2017-04-20
,
Chirikjian, Gregory
Many stochastic problems of interest in engineering and science involve
random, rigid-body motions. In this talk, a variety of stochastic
phenomena that evolve on the group of rigid-body motions will be
discussed together with tools from harmonic analysis and Lie theory to
solve the associated equations. These phenomena include mobile robot
path planning and camera calibration. Current work on multi-robot team
diagnosis and repair, information fusion, and self-replicating robots will
also be discussed. In order to quantify the robustness of such robots,
measures of the degree of environmental uncertainty that they can
handle need to be computed. The entropy of the set of all possible
arrangements (or configurations) of spare parts in the environment is one
example of such a measure and has led us to study problems at the
foundations of statistical mechanics and information theory. These and
other topics in robotics lend themselves to the same mathematical tools,
which also will be discussed in this talk.