On second order consensus protocols allowing joint-agent interactions in robust formation control

This work of Thesis is concerned with a second order consensus protocol, where a nonlinear interaction dynamics is introduced in order to fulfil some robustness requirements. The proposed protocol is set in the Joint-Agent Interaction framework, which allows a network to reach consensus even in the presence of malicious or faulty agents. This approach was introduced in some recent works by Angeli and Manfredi, where, using the language of Petri Nets and siphons, some topological conditions were proven to be necessary and sufficient for structural consensuability. Nevertheless, their results were only limited to a first order protocol, due to some monotonicity assumptions regarding the network state variables. Our goal, instead, is extending their valuable results in the context of second order consensus protocols. The present study is developed with respect to a restricted class of topologies, where agents are grouped in interaction triplets. A piece-wise linear interaction function is assigned in order to ensure the existence of some virtual springs within the network. Some rules are provided in order to detect the springs in a network; moreover a graph search algorithm is proposed for this task being performed automatically. By introducing a dissipation term in the virtual spring dynamics, the network evolution is constrained on a mainfold. The analysis of such a reduced dynamical system is performed by means of a recursive algebraic technique, leading to the detection of further springs in the residual dynamics. Therefore, the consensuability analysis is carried out using a cascade approach. In the final part, some simulation results concerning the network robustness are presented. First, a rendez vous task is shown to be completed even in the presence of malicious agents. Then, a formation control task is performed when some agents are force disturbed. Throughout the work, the validity of the assertions is proved by means of formal arguments, while their effectiveness is shown by simulations