Stochastic Models in Robotics - Gregory Chirikjian

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.