The purpose of this work is to develop algorithms for controlling multiple autonomous mobile robots, in dynamic environments. In such environments, the robots can do several complex tasks. One of the main tasks, for example, is to move to another region of the environment without colliding with obstacles, which can be static or dynamic.

In general, this task has been done with path planning algorithms. In a dynamic environment, such as in versions of soccer for robots [2], it is crucial that the robot makes decisions in a short time. Therefore, the path planning algorithms cannot spend much run-time, because they can reduce the efficiency of the robot operations.

Locally Oriented Potential Fields (LOPF), proposed by [6], is a path planning technique that is applicable to multiple robots. This is based on numerical solutions of Boundary Value Problems which generate a given trajectory of a particular Elliptic Partial Differential Equation. It will be shown that this method is able to find a path (if it exists) from actual robot position to the goal, and can control multiple autonomous mobile robots, each one with distinct behaviors, by using the same environment grid.

upwind scheme, path planning, path planning BVP based, numerical methods, robotics.