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Anna YershovaDept. of Computer Science, Duke University
October 20, 2009
Anna YershovaAnna Yershova NIFP Workshop, Rice University
Sampling and Searching Methods inSampling and Searching Methods inRobotics and Computational BiologyRobotics and Computational BiologySampling and Searching Methods inSampling and Searching Methods inRobotics and Computational BiologyRobotics and Computational Biology
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Anna YershovaAnna Yershova
IntroductionIntroduction
Research ThemeResearch ThemeResearch ThemeResearch Theme
Underlying spaces in many real-world problems have similar geometric and topological structures. Ideas and methods used to solve these problems are shared across disciplines.
Examples: Configuration and state spaces in motion planning Information spaces in robotics Conformation spaces in structural computational biology
High-dimensional manifolds, or collections of manifolds
NIFP Workshop, Rice University
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Motion PlanningTechnical ContributionsTechnical Contributions
Contributions by TopicContributions by TopicContributions by TopicContributions by Topic
Anna YershovaAnna Yershova
Motion Planning• uniform deterministic sampling over configuration spacesuniform deterministic sampling over configuration spaces• efficient nearest-neighbor computations• guided sampling for efficient exploration
Planning Under Sensing Uncertainty• mapping and pursuit-evasion with a wall-following robot
Structural Computational Biology• exact protein structure determination from sparse NMR
data
NIFP Workshop, Rice University
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Sampling SpheresSampling SpheresSampling SpheresSampling Spheres
Anna YershovaAnna Yershova
Technical ContributionsTechnical Contributions Motion Planning
+ uniform
deterministic
+ incremental
grid structure
Ordering on faces +Ordering inside faces
Performance of many motion planning algorithms can be significantly improved using careful sampling over configuration spaces
NIFP Workshop, Rice University
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Sampling Sampling SOSO(3)(3)Sampling Sampling SOSO(3)(3)
Anna YershovaAnna Yershova
Technical ContributionsTechnical Contributions Motion Planning
Hopf coordinates preserve the fiber bundle structure of RP3
Locally, RP3 is a product of S1 and S2
Joint work with J.C.Mitchell
NIFP Workshop, Rice University
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OutcomesOutcomesOutcomesOutcomes
Anna YershovaAnna Yershova
Technical ContributionsTechnical Contributions Motion Planning
Publications:Publications: Generating Uniform Incremental Grids on SO(3) Using the Hopf Fibrations
(with S. Jain, S. M. LaValle and J.C. Mitchell)International Journal on Robotics Research (IJRR 2009), in press
Generating Uniform Incremental Grids on SO(3) Using the Hopf Fibrations(with S. M. LaValle and J. C. Mitchell)International Workshop on the Algorithmic Foundations of Robotics (WAFR 2008)
Deterministic sampling methods for spheres and SO(3) (with S. M. LaValle)IEEE International Conference on Robotics and Automation (ICRA 2004)
Incremental Grid Sampling Strategies in Robotics (with S. R. Lindemann, and S. M. LaValle)International Workshop on the Algorithmic Foundations of Robotics (WAFR 2004)
Open-source library:Open-source library: http://msl.cs.uiuc.edu/~yershova/sampling/sampling.tar.gz
NIFP Workshop, Rice University
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Motion PlanningTechnical ContributionsTechnical Contributions
Contributions by TopicContributions by TopicContributions by TopicContributions by Topic
Anna YershovaAnna Yershova
Motion Planning• uniform deterministic sampling over configuration spaces• efficient nearest-neighbor computationsefficient nearest-neighbor computations• guided sampling for efficient exploration
Planning Under Sensing Uncertainty• mapping and pursuit-evasion with a wall-following robot
Structural Computational Biology• exact protein structure determination from sparse NMR
data
NIFP Workshop, Rice University
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47
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5
1
3
2
9
8
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l5
l1 l9
l6
l3
l10 l7
l4
l8
l2
Technical ContributionsTechnical Contributions Motion Planning
Kd-trees with modified metricKd-trees with modified metricKd-trees with modified metricKd-trees with modified metric
Anna YershovaAnna Yershova
Main idea:
construction: unchanged procedure
