Most recently, I explored topological perspectives on privacy. One discovery is that homology in relations provides lower bounds on how long an individual can defer de-anonymization. In conjunction with my previous work on strategy complexes, this result shows the manner in which a fully controllable system can obfuscate its strategies and goals.

Previously, I explored topological methods for planning and control. One novel result was a graph controllability theorem:

if and only if

the graph's strategy complex is homotopic to a sphere of

dimension two less than the number of states in the graph.

My broader robotics interests include the mechanics of manipulation, nonprehensile manipulation, parts assembly, cooperating robots, planning under uncertainty, probabilistic strategies, sensing strategies, and automatic planning.

I am interested in making robots act purposefully and successfully in a world in which most everything is uncertain. Sensors are noisy, actions are imprecise, and objects are often in the wrong location. Despite such obstacles to purposeful action, there are many tasks that can be accomplished successfully. Humans, animals, and some machines are proof. Providing robots with the ability to operate autonomously and purposefully requires an understanding of how different tasks may be accomplished by different repertoires of actions.

My work is motivated by several desires. First, I would like to program robots more easily than is currently possible. Second, I would like to understand the scope and limitations of autonomous systems, whether biological or artificial. Third, I would like to reduce the complexity of design and planning by codifying the design parameters required to achieve a given level of automation. An underlying goal of my research is to understand the relationship between sensing, action, and prediction. In the past, I have explored various extreme points in this space. With Matt Mason I explored sensorless strategies, for my thesis work I looked at randomized strategies, and for my early faculty work I investigated fast-action minimal-sensing strategies. My research draws on tools from geometry, mechanics, planning, probability, and topology.

See also my tenure statement.

In the now somewhat distant past, I collaborated with Dr. Gordon Rule in the Department of Biological Sciences on a method for determining proteinstructurehomology from sparse NMR data. Of particular interest to me was the extent to which topological shapes could act as fingerprint identifiers of proteins. One novel result of this work was a method for representing and comparing proteins using line weavings.For more details please see the following: PEPMORPH Proteins, Knots, and Line Weavings

- I have been interested in understanding the interplay of manipulation and
locomotion.
Matt Mason,
Siddhartha Srinivasa,
and I investigated this problem using a mobile manipulator
called the
Mobipulator.

- I have been interested in protein homology, in particular determining
structural homology from sparse NMR data and modeling protein
structures in terms of line weavings. I worked together with Gordon
Rule in the Department of Biological Sciences.

- I have been interested in sensing strategies that acquire object shape and configuration concurrently during manipulation. This line of research began with the Ph.D. thesis of my student Yan-Bin Jia, extended into my own thinking, and continued with my student Mark Moll.

- Siddhartha Srinivasa
(co-advised with Matt
Mason), Robotics.
Ph.D., August 2005. Thesis title:
*Control Synthesis for Dynamic Contact Manipulation.*First post-Ph.D. job: Intel Research Laboratory, Pittsburgh.

- Mark Moll, Computer
Science. Ph.D., July 2002. Thesis title:
*Shape Reconstruction Using Active Tactile Sensors.*First post-Ph.D. job: Research Associate, Physical and Biological Computing Group, Rice University, then at USC-ISI, now a Research Scientist at Rice.

- Jovan Popovic,
Computer Science. Ph.D., July 2001. Thesis title:
*Interactive Design of Rigid-Body Simulations for Computer Animation.*First post-Ph.D. job: Assistant Professor, MIT.

- Yan-Bin Jia, Robotics.
Ph.D., November 1997. Thesis title:
*Geometric and Dynamic Sensing: Observation of Pose and Motion through Contact.*First post-Ph.D. post-CMU job: University of Minnesota. Now a tenured professor at Iowa State.

- Nina Zumel,
Robotics. Ph.D., January 1997. Thesis title:
*A Nonprehensile Method for Reliable Parts Orienting.*First post-Ph.D. job: AI group, Stanford Research Institute. For many years she had her own company, Quimba Software. She is now at Win-Vector LLC.

- Tamara Abell, Robotics. M.S., December 1995, currently at Apple.

