Groups of robots that move in precise formations could be used to sense an environment from multiple points of view or navigate a warehouse in a compact manner. The challenge is to build formations in a distributed manner, meaning there is no leader telling every robot where to go. Instead robots must react to neighboring robots within a limited sensing range.
To solve this problem, Sabattini et al. propose an elegant algorithm that guarantees robots will move in formations of any desirable shape without bumping into each other. Let’s start with a simple scenario where N robots are asked to form a polygon with N edges of length L. Such a polygon can hold in a circle of radius R as shown in the figure below. Robots reach that configuration by being repulsed from the center of the circle until they are at a distance R, along the circle. Combine that with a rule to make each robot repulse from neighbors that are closer than a distance L and you get a polygon. However, using these two rules alone, robots would form polygons oriented in any direction. To make sure the polygon points in the right direction, simply attract one of the robots to a specific position (a* in the figure). All the other robots will then adapt to this robot to form a polygon oriented in the desired manner.
So how do you go from making a polygon to making any arbitrary shape? The trick is to cleverly change the coordinate system of the robots so that they think they are forming a polygon, when in fact they are forming the desired shape. This can be seen in the figure below which shows simulated robots in a real coordinate system, and in the transformed coordinate system.
Robot trajectories simulated with Matlab: black dots are the starting positions, red stars are the final positions. Trajectories are plotted with respect to the real reference frame (left) and the transformed one (right).
Experiment were conducted in matlab, Player/Stage and in reality using three Roomba vacuum cleaners. The Roombas were equipped with a gumstix computer and wireless hardware. During formation, robots would calculate their position using odometry and transmit their location to neighboring robots using WiFi. Results show that the proposed algorithm is successful in creating the desired formations, regardless of the original positions of the robots.
In the future, authors hope to optimize robot trajectories, avoid obstacles in the environment and control the heading of the individual robots.
