The effectiveness of robot-manipulators is determined to a great extent by the speed of making this or that movement needed for carrying out the task. According to this the problem of optimal robot control is often divided into two subproblems solved separately. In the autonomous regime the trajectory planning is fulfilled for providing the robot movement time close to the minimal. The problem of a robot reaching a moving aim under the existence of movable (or in particular immovable) obstacles is considered in the report. This problem is represented as two-person zero-sum game, taking place in a metric space X.