On barycentric coordinates in control of a thruster driven spacecraft

We consider a problem of control of a planar spacecraft model equipped with thrusters with unilateral action. The model corresponds to a physical simulator of microgravity motion constructed in Space Research Center in Warsaw. We consider conditions of small time controllability and design of control law with a limited number of thruster. It is shown that with representation of controls in barycentric coordinates we can provide simple tests which allow us to verify if a requested control value is admissible for a given thruster set. The barycentric representation allows also to develop formulas for optimal controls under certain assumptions. The results were illustrated by computer simulations.