- Shushman Choudhury, M.S., Robotics, 2017.
- Joel Chestnutt, Ph.D., Computer Science, CMU, 2007.
- Jason O'Kane, Ph.D., Computer Science, UIUC, 2007.
- Guillermo Bermejo, Ph.D., Chemistry, CMU, 2007.
- Keith Kotay, Ph.D., Computer Science, Dartmouth, 2003.
- Alexander Grishaev, Ph.D., Chemistry, CMU, 2001.
- Dongmei Zhang, Ph.D., Robotics, CMU, 1999.
- Tom Ault, Robotics, CMU, proposed 1998.
- Barry Brumitt, Ph.D., Robotics, CMU, 1997.
- George Paul, Ph.D., Robotics, CMU, 1997.
- J. Dan Morrow, Ph.D., Robotics, CMU, 1997.
- Cheng-Hua Wang, Ph.D., Robotics, CMU, 1997.
- David Simon, Ph.D., Robotics, CMU, 1996.
- Srinivas Akella, Ph.D., Robotics, CMU, 1996.
- Kevin Lynch, Ph.D., Robotics, CMU, 1996.
- David Wettergreen, Ph.D., Robotics, CMU, 1995.
- Sanjiv Singh, Ph.D., Robotics, CMU, 1995.
- Sing Bing Kang, Ph.D., Robotics, CMU, 1994.
- Prasad Chalasani, Ph.D., Computer Science, 1994.
- Rudi Stouffs, Ph.D., Architecture, CMU, 1994.
- Alan Christiansen, Ph.D., Computer Science, CMU, 1992.
- Harry Kim, Ph.D., Robotics, CMU, 1991.

- Michael Erdmann.
Deception, Delay, and
Detection of Strategies.,
arXiv 1906.11513, June 2019.

Privacy: Lattice Structures and Information Bubbles for Inference and Obfuscation, arXiv 1712.04130, December 2017.

- D. Dolev, M. Erdmann, N. Lutz, M. Schapira, and A. Zair.
Brief Announcement: Stateless Computation.

*Proceedings of the 2017 ACM Symposium on Principles of Distributed Computing*, Washington D.C., pp. 419-421.

- N. Chavan-Dafle, A. Rodriguez, R. Paolini, B. Tang, S. Srinivasa,
M. Erdmann, M. T. Mason, I. Lundberg, H. Staab, and T. Fuhlbrigge.
Extrinsic Dexterity: In-Hand Manipulation with External Forces.

*Proceedings of the 2014 IEEE International Conference on Robotics and Automation*, Hong Kong.

- Y.-B. Jia, M. T. Mason, and M. A. Erdmann.
Multiple Impacts: A State Transition Diagram Approach.

*International Journal of Robotics Research,*Vol. 32, No. 1, 2013, pp. 84-114.

- Michael Erdmann.
On the Topology of Discrete Planning with Uncertainty.
In
*Advances in Applied and Computational Topology*,

Proceedings of Symposia in Applied Mathematics, Volume 70, edited by Afra Zomorodian. American Mathematical Society. 2012.

- Michael Erdmann.
On the Topology of Discrete Strategies.

*International Journal of Robotics Research,*Vol. 29, No. 7, 2010, pp. 855-896.

- Michael Erdmann.
On the Topology of Plans.

*8th Workshop on the Algorithmic Foundations of Robotics*, Guanajuato, Mexico, December 2008.

- Y.-B. Jia, M. T. Mason, and M. A. Erdmann.
A State Transition Diagram for Simultaneous Collisions with
Application in Billiard Shooting.

*8th Workshop on the Algorithmic Foundations of Robotics*, Guanajuato, Mexico, December 2008.

- M. A. Erdmann.
Protein Similarity from Knot Theory: Geometric Convolution and Line Weavings.

*Journal of Computational Biology*, Vol. 12, No. 6, 2005, pp. 609-637.

(Clarification/Erratum: In Section 6.2.3 of the paper we defined the "L2 measure" using a sum of integrals, each measuring a squared error between two lines.

Our code inadvertently computed the sum of the square roots of these integrals.

Thus the dimensions of the "L2" values reported are actually square-root-Angstroms not Angstroms.)

- S. S. Srinivasa, M. A. Erdmann, and M. T. Mason.
Using Projected Dynamics to Plan Dynamic Contact Manipulation.

