Source-Seeking Problem with Robot Swarms

We present an algorithm to solve the problem of locating the source, or maxima, of a scalar field using a robot swarm. We demonstrate how the robot swarm determines its direction of movement to approach the source using only field intensity measurements taken by each robot. In contrast with the current literature, our algorithm accommodates a generic (non-degenerate) geometry for the swarm's formation. Additionally, we rigorously show the effectiveness of the algorithm even when the dynamics of the robots are complex, such as a unicycle with constant speed. Not requiring a strict geometry for the swarm significantly enhances its resilience. For example, this allows the swarm to change its size and formation in the presence of obstacles or other real-world factors, including the loss or addition of individuals to the swarm on the fly. For clarity, the article begins by presenting the algorithm for robots with free dynamics. In the second part, we demonstrate the algorithm's effectiveness even considering non-holonomic dynamics for the robots, using the vector field guidance paradigm. Finally, we verify and validate our algorithm with various numerical simulations.

Resilient source seeking with robot swarms

We present a solution for locating the source, or maximum, of an unknown scalar field using a swarm of mobile robots. Unlike relying on the traditional gradient information, the swarm determines an ascending direction to approach the source with arbitrary precision. The ascending direction is calculated from measurements of the field strength at the robot locations and their relative positions concerning the centroid. Rather than focusing on individual robots, we focus the analysis on the density of robots per unit area to guarantee a more resilient swarm, i.e., the functionality remains even if individuals go missing or are misplaced during the mission. We reinforce the robustness of the algorithm by providing sufficient conditions for the swarm shape so that the ascending direction is almost parallel to the gradient. The swarm can respond to an unexpected environment by morphing its shape and exploiting the existence of multiple ascending directions. Finally, we validate our approach numerically with hundreds of robots. The fact that a large number of robots always calculate an ascending direction compensates for the loss of individuals and mitigates issues arising from the actuator and sensor noises.