Rigorous Movement of Convex Polygons on a Path Using Multiple Robots

This paper describes an approach for pushing a convex polygonal object with rigor using multiple robots, along a desired rectilinear path in a two-dimensional polygonal environment. The goal is to rigorously push the object along the path while preserving its orientation and alignment, as well as precisely rotating it about its center when necessary. A path planning algorithm is presented which computes a shortest-path approximation between two points in the environment. In general, the path requires both translations and rotations of the object along the way. Robots are arranged into three groups, where each group is assigned a task of either pushing the object towards its goal or adjusting it as it veers off from the desired path. Each robot is computationally simple in that it merely moves towards a target point somewhere on the boundary of the object. As the robots move towards these target points, they cooperatively push the object with no interaction between one another. The robots rely on only three parameters to push the object: the orientation of the object, the current target point and the task they are required to perform. The target points are provided by a global control & monitoring system that monitors the progress and stability of the robots as they push the object along the path, providing direction to the robots in terms of tasks such as pushing, rotating, re-alignment, re-orientation or repositioning commands. We verified our algorithm with a number of simulations that address the usefulness of the solution as well as the effects that an increase in the number of robots will have on the runtime and the data communication load.