*Proceedings of the 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems*, Edmonton, Canada, pp. 3618-3623.

- S. S. Srinivasa, M. A. Erdmann, and M. T. Mason.
Control Synthesis for Dynamic Contact Manipulation.

*Proceedings of the 2005 IEEE International Conference on Robotics and Automation*, Barcelona, Spain, pp. 2523-2528.

- M. A. Erdmann.
Protein Similarity from Knot Theory and Geometric Convolution.

*Proceedings of the 2004 ACM International Conference on Research in Computational Molecular Biology*, San Diego, CA, pp. 195-204.

- J. Popovic, S. M. Seitz, and M. A. Erdmann.
Motion Sketching for Control of Rigid-Body Simulations.

*ACM Transactions on Graphics*, Vol. 22, No. 4, 2003, pp. 1034-1054.

- S. S. Srinivasa, M. A. Erdmann, and M. T. Mason.
Bilateral Time-Scaling for Control of Task Freedoms of a Constrained Nonholonomic System.

*Proceedings of the 2003 IEEE International Conference on Robotics and Automation*, Taipei, Taiwan, pp. 3391-3396.

- Mark Moll and Michael A. Erdmann.
Reconstructing the Shape and Motion of Unknown Objects with Active
Tactile Sensors.

In Jean-Daniel Boissonnat, Joel Burdick, Ken Goldberg, and Seth Hutchinson, editors,*Algorithmic Foundations of Robotics V*, Springer Verlag, December 2002.

- M. Moll and M. A. Erdmann.
Manipulation of Pose Distributions.
*International Journal of Robotics Research,*Vol. 21, No. 3, 2002, pp. 277-292.

- M. Moll, K. Y. Goldberg, M. A. Erdmann, and R. Fearing.
Aligning Parts for Micro Assemblies.
*Assembly Automation,*Vol. 22, No. 1, 2002, pp. 46-54.

- Siddhartha S. Srinivasa, Christopher R. Baker, Elisha Sacks,
Grigoriy B. Reshko, Matthew T. Mason, and Michael A. Erdmann.
Experiments with Nonholonomic Manipulation.
*Proceedings of the 2002 IEEE International Conference on Robotics and Automation*, Washington, DC, pp. 2042-2047.

- Mark Moll and Michael A. Erdmann.
Dynamic Shape Reconstruction Using Tactile Sensors.

*Proceedings of the 2002 IEEE International Conference on Robotics and Automation*, Washington, DC, pp. 1636-1641.

- Mark Moll, Ken Goldberg, Michael A. Erdmann and Ron Fearing.
Orienting Micro-Scale Parts with Squeeze and Roll Primitives.

*Proceedings of the 2002 IEEE International Conference on Robotics and Automation*, Washington, DC, pp. 1931-1936.

- Mark Moll and Michael Erdmann.
Reconstructing Shape from Motion Using Tactile Sensors.

*Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and System*, Wailea, Hawaii, pp. 692-700.

- J. Popovic, S. Seitz, M. Erdmann, Z. Popovic, and A. Witkin.
Interactive Manipulation of Rigid Body Simulation.

*ACM SIGGRAPH*, July 2000, pp. 209-217.

- Mark Moll and Michael Erdmann.
Uncertainty Reduction Using Dynamics.

*Proceedings of the 2000 IEEE International Conference on Robotics and Automation*, San Francisco, California, pp. 3673-3680.

- Yan-Bin Jia and Michael Erdmann.
Pose and Motion from Contact.

*International Journal of Robotics Research*, Vol. 18, No. 5, 1999, pp. 466-490.

- Michael Erdmann.
An Exploration of Nonprehensile Two-Palm Manipulation.

*International Journal of Robotics Research*, Vol. 17, No. 5, 1998, pp. 485-503.

- Yan-Bin Jia and Michael Erdmann.
Observing Pose and Motion through Contact.

*Proceedings of the 1998 IEEE International Conference on Robotics and Automation*, Leuven, Belgium, pp. 723-729. Full paper (430KB postscript, 8 pages).

- Michael Erdmann.
Shape Recovery from Passive Locally Dense Tactile Data.

