  This paper investigates how group-control can be effectively used for motion
planning for microrobot swarms in a global field. We prove that Small-Time
Local Controllability (STLC) in robot positions is achievable through
group-control, with the minimum number of groups required for STLC being
$\log_2(n + 2) + 1$ for $n$ robots. We then discuss the complexity trade-offs
between control and motion planning. We show how motion planning can be
simplified if appropriate primitives can be achieved through more complex
control actions. We identify motion planning problems that balance the number
of robot groups and motion primitives with planning complexity. Various
instantiations of these motion planning problems are explored, with simulations
to demonstrate the effectiveness of group-control.
