Controllability of a Planar Body with Unilateral Thrusters
Kevin M. Lynch
Abstract
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, we get a new property with each additional thruster: one thruster yields small-time accessibility on the body's state space TSE(2); two thrusters yield global controllability on TSE(2); and three thrusters yield small-time local controllability at zero velocity states.
Figure 2: This planar body is small-time locally controllable at zero
velocity states because the three unilateral thrusters provide lines
of force which positively span the plane and
meet at a single point not at the center of mass.