Computer scientists are often concerned about lower bounds: what is the
least amount of time or memory required to solve a problem? This talk
will explore a few fundamental problems in robotics from an equally
minimalist perspective, motivated by problems in motion planning and
manipulation of flexible materials including paper, cloth, and string.
What is the fastest trajectory to move a vehicle with particular motion
capabilities from one location and orientation to another, among
infinitely many possible trajectories? How many fingers are needed to
immobilize a bendable (but not stretchable) piece of cloth? How many
degrees of freedom (motors) must a mechanism have to tie a knot in a
piece of string? We will show analytical and geometric solutions to
each of these problems, as well as a few machines built based on
algorithms and principles discovered.