A Distributed Level Curve Tracking Control Law for Multi-Agent Systems

Control laws for a multi-agent system to follow level curves of a spatially distributed scalar field generally require sharing field measurements among the agents for gradient estimation. This paper presents a distributed control law that does not rely on the communication of the field measurements nor the estimation of the gradient. Each agent only modulates its speed according to local measurements of the field and relative positions of its neighbors. The distributed control law scales to large swarms with connected undirected visibility graph. Stability is justified in a singular perturbation framework. The efficiency of the control law is validated through simulations demonstrating level curve tracking behaviors of 2-dimensional scalar fields.