Abstract: A motion of a vehicle is controlled according to a sequential compositions of the elementary paths following a transformation of one of a first pattern, a second pattern, and a third pattern. These three patterns are predetermined and form an exhaustive set of patterns. The three patterns are represented by corresponding functions stored in a memory. The functions representing the patterns are used, in response to receiving an initial state and a target state of the vehicle, to determine parameters of the minimum-curvature path. The motion of the vehicle is controlled according to the parameters of the minimum-curvature path.

Abstract: A motion of a vehicle is controlled according to a sequential compositions of the elementary paths following a transformation of one of a first pattern, a second pattern, and a third pattern. The first pattern defines a forward motion of the vehicle from a first state to a second state while turning left followed by a backward motion of the vehicle from the second state to a third state while turning right, wherein the orientation of the first state is opposite to the orientation of the second state, and wherein the orientation of the first state is equal to the orientation of the second state. The second pattern defines the motion of the vehicle from a fourth state to a fifth state while moving left, wherein the orientation of the fifth state is leftward perpendicular to the orientation of the fourth state.