Personal Wiki of Subhrajit Bhattacharya

In this project we investigate certain equivalence classes (mainly homology and homotopy) of sub-manifolds of Euclidean spaces punctured by arbitrary-shaped obstacles, and ways of computing invariants for them. We also investigate its application in robot path planning with topological constraints.

Publications

1. Shunsaku Yadokoro and Subhrajit Bhattacharya, "Weighted Combinatorial Laplacian and its Application to Coverage Repair in Sensor Networks",, 2024. arXiv:2312.04825 [cs.RO]. (BibTeX)
   
   [  Electronic pre-print on arXiv.org  ]
2. Mohammad Saleh Teymouri and Subhrajit Bhattacharya, "Landmark-based distributed topological mapping and navigation in GPS-denied urban environments using teams of low-cost robots", Autonomous Agents and Multi-Agent Systems (AGNT) Springer Nature, 2024. DOI:10.1007/s10458-024-09635-y. (BibTeX)
   
   [  PDF on Springer website | URL  |  Electronic pre-print version on arXiv.org  ]
3. Xiaolong Wang, Alp Sahin and Subhrajit Bhattacharya, "Coordination-free Multi-robot Path Planning for Congestion Reduction Using Topological Reasoning", Journal of Intelligent and Robotic Systems (JINT) Springer Nature, 2023. DOI:10.1007/s10846-023-01878-3. (BibTeX)
   
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   PDF on Springer website  |  Electronic pre-print version on arXiv.org  ]
4. Alp Sahin and Subhrajit Bhattacharya, "Optimal Path Planning in Distinct Topo-Geometric Classes using Neighborhood-augmented Graph and its Application to Path Planning for a Tethered Robot in 3D",, 2023. arXiv:2306.01203 [cs.RO]. (BibTeX)
   
   [  Electronic pre-print on arXiv.org  ]
5. Xiaolong Wang, Alp Sahin, Subhrajit Bhattacharya, "Coordination-free Multi-robot Path Planning for Congestion Reduction Using Topological Reasoning",, 2022. arXiv:2205.00955 [cs.RO]. (BibTeX)
   
   [  Electronic pre-print on arXiv.org  ]
6. Wenying Wu, Subhrajit Bhattacharya and Amanda Prorok, "Multi-Robot Path Deconfliction through Prioritization by Path Prospects", In Proceedings of IEEE International Conference on Robotics and Automation (ICRA). May, 2020. (BibTeX)
   
   [  PDF on IEEE website  |  Preprint on arXiv  ]
7. Subhrajit Bhattacharya and Robert Ghrist, "Path Homotopy Invariants and their Application to Optimal Trajectory Planning", Annals of Mathematics and Artificial Intelligence, 84(3-4):139-160, Springer International Publishing, December, 2018. (BibTeX)
   
   [  PDF on publisher's website  |  Electronic pre-print on arXiv.org  |  PDF of related conference paper  ]
8. Rattanachai Ramaithitima and Subhrajit Bhattacharya, "Landmark-based Exploration with Swarm of Resource Constrained Robots", In Proceedings of IEEE International Conference on Robotics and Automation (ICRA). May 21-25, 2018. (BibTeX)
   
   [  PDF on IEEE website  ]
9. Subhrajit Bhattacharya and Robert Ghrist, "Path Homotopy Invariants and their Application to Optimal Trajectory Planning", electronic pre-print, 2017. arXiv:1710.02871 [cs.RO]. (BibTeX)
   
   [  Electronic pre-print on arXiv.org  |  PDF of related conference paper  ]
10. Monroe Kennedy III, Dinesh Thakur, M. Ani Hsieh, Subhrajit Bhattacharya and Vijay Kumar, "Optimal Paths for Polygonal Robots in SE(2)", In Proceedings of the ASME 2017 International Design Engineering Technical Conferences (IDETC). Cleveland, OH, USA, Aug, 2017. (BibTeX)
    
    [  PDF  ]
11. Subhrajit Bhattacharya, "A Search Algorithm for Simplicial Complexes", Electronic Pre-print, August, 2016. arXiv:1607.07009 [cs.DM]. (BibTeX)
    
