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Further results on formation infeasibility and velocity alignment

In previous work, we deduced that formation infeasibility results in velocity alignment in multi-agent systems with bidirectional communication topology and single integrator as well as nonholonomic kinematics. This paper contains additional results regarding the connection between formation infeasibility and velocity alignment. In particular, we obtain an analytic expression for the resulting common velocity vector in the case of formation infeasibility and extend the results to the case of unidirectional communication topology. The results are then extended to the case of a leader-follower architecture in which the followers are not aware of a global objective while the leaders are responsible for driving the team to the interior of a desired leader formation. When this formation is infeasible, we show that both leaders and followers attain a common velocity vector, of which an