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 controllability on TSE(2); and three thrusters suffice for small-time local controllability at zero velocity states.