The article describes the solution of the problem of mobile robot ultrasonic positioning in a confined space. The solution of this task is overdue, if necessary, calculate the coordinates of a moving object in an enclosed area of a small size. Most available technology in this case is ultrasonic technology, since it provides sufficient accuracy and more simple to implement. Methods for solving the problem is using a triangulation system, consisting of an object with an ultrasonic emitter and four sensors located at the corners of the permissible area. The mathematical model of the system is a system of nonlinear equations, numerical method can be applied to solve a. The authors compare two numerical methods for solving the ultrasonic positioning tasks: the simplest gradient method and the Levenberg-Marquardt method. The final choice was made in favor of the Levenberg-Marquardt.
Keywords: Ultrasound positioning, mobile robot positioning, numerical method, the simplest gradient method, Levenberg-Marquardt algorithm