bound shape uncertainty with shape functions
Future Work
Construction in Cluttered Terrain
• Use models to build other structures
• Reliable construction with found objects
• Extend to probabilistic setting
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At UB
• Teaching CSE 668: Advanced Robotics
– Spring 2015 (MWF 12:00pm)
– Previously called (Animate Vision Principles)
• Looking for Students
– Take my class/work on a project with me
– E-mail: nnapp@buffalo.edu
– Office hours: Tue/Thur 10:00-11:00am
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