    [  Electronic pre-print on arXiv.org  ]
12. Rattanachai Ramaithitima, Mickey Whitzer, Subhrajit Bhattacharya and Vijay Kumar, "Automated Creation of Topological Maps in Unknown Environments Using a Swarm of Resource-Constrained Robots", In Proceedings of IEEE International Conference on Robotics and Automation (ICRA). May 16-21, 2016. (BibTeX)
    
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    abstract on conference website  ]
13. Rattanachai Ramaithitima, Mickey Whitzer, Subhrajit Bhattacharya and Vijay Kumar, "Automated Creation of Topological Maps in Unknown Environments Using a Swarm of Resource-Constrained Robots", IEEE Robotics and Automation Letters (RA-L), 1(2):746-753, January, 2016. DOI: 10.1109/LRA.2016.2523600. (BibTeX)
    
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    PDF on IEEE website  ]
14. Subhrajit Bhattacharya and Mihail Pivtoraiko, "A Classification of Configuration Spaces of Planar Robot Arms for a Continuous Inverse Kinematics Problem", Acta Applicandae Mathematicae, 139(1):133-166, Springer, October, 2015. DOI: s10440-014-9973-1. (BibTeX)
    
    [  Link to article on Springer web-site  |  Related electronic pre-print on arXiv.org  |  HTML5 + Javascript simulation  ]
15. Subhrajit Bhattacharya and Robert Ghrist, "Path Homotopy Invariants and their Application to Optimal Trajectory Planning", In Proceedings of IMA Conference on Mathematics of Robotics (IMAMR). St Anne's College, University of Oxford, September 9-11, 2015. (BibTeX)
    
    [  PDF  |  conference website  ]
16. Rattanachai Ramaithitima, Mickey Whitzer, Subhrajit Bhattacharya and Vijay Kumar, "Sensor Coverage of Unknown Environments by Robot Swarms Using Limited Local Sensing", In Proceedings of IEEE International Conference on Robotics and Automation (ICRA). May 26-30, 2015. (BibTeX)
    
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    PDF on IEEE website  ]
17. Subhrajit Bhattacharya, Robert Ghrist and Vijay Kumar, "Persistent Homology for Path Planning in Uncertain Environments", [Original title: "Persistent homology in coefficients for robot path planning in uncertain environments"]. pre-print, April, 2015. (BibTeX)
    
    [  pre-print (PDF) of an earlier version  ]
18. Subhrajit Bhattacharya, Soonkyum Kim, Hordur Heidarsson, Gaurav Sukhatme and Vijay Kumar, "A Topological Approach to using cables to separate and manipulate sets of objects", International Journal of Robotics Research, 34(6):799-815, April, 2015. DOI: 10.1177/0278364914562236. (BibTeX)
    
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    PDF on Sagepub's web-site  |  Related pre-print on homotopy invariants  |  Video of dynamic simulations and experiment  ]
19. Subhrajit Bhattacharya, Robert Ghrist and Vijay Kumar, "Persistent Homology for Path Planning in Uncertain Environments", IEEE Transactions on Robotics (T-RO), 31(3):578-590, March, 2015. DOI: 10.1109/TRO.2015.2412051. (BibTeX)
    
    [  PDF on IEEE Xplore  |  pre-print (PDF) of an earlier version  ]
20. Vijay Govindarajan, Subhrajit Bhattacharya and Vijay Kumar, "Human-Robot Collaborative Topological Exploration for Search and Rescue Applications", [Nominated for Best Paper Award]. In International Symposium on Distributed Autonomous Robotic Systems (DARS)., 2014. (BibTeX)
    
    [  PDF  ]
21. Subhrajit Bhattacharya and Mihail Pivtoraiko, "A Classification of Configuration Spaces of Planar Robot Arms with Application to a Continuous Inverse Kinematics Problem", Electronic pre-print, September, 2013-14. arXiv:1309.7960 [math.DG]. (BibTeX)
    
