Decentralized multi-agent tracking of unknown environmental level sets by a team of nonholonomic robots

We consider a team of nonholonomic Dubins-car like robots traveling forward over paths with bounded curvatures in a planar region supporting an unknown scalar field. Every robot measures the field value at its location and has no communication facilities; the robots are anonymous to one another. The objective is to detect and localize the level set where the unknown field assumes a given value. We present a new distributed navigation and guidance strategy that ensures convergence of all robots to the desired level set and its subsequent display via stable circulation of the robots along this set. Moreover, this strategy prevents collisions between the robots and ultimately provides their sub-uniform distribution over the level set, so that the entire team effectively and representatively portrays this set. The proposed control strategy does not employ gradient estimation, which typically needs ineffective concentration of robots into tight clusters, and is non-demanding with respect to both computation and motion. Its mathematically rigorous justification is provided. The effectiveness of the proposed guidance law is confirmed by computer simulations and real-world experiments.