An algorithm of trajectory control for the movement of a mobile robot without measuring the position coordinates

The paper considers the problem of controlling the movement of a mobile robot along a given smooth trajectory without measuring its position coordinates. To solve the problem, an adaptive observer of the local coordinates of a moving object is used by measuring the linear speed, yaw angle, and range to a beacon with known coordinates. Then the minimum distance from the robot to the given smooth trajectory is determined. Based on the estimates for the coordinates of the robot and the distance to the curve, we synthesized the control law of the movement along the trajectory with the desired speed under the conditions of uncertainty of the mathematical model. The motion control algorithm is based on the robust sequential compensator method, which ensures that the deviations of the robot from a given trajectory are limited. The proposed coordinate observer ensures asymptotic convergence of the estimation errors to zero. In this paper, we propose two algorithms for determining the minimum distance from the robot to the trajectory: an exact analytical calculation and a nonlinear observer that guarantees the convergence of the estimate to the true value in an arbitrarily short time. The trajectory regulator ensures the movement of the robot along a given trajectory with a limited error. The application of the proposed approach allows one to solve the issues of controlling the movement of a mobile robot without measuring the position coordinates. The approach can be widely applied for controlling self-driving vehicles when they run in tunnels or under a bridge, where it is not possible to measure their coordinates using the satellite navigation systems (GLONASS or GPS).