query: modify metric between the query point and enclosing rectangles in the kd-tree
l1
l8
1
l2l3
l4 l5 l7 l6
l9l10
3
2 5 4 11
9 10
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6 7
[0,1]xS1
NIFP Workshop, Rice University
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Technical ContributionsTechnical Contributions Motion Planning
Anna YershovaAnna Yershova
Publications:Publications: Improving Motion Planning Algorithms by Efficient Nearest Neighbor Searching
(with S. M. LaValle)IEEE Transactions on Robotics 23(1):151-157, February 2007
Efficient Nearest Neighbor Searching for Motion Planning(with S. M. LaValle)In Proc. IEEE International Conference on Robotics and Automation (ICRA 2002)
Open-source library:Open-source library:
http://msl.cs.uiuc.edu/~yershova/mpnn/mpnn.tar.gz
Also implemented in Move3D at LAAS, and KineoWorksAlso implemented in Move3D at LAAS, and KineoWorksTMTM
OutcomesOutcomesOutcomesOutcomes
NIFP Workshop, Rice University
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Sensing Uncertainty in RoboticsTechnical ContributionsTechnical Contributions
Contributions by TopicContributions by TopicContributions by TopicContributions by Topic
Anna YershovaAnna Yershova
Motion Planning• uniform deterministic sampling over configuration spaces• efficient nearest-neighbor computations• guided sampling for efficient exploration
Planning Under Sensing Uncertainty• mapping and pursuit-evasion with a wall-following robotmapping and pursuit-evasion with a wall-following robot
Structural Computational Biology• exact protein structure determination from sparse NMR
data
NIFP Workshop, Rice University
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Technical ContributionsTechnical Contributions Sensing Uncertainty in Robotics
Planning in Information SpacesPlanning in Information SpacesPlanning in Information SpacesPlanning in Information Spaces
I-space: space of all cut diagrams of planar environments
Anna YershovaAnna Yershova NIFP Workshop, Rice University
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OutcomesOutcomesOutcomesOutcomesTechnical ContributionsTechnical Contributions Sensing Uncertainty in Robotics
Publications: Publications: Mapping and Pursuit-Evasion Strategies For a Simple Wall-Following Robot
(with B. Tovar, R. Ghrist, and S. M. LaValle)submitted to IEEE Transactions on Robotics, 2009
Extracting Visibility Information by Following Walls(with B. Tovar, and S. M. LaValle)In Dagstuhl Seminar Proceedings, 06421,Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI),Schloss Dagstuhl, Germany, 2007.
Information Spaces for Mobile Robots(with B. Tovar, J. M. O'Kane, and S. M. LaValle)invited paper at Fifth International Workshop on Robot Motion and Control (RoMoCo 2005)
Bitbots: Simple Robots Solving Complex Tasks(with B. Tovar, R. Ghrist, and S. M. LaValle)In Proc. The Twentieth National Conference on Artificial Intelligence (AAAI 2005)
Anna YershovaAnna Yershova NIFP Workshop, Rice University
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Structural Computational GeometryTechnical ContributionsTechnical Contributions
Contributions by TopicContributions by TopicContributions by TopicContributions by Topic
Motion Planning• uniform deterministic sampling over configuration spaces• efficient nearest-neighbor computations• guided sampling for efficient exploration
Planning Under Sensing Uncertainty• mapping and pursuit-evasion with a wall-following robot
Structural Computational Biology• exact protein structure determination from sparse exact protein structure determination from sparse
NMR dataNMR data
Anna YershovaAnna Yershova NIFP Workshop, Rice University
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Technical ContributionsTechnical Contributions Structural Computational Geometry
RDC Equations for a Protein PortionRDC Equations for a Protein PortionRDC Equations for a Protein PortionRDC Equations for a Protein Portion
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Anna YershovaAnna Yershova NIFP Workshop, Rice University
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Preliminary Results: 13dz helixPreliminary Results: 13dz helixPreliminary Results: 13dz helixPreliminary Results: 13dz helix
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Protein RMSD (Hz) Alignment Tensor (Syy, Szz)
Ubq :25-31
CH : 0.32
NH: 0.24
(23.66, 16.48)
(53.25, 7.65)
Conformation of the portion [25-31] of the helix for human ubiquitin computed using NH and CH RDCs in two media (red) has been superimposed on the same portion from high-resolution X-ray structure (PDB Id: 1UBQ) (green). The backbone RMSD is 0.58 Å.
