Multi-robot formation control for source location in unknown scalar fields under available/unavailable velocity information

In this paper, multi-robot collaborative source location of unknown scalar fields is investigated in the presence/absence of velocity information. A neural network is employed to approximate the unknown scalar fields, where the corresponding gradient as a driving term of navigation strategies is estimated by adaptive techniques for unknown weight vectors and partial derivatives of approximation errors from the neural network. Via utilising the gradient estimation and constructing auxiliary variables, we devise event-triggered mechanisms to serve the controller design. For robots with the Euler-Lagrange dynamics in the constraint of local communications characterised by undirected and connected graphs, based on the estimated gradient and the constructed auxiliary variables, event-triggered formation controllers as navigation strategies are proposed under available/unavailable velocities, in which passive filters about virtual formation centres and intermediate states with auxiliary variables are invented to make up for related roles from velocities in the scenario of unavailable velocities. According to relevant theory of directed graphs, the above controllers are extended from undirected and connected graphs to directed and strongly connected ones, where the Filippov theory, distributed principles and inequality techniques are used to argue the performance of the corresponding controllers. In comparison with the existing method, we conduct simulation tests to verify the effectiveness of the offered control schemes in two cases with available/unavailable velocities.