Planning Terminal-Optimal Motion of a Robot in a Horizontal Plane Bypassing a Static Obstacle for the Extreme Case

The current level of development of technology and engineering, demands of society determine the need to develop unmanned vehicles and systems. Today, there is a wide variety of theoretical methods for planning the motion of robots, which differ in their efficiency in various conditions. Among the methods of motion planning, a group of methods based on the use of artificial potential fields (APF) stands out. In practice, various problems may arise in which the robot must find itself in the end point with the required linear velocity within the allotted time. The use of APF methods for such problems leads to a significant complication of the type of the potential energy function of the field. In addition, such methods are characterized by the problem of local field minima and oscillations of the robot near an obstacle. In this paper, a particular method is proposed that differs from existing methods, which eliminates this problem, allowing the robot to reach the target point in the allotted time for the extreme case. As the extreme case, the location of the obstacle center, the initial and final points of the robot’s center of mass and its velocity vector on one straight line is considered. The proposed private method VC/APF₂ + BC_τ⁰ of optimal planning of robot motion with bypass of a static obstacle is based on: the combined use of variational calculus (VC) and an artificial potential field (repelling the robot from the obstacle boundaries), the lines of force of which are perpendicular to the robot velocity vector (APF₂); on dividing the robot motion along the horizontal plane into stages (modes) for given initial and final coordinates and zero robot velocities, its travel time (BC_τ⁰).

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