    [  Electronic pre-print on arXiv.org  |  PDF  |  HTML5 + Javascript simulation  ]
22. Soonkyum Kim, Subhrajit Bhattacharya, Robert Ghrist and Vijay Kumar, "Topological Exploration of Unknown and Partially Known Environments", In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Tokyo, Japan, November 3-7, 2013. [DOI: 10.1109/IROS.2013.6696907]. (BibTeX)
    
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    PDF  |  video  |  conference site  ]
23. Soonkyum Kim, Subhrajit Bhattacharya, Hordur Heidarsson, Gaurav Sukhatme and Vijay Kumar, "A Topological Approach to Using Cables to Separate and Manipulate Sets of Objects", In Proceedings of the Robotics: Science and System (RSS). Syndey, Australia, June 24-28, 2013. (BibTeX)
    
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    PDF  |  video on Youtube  ]
24. Subhrajit Bhattacharya, David Lipsky, Robert Ghrist and Vijay Kumar, "Invariants for Homology Classes with Application to Optimal Search and Planning Problem in Robotics", Annals of Mathematics and Artificial Intelligence (AMAI), 67(3):251-281, Springer, March, 2013. DOI: 10.1007/s10472-013-9357-7. (BibTeX)
    
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    PDF on Springer web-site  |  Related paper on arXiv.org  |  YAGSBPL library  ]
25. Soonkyum Kim, Koushil Sreenath, Subhrajit Bhattacharya and Vijay Kumar, "Optimal Trajectory Generation Under Homology Class Constraints", In 51st IEEE Conference on Decision and Control. 10-13 Dec, 2012. (BibTeX)
    
    [  PDF on IEEE web-site  ]
26. Subhrajit Bhattacharya, Maxim Likhachev and Vijay Kumar, "Topological Constraints in Search-based Robot Path Planning", Autonomous Robots, 33(3):273-290, Springer Netherlands, October, 2012. DOI: 10.1007/s10514-012-9304-1. (BibTeX)
    
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    Supplementary videos on Springer web-site  ||   Application to topological object separation  |  Related paper on Homotopy path planning  |  AMAI'13 paper with generalization to arbitrary dimension  ||   Old Code for the 2D results appearing in the AAAI paper  ::   MATLAB code for uniformly discretized environment  |  MATLAB code for visibility graph  |  C++ code (planning with homotopy class constraints & homotopy class exploration with dynamic obstacles & non-Euclidean cost)  ||   Newer implementations using the YAGSBPL library  ::   Bare-bones C++ implementation of homology/homotopy path planning in 2D (YAGSBPL 2.1 included)  |  Implementation of differential (N-1)-form for D-dimensional Euclidean spaces with obstacles (based on AMAI paper) and topological path planning in 3-dimensional space (YAGSBPL 2.0 included)  ]
27. Subhrajit Bhattacharya, David Lipsky, Robert Ghrist and Vijay Kumar, "Invariants for Homology Classes with Application to Optimal Search and Planning Problem in Robotics", Electronic pre-print, Aug, 2012. arXiv:1208.0573 [math.AT]. (BibTeX)
    
    [  Electronic pre-print on arXiv.org  |  PDF  |  See the published AMAI'13 paper  |  See the related AURO'12 paper  ]
28. Subhrajit Bhattacharya, Maxim Likhachev and Vijay Kumar, "Search-based Path Planning with Homotopy Class Constraints in 3D", [Extended abstract with non-technical summary of our RSS12 paper.]. In Invited paper for sub-area spotlights track on 'Best-paper talks', Proceedings of Twenty-Sixth Conference on Artificial Intelligence (AAAI-12). 22-26 July, 2012. (BibTeX)
    
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    PDF  |  See RSS'12 paper for more details  |  See AURO'12 paper for more details  ]
29. Soonkyum Kim, Koushil Sreenath, Subhrajit Bhattacharya and Vijay Kumar, "Trajectory Planning for Systems with Homotopy Class Constraints", In 13th International Symposium on Advances in Robot Kinematics (ARK). Innsbruck, Austria, Springer, Netherlands, jun, pages 83-90, 2012. (BibTeX)
    
