Michael Erdmann's Research Page

Recent Interests

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:

A system can reach any state in a graph with control uncertainty
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.

Robotics

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.

Robotics Motivations

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.


Computational Molecular Biology

In the now somewhat distant past, I collaborated with Dr. Gordon Rule in the Department of Biological Sciences on a method for determining protein structure homology 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


Older Projects:


Former Students



Thesis Committees

Papers and Reports

(Click here for a publication list auto-generated by the Robotics Institute.)


For related work in our laboratory take a look at:

Manipulation Lab Research Papers

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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