Entropy Driven Height Profile Estimation with Multiple UAVs under Sparsity Constraints

This paper shows an application of a multi-agent distributed learning system for UAV-based exploration under sparsity constraints. It is assumed that Unmanned Aerial Vehicles (UAVs) cooperatively explore a static spatial field that can be represented with a few non-zero coefficients, i.e., the model of a process is sparse. The recovery of the sparse model in a distributed setting is solved with a Distributed LASSO (DLASSO) algorithm that implements an Alternating Direction Method of Multipliers (ADMM). Based on the cooperatively estimated model, a swarm of UAVs decides on its next movements using optimal experiment design strategies. To this end, second order information of the optimization problem is approximated using a theory of slantly differentiable functions. Also, an additional adaptive trade-off parameter between exploration of new areas and exploitation of the already obtained information is proposed and tested. The experiments are performed in a laboratory environment with two UAVs measuring a height profile with an ultrasonic sensor. The experiments show that the proposed method is very useful for time consuming measurements, if the observed process can be assumed to be sparse. Also, the adaptive method increases the overall system performance with respect to the number of measurements.