    [  PDF on Springer web-site  ]
30. Subhrajit Bhattacharya, "Topological and Geometric Techniques in Graph-Search Based Robot Planning", PhD thesis, University of Pennsylvania, 2012. (BibTeX)
    
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    PDF of thesis  |  Presentation and movies  |  [X]Proposition 5.3.1 and Corollary 5.3.2 assume that the metric tensor is isotropic in the given coordinate chart (scalar multiple of Kronecker delta) for the application to robot coverage & exploration. See recent publication or related report for more general statements of the proposition & the corollary.
    Addendum  ]
31. Subhrajit Bhattacharya, Maxim Likhachev and Vijay Kumar, "Identification and Representation of Homotopy Classes of Trajectories for Search-based Path Planning in 3D", [Original title: Identifying Homotopy Classes of Trajectories for Robot Exploration and Path Planning] [Winner of Best Paper Award]. In Proceedings of Robotics: Science and Systems. 27-30 June, 2011. (BibTeX)
    
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    PDF  |  Supplimentary notes  |  Short presentation  |  Poster  |  YAGSBPL library  |  Best Paper Award  |  See the related AURO'12 paper  ]
32. Subhrajit Bhattacharya, Maxim Likhachev and Vijay Kumar, "A Homotopy-like Class Invariant for Sub-manifolds of Punctured Euclidean Spaces", [See a more recent and refined recent work at arXiv:1208.0573]. Electronic pre-print, March, 2011. arXiv:1103.2488 [math.DG]. (BibTeX)
    
    [  Electronic pre-print on arXiv.org  |  See more recent and refined version of this work at arXiv:1208.0573  |  YAGSBPL library  |  See the related AURO'12 paper for more details  |  See the related AMAI'13 paper for a more refined work  ]
33. Subhrajit Bhattacharya, Vijay Kumar and Maxim Likhachev, "Search-based Path Planning with Homotopy Class Constraints", In Proceedings of The Third Annual Symposium on Combinatorial Search. Atlanta, Georgia, 8-10 July, 2010. (BibTeX)
    
    [   [X]For the simple cases in 2-dimensions we have not distinguished between homotopy and homology. The distinction however does exist even in 2-d. See our more recent AURO 2012 paper or RSS 2011 paper for a comprehensive discussion on the distinction between homotopy and homology, examples illustrating the distinction, and its implications in robot planning problems.
    Addendum  |  External link not working? [X]
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    PDF extended abstract  |  Poster  |  Project Page  |  See AAAI paper with same title for more details  |  See more recent work with significant developments  |  See the related AURO'12 paper  ]
34. Subhrajit Bhattacharya, Vijay Kumar and Maxim Likhachev, "Search-based Path Planning with Homotopy Class Constraints", In Proceedings of The Twenty-Fourth AAAI Conference on Artificial Intelligence. Atlanta, Georgia, 11-15 July, 2010. (BibTeX)
    
    [   [X]For the simple cases in 2-dimensions we have not distinguished between homotopy and homology. The distinction however does exist even in 2-d. See our more recent AURO 2012 paper or RSS 2011 paper for a comprehensive discussion on the distinction between homotopy and homology, examples illustrating the distinction, and its implications in robot planning problems.
    Addendum  |  External link not working? [X]
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    PDF  |  PPT Presentation  |  Project Page  |  MATLAB code for uniformly discretized environment  |  MATLAB code for visibility graph  |  C++ code (planning with homotopy class constraints & homotopy class exploration with dynamic obstacles & non-Euclidean cost)  ]

Code

1. Codes related to implementation and demonstration of Homotopy Class constraints in Robot Path planning on 2-dimensional planes (AAAI'10 paper)
   1. MATLAB code for uniformly discretized environment
   2. MATLAB code for visibility graph
   3. C++ code (planning with homotopy class constraints & homotopy class exploration with dynamic obstacles & non-Euclidean cost)

Research Projects Mathematics