  We present a task-centered formal analysis of the relative power of several
robot designs, inspired by the unique properties and constraints of micro-scale
robotic systems. Our task of interest is object manipulation because it is a
fundamental prerequisite for more complex applications such as micro-scale
assembly or cell manipulation. Motivated by the difficulty in observing and
controlling agents at the micro-scale, we focus on the design of boundary
interactions: the robot's motion strategy when it collides with objects or the
environment boundary, otherwise known as a bounce rule. We present minimal
conditions on the sensing, memory, and actuation requirements of periodic
``bouncing'' robot trajectories that move an object in a desired direction
through the incidental forces arising from robot-object collisions. Using an
information space framework and a hierarchical controller, we compare several
robot designs, emphasizing the information requirements of goal completion
under different initial conditions, as well as what is required to recognize
irreparable task failure. Finally, we present a physically-motivated model of
boundary interactions, and analyze the robustness and dynamical properties of
resulting trajectories.
