Third-order consensus for robust distributed formation control of double integrator vehicles

Abstract

This paper presents the development of a robust distributed and cooperative control algorithm for formation tracking by teams of vehicles modeled as double integrators, and exemplifies its use through the application to multirotor vehicles. To achieve coordination between the vehicles in a distributed manner, in the sense that only local information is either exchanged or perceived, consensus-based protocols are considered. Consensus protocols for agents modeled with up to three integrators are presented, and the third-order protocol is analyzed under any time-invariant sensing or communication topology. The analysis seeks to determine exact bounds on the coupling gains of the protocol that lead to convergence. To that end, an extension of the Routh–Hurwitz criterion to polynomials with complex coefficients is used, leading to novel necessary and sufficient conditions for convergence. Moreover, these novel bounds turn out to be a generalization of the ones described in the literature for second-order consensus, as the latter can be recovered as a special case. The effect of disturbances acting upon the agents is also analyzed and related to their ability to achieve robust consensus in the sense that bounded disturbances do not lead to instability. Further results are derived for the case of constant disturbances, a special case that is particularly relevant for formation control. The third-order consensus protocol is then explored to incorporate integral action in a formation tracking controller used for double integrator vehicles and thereby enable constant disturbance rejection. Finally, experiments resulting from the application of the proposed control algorithms to multirotor vehicles are presented, in order to validate the analysis and demonstrate the usefulness of this approach.