Resource-aware cooperative level surface tracking control in 3D time-varying scalar field

We propose a resource-aware level surface tracking control law for multi-robot systems in unknown 3D time-varying scalar fields. Existing control laws generally require communications and GPS for gradient estimation which may be inapplicable when these resources are limited, such as in underwater or intentional electromagnetic interference environments. The proposed control law only uses the local measurements of the field and observed relative positions of neighbors to seek the desired level surfaces. A sub-objective method is developed to satisfy additional constraints for tracking the 3D level surfaces. We prove that the swarm center can converge to the desired level surfaces while the sub-objective function can be optimized locally. The convergence domain of input-to-state stability is derived theoretically. Finally, we present an application of the proposed control law to track ocean pollutant leakage by simulations using the real ocean flow data.