-60
-40
-20
0
20
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-60 -40 -20 0 20 40 60
back-computed RDCs
exp
erim
enta
l RD
Cs
NH RDCs CH RDCs
Technical ContributionsTechnical Contributions Structural Computational Geometry
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OutcomesOutcomesOutcomesOutcomesTechnical ContributionsTechnical Contributions Structural Computational Geometry
Protein Structure Determination using Sparse Orientational Restraints from NMR Data (with C. Tripathy, P. Zhou, B. R. Donald)Biochemistry Department Retreat, NC Biotechnology Center, RTP, NC, 2009.Winner of Best Poster Award.
Anna YershovaAnna Yershova NIFP Workshop, Rice University
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Apply and extend the mathematical tools needed for solving problems in
Robotics Algebraic varieties Trajectories
Computational Biology Other NMR data Other imaging techniques
potentially other disciplines
Technology transfer between disciplines
ConclusionsConclusions
Conclusions and Future GoalsConclusions and Future GoalsConclusions and Future GoalsConclusions and Future Goals
Anna YershovaAnna Yershova NIFP Workshop, Rice University
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ConclusionsConclusions
Conclusions and Future DirectionsConclusions and Future DirectionsConclusions and Future DirectionsConclusions and Future Directions
Thank you!
Anna YershovaAnna Yershova NIFP Workshop, Rice University
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Motion PlanningTechnical ContributionsTechnical Contributions
Contributions by TopicContributions by TopicContributions by TopicContributions by Topic
Anna YershovaAnna Yershova
Motion Planning• uniform deterministic sampling over configuration spaces• efficient nearest-neighbor computations• guided sampling for efficient explorationguided sampling for efficient exploration
Planning Under Sensing Uncertainty• mapping and pursuit-evasion with a wall-following robot
Structural Computational Biology• exact protein structure determination from sparse NMR
data
NIFP Workshop, Rice University
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Technical ContributionsTechnical Contributions Motion Planning
KD-Tree-Based Dynamic DomainKD-Tree-Based Dynamic DomainKD-Tree-Based Dynamic DomainKD-Tree-Based Dynamic Domain
Anna YershovaAnna Yershova NIFP Workshop, Rice University
Courtesy of Kineo CAM330 degrees of
freedom
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OutcomesOutcomesOutcomesOutcomes
Anna YershovaAnna Yershova
Technical ContributionsTechnical Contributions Motion Planning
Publications:Publications: Adaptive Tuning of the Sampling Domain for Dynamic-Domain RRTs
(with L. Jaillet, S. M. LaValle and T. Simeon)In Proc. IEEE International Conference on Intelligent Robots and Systems (IROS 2005)
Dynamic-Domain RRTs: Efficient Exploration by Controlling the Sampling Domain (with L. Jaillet, T. Simeon, and S. M. LaValle)In Proc. IEEE International Conference on Robotics and Automation (ICRA 2005)
Also implemented in Also implemented in Move3D at LAAS KineoWorksTM
Toyota Corporation
NIFP Workshop, Rice University
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