The known algorithms for planning the trajectory of movement of mobile robots in an unknown environment have high computational complexity or do not allow finding the trajectory that is optimal along the length of the path, while maintaining a safe distance from obstacles. The aim of the work is to increase the efficiency of solving the problem of planning the trajectory of movement of mobile robots from the initial position to the final position in an unknown environment with obstacles, taking into account the limited capabilities (sensory and computational) of mobile robots. The solution to this problem was carried out on the basis of step-by-step optimization of the current position of the robot relative to a given target. The proposed method analyzes the possibility of a robot moving in directions determined by means of analytical geometry based on measurements of on-board distance sensors. An element of scientific novelty is the procedure for calculating trajectory segments based on the choice of an intermediate state and correcting the trajectory taking into account the measurements of the on-board distance sensors of the mobile robot. The proposed method makes it possible to search for the trajectory of a mobile robot in an unknown environment while ensuring a given distance to obstacles. The use of the presented algorithm allows the robot to maintain a high efficiency of the task while functioning in conditions of information deficiency. The reliability of the results was confirmed in the course of software simulation. The solution of the problem, taking into account these features, made it possible to reduce the computational complexity of the method, as well as to remove restrictions on the use of trajectory planning algorithms for mobile robots with low-performance on-board sensors and computing devices. The presented algorithm is implemented in the form of software in the Python programming language, which can be used to simulate autonomous control systems for mobile robots.