LAUSR

Abstract Three-dimensional attainability set “at instant” for a non-linear controlled system is studied, which is often called the “Dubins car”. A controlled object moves in the plane. It has linear velocity of a constant magnitude and bounded turn radius. The case is explored when the object can turn to one side only. Moreover, a rectilinear motion is prohibited by the constraints onto the control. We prove that the sections of the attainability set by planes orthogonal to the angle coordinate are convex. The geometric structure of these sections is analyzed.