*1998 Workshop on the Algorithmic Foundations of Robotics*. Full paper (11MB postscript, 23 pages).

Here (3.7MB postscript, 13 pages) is the shorter version from the proceedings.

- Nina Zumel and Michael Erdmann.
Nonprehensile Manipulation for Orienting
Parts in the Plane.

*Proceedings of the 1997 IEEE International Conference on Robotics and Automation*, Albuquerque, New Mexico, pp. 2433-2439. Full paper (391KB postscript, 7 pages).

- Yan-Bin Jia and Michael Erdmann.
Geometric Sensing of Known Planar Shapes.

*International Journal of Robotics Research*, Vol. 15, No. 4, 1996, pp. 365-392.

- Yan-Bin Jia and Michael Erdmann.
Pose from Pushing.

*Proceedings of the 1996 IEEE International Conference on Robotics and Automation*, Minneapolis, Minnesota, pp. 165-171.

- Nina Zumel and Michael Erdmann.
Nonprehensile Two Palm Manipulation
with Non-Equilibrium Transitions between Stable States.

*Proceedings of the 1996 IEEE International Conference on Robotics and Automation*, Minneapolis, Minnesota, pp. 3317-3323.

- Michael Erdmann.
An Exploration of Nonprehensile Two-Palm
Manipulation: Planning and Execution.

*Seventh International Symposium on Robotics Research*, October 21-24, 1995, Herrsching, Germany.

[Click here for full postscript version (2.5MB).]

[A revised version (2.1MB) of this paper appeared in the*International Journal of Robotics Research*, Vol. 17, No. 5, 1998.]

- Tamara Abell and Michael Erdmann.
Stably Supported Rotations of a
Planar Polygon with Two Frictionless Contacts.

*Proceedings of the 1995 IEEE/RSJ International Conference on Intelligent Robots and System*, Pittsburgh, Pennsylvania, pp. 411-418.

- Michael Erdmann.
Understanding Action and Sensing by Designing Action-Based Sensors.

*International Journal of Robotics Research*, Vol. 14, No. 5, 1995, pp. 483-509.

- Michael Erdmann.
On a Representation of Friction in Configuration Space.

*International Journal of Robotics Research*, Vol. 13, No. 3, 1994, pp. 240-271.

- Michael Erdmann.
Randomization for Robot Tasks: Using Dynamic
Programming in the Space of Knowledge States.

*Algorithmica*, Vol. 10, 1993, pp. 248-291.

- Michael Erdmann, Matthew T. Mason, and George Vanecek, Jr.

Mechanical Parts Orienting: The Case of a Polyhedron on a Table.

*Algorithmica*, Vol. 10, 1993, pp. 226-247.

- Michael Erdmann.
Randomization in Robot Tasks.

*International Journal of Robotics Research*, Vol. 11, No. 5, 1992, pp. 399-436.

- Michael Erdmann and Matthew T. Mason.
An Exploration of Sensorless Manipulation.

*IEEE Journal of Robotics and Automation*, Vol. 4, No. 4, 1988, pp. 369-379.

- Michael Erdmann and Tomas Lozano-Perez.
On Multiple Moving Objects.

*Algorithmica*, Vol. 2, No. 4, 1987, pp. 477-521.

- Michael Erdmann.
Using Backprojections for Fine Motion Planning with Uncertainty.

*International Journal of Robotics Research*, Vol. 5, No. 1, 1986, pp. 19-45.

For related work in our laboratory take a look at:

We gratefully acknowledge support by NSF, DARPA, and AFOSR for this research.

Relevant support from NSF includes a Research Initiation Award IRI-9010686 and REU supplement, a Presidential Young Investigator Award IRI-9157643, grant IRI-9213993 (with REU supplement IRI-9443084), grant IRI-9503648 (with REU supplements IRI-9642850 and IRI-9741440, and a Creativity Extension), grant IIS-9820180, grant IIS-0222875, and grant IIS-1409003.

Any opinions, findings, and conclusions or recommendations expressed in this research are those of the author(s) and do not necessarily reflect the position or the policy of the National Science Foundation, DARPA, the Air Force, or the U.S. Government. No official endorsement should be inferred.

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