This paper investigates the minimal number of unilateral thrusters required
for different versions of nonlinear controllability of a planar rigid body
. For one to three unilateral thrusters, one gets a new property with each
additional thruster: one thruster suffices for small-time accessibility on
the body's state space TSE(2); two thrusters suffice for global controllabi
lity on TSE(2); and three thrusters suffice for small-time local controllab
ility at zero velocity states.