1. 1 Anna Yershova Dept. of Computer Science, Duke University October 20, 2009 Anna Yershova NIFP Workshop, Rice University Sampling and Searching Methods in Robotics and Computational Biology

2. 2 Anna Yershova Introduction Research 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. 3 Motion Planning Technical Contributions Contributions by Topic Anna Yershova Motion Planning uniform deterministic sampling over configuration spaces 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 NMR data NIFP Workshop, Rice University

4. 4 Sampling Spheres Anna Yershova Technical 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

5. 5 Sampling SO(3) Anna Yershova Technical Contributions Motion Planning Hopf coordinates preserve the fiber bundle structure of RP 3 Locally, RP 3 is a product of S 1 and S 2 Joint work with J.C.Mitchell NIFP Workshop, Rice University

6. 6 OutcomesOutcomes Anna Yershova Technical Contributions Motion PlanningPublications: 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: http://msl.cs.uiuc.edu/~yershova/sampling/sampling.tar.gz NIFP Workshop, Rice University

7. 7 Motion Planning Technical Contributions Contributions by Topic Anna Yershova Motion Planning uniform deterministic sampling over configuration spaces efficient nearest-neighbor computations 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

8. 8 4 7 6 5 1 3 2 9 8 10 11 l5l5 l1l1 l9l9 l6l6 l3l3 l 10 l7l7 l4l4 l8l8 l2l2 Technical Contributions Motion Planning Kd-trees with modified metric Anna Yershova Main idea: construction: unchanged procedure query: modify metric between the query point and enclosing rectangles in the kd-tree l1l1 l8l8 1 l2l2 l3l3 l4l4 l5l5 l7l7 l6l6 l9l9 l 10 3 25411 910 8 67 [0,1]xS 1 NIFP Workshop, Rice University

9. 9 Technical Contributions Motion Planning Anna Yershova 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: http://msl.cs.uiuc.edu/~yershova/mpnn/mpnn.tar.gz Also implemented in Move3D at LAAS, and KineoWorks TM OutcomesOutcomes NIFP Workshop, Rice University

10. 10 Sensing Uncertainty in Robotics Technical Contributions Contributions by Topic Anna 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 robot mapping and pursuit-evasion with a wall-following robot Structural Computational Biology exact protein structure determination from sparse NMR data NIFP Workshop, Rice University

11. 11 Technical Contributions Sensing Uncertainty in Robotics Planning in Information Spaces I-space: space of all cut diagrams of planar environments Anna Yershova NIFP Workshop, Rice University

12. 12 OutcomesOutcomes Technical Contributions Sensing Uncertainty in RoboticsPublications: 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 Yershova NIFP Workshop, Rice University

13. 13 Structural Computational Geometry Technical Contributions Contributions 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 NMR data exact protein structure determination from sparse NMR data Anna Yershova NIFP Workshop, Rice University

14. 14 Technical Contributions Structural Computational Geometry RDC Equations for a Protein Portion 14 Anna Yershova NIFP Workshop, Rice University

15. 15 Preliminary Results: 13dz helix 15 ProteinRMSD (Hz)Alignment Tensor (S yy, S zz ) Ubq  :25-31 C  H  : 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. Technical Contributions Structural Computational Geometry

16. 16 OutcomesOutcomes Technical 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 Yershova NIFP Workshop, Rice University

17. 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 disciplinesConclusions Conclusions and Future Goals Anna Yershova NIFP Workshop, Rice University

18. 18Conclusions Conclusions and Future Directions Thank you! Anna Yershova NIFP Workshop, Rice University

19. 19 Motion Planning Technical Contributions Contributions by Topic Anna Yershova Motion Planning uniform deterministic sampling over configuration spaces efficient nearest-neighbor computations guided sampling for efficient exploration 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

20. 20 Technical Contributions Motion Planning KD-Tree-Based Dynamic Domain Anna Yershova NIFP Workshop, Rice University Courtesy of Kineo CAM 330 degrees of freedom

21. 21 OutcomesOutcomes Anna Yershova Technical Contributions Motion PlanningPublications: 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 Move3D at LAAS KineoWorks TM Toyota Corporation NIFP Workshop, Rice University