Chaotic Transitions in Wall Following Robots

In this paper we examine how simple agents similar to Braitenberg vehicles can exhibit chaotic movement patterns. The agents are wall following robots as described by Steve Mesburger and Alfred Hubler in their paper “Chaos in Wall Following Robots”. These agents uses a simple forward facing distance sensor, with a limited field of view (Φ) for navigation. An agent drives forward at a constant velocity and uses the sensor to turn right when it is too close to an object and left when it is too far away. For a flat wall the agent stays a fixed distance from the wall and travels along it, regardless of the sensor’s capabilities. But, if the wall represents a periodic function, the agent drives on a periodic path when the sensor has a narrow field of view. The agent’s trajectory transitions to chaos when the sensor’s field of view is increased. Numerical experiments were performed with square, triangle, and sawtooth waves for the wall, to find this pattern. The bifurcations of the agents were analyzed, finding both border collision and period doubling bifurcations. Detailed experimental results will be reported in the final version. ∗The research reported in this document/presentation was performed in connection with contract/instrument W911QX-09-C-0055 with the U.S. Army Research Laboratory. The views and conclusions contained in this document/presentation are those of the authors and should not be interpreted as presenting the official policies or position, either expressed or implied, of the U.S. Army Research Laboratory or the U.S. Government unless so designated by other authorized documents. Citation of manufacturers or trade names does not constitute an official endorsement or approval of the use thereof. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon.