Robert Bryant

Many problems in mechanics and control theory involve motion planning when there are constraints on how the objects can move in configuration space. For example, wheels, balls, or more general shapes that roll over a surface without twisting or slipping move in a configuration space in such a way that motion is only possible in certain directions and not in others. Developing methods to effectively control such motions turns out to have surprising connections with differential geometry, and (in an insight that is originally due to Élie Cartan) even with the 14-dimensional exceptional group now known as [latex]G_2[/latex].
In this talk, I will explain some physical motivation and history of this kind of problem, including some recent surprising results recently due to Nurowski and An showing that exceptional geometry can show up in a simple mechanical system in some very unexpected ways.