Anna Yershova Dept. of Computer Science, Duke University October 20, 2009

1

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

X

ksfhjdsf

2

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

3

Motion PlanningTechnical ContributionsTechnical Contributions

Contributions by TopicContributions by TopicContributions by TopicContributions by Topic


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


4

Sampling SpheresSampling SpheresSampling SpheresSampling Spheres


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


5

Sampling Sampling SOSO(3)(3)Sampling Sampling SOSO(3)(3)



Hopf coordinates preserve the fiber bundle structure of RP3

Locally, RP3 is a product of S1 and S2

Joint work with J.C.Mitchell


6

OutcomesOutcomesOutcomesOutcomes



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


7




Motion Planning• uniform deterministic sampling over configuration spaces• efficient nearest-neighbor computationsefficient nearest-neighbor computations• guided sampling for efficient exploration



data


8

47

6

5

1

3

2

9

8

10

11

l5

l1 l9

l6

l3

l10 l7

l4

l8

l2


Kd-trees with modified metricKd-trees with modified metricKd-trees with modified metricKd-trees with modified metric


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

8

6 7

[0,1]xS1


9



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



10

Sensing Uncertainty in RoboticsTechnical ContributionsTechnical Contributions



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


data


11

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


12

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)


13

Structural Computational GeometryTechnical ContributionsTechnical Contributions


Motion Planning• uniform deterministic sampling over configuration spaces• efficient nearest-neighbor computations• guided sampling for efficient exploration


Structural Computational Biology• exact protein structure determination from sparse exact protein structure determination from sparse

NMR dataNMR data


14

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

14


15

Preliminary Results: 13dz helixPreliminary Results: 13dz helixPreliminary Results: 13dz helixPreliminary Results: 13dz helix

15

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

40

60

-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

16

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.


17

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


18

ConclusionsConclusions

Conclusions and Future DirectionsConclusions and Future DirectionsConclusions and Future DirectionsConclusions and Future Directions

Thank you!


19




Motion Planning• uniform deterministic sampling over configuration spaces• efficient nearest-neighbor computations• guided sampling for efficient explorationguided sampling for efficient exploration



data


20


KD-Tree-Based Dynamic DomainKD-Tree-Based Dynamic DomainKD-Tree-Based Dynamic DomainKD-Tree-Based Dynamic Domain


Courtesy of Kineo CAM330 degrees of

freedom

21




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


Documents

Anna Yershova Dept. of Computer Science, Duke University October 20, 2009