Introduction. Problems of the remote control of mobile vehicles maneuvering in a space-limited environment have recently attracted great interest [4–12, 16, 17]. This is because of the necessity of supporting various industrial processes, performing handling operations at large warehouse terminals, providing production maintenance in hazardous conditions, etc. To solve practical problems, the range of types of wheeled robots is constantly extended. Among them are oneand multilink robots with one or several steerable wheels, which highly improve their mobility and usability. It is of scientific interest to examine the limiting capabilities of certain types of mobile robots on a flat surface. Here we will design a path for oneand two-link mobile robots with two and three steerable wheels in an L-shaped holding alley as a typical obstacle. As a mobile robot moves in such an alley, its longitudinal velocity vector turns by an angle of /2, or nearly so. In motion planning, more complicated obstacles can be considered to consist of such alleys. Since the more there are steerable wheels, the higher the manoeuvrability of robots [5, 6, 10, 16], we will discuss some geometrical and kinematic grounds for planning a path of a oneand two-link robots with two and three steerable wheels, respectively. Dynamic models will be developed, and examples will be given. 1. Path Planning for a One-Link Robot. Let us consider one of the possible approaches to the path planning for a one-link one-dimensional robot (modeled by a straight-line segment) with two steerable wheels at the ends. Increasing the number of steerable wheels improves the maneuverability of the vehicle so that it can execute composite paths in one or two continuous maneuvers. Let the sensors of a one-link robot (as a nonholonomic system) measure the three generalized coordinates defining its position on a plane at every instant. Let also the sideways overturning of the robot be impossible. The frictional constraints between the wheels and the flat supporting sufrace are bilateral. Figure 1 shows (top view) a one-link robot AB in an L-shaped holding alley with legs I and II. The wheels A and B are steerable, i.e., can be turned about the vertical axis, and their size is neglected. Let us determine path 1 of the typical (moving) point K 0 of the robot A B 0 0 that moves extremely close to the left corner (pointO). Then, the point A 0 continuously moves along the wall OS, while the point B 0 moves along the wall PO. The current angle between the robot and the horizontal is denoted by . During such motion, the family of intervals A B 0 0 is described by the equations