Abstract: The study proposes a mathematical model of the Ground Unmanned Vehicle (GUV) which allows to determine the trajectory in two-dimensional coordinates and orientation angles of the unmanned vehicle. The moment reachability set for a third-order nonlinear controlled system, often called the "Dubins machine" is investigated. The object moves on a plane with a constant linear velocity and asymmetrically specified restrictions on turns to the right and to the left. The statement about the number and nature of control switches leading to the boundary of the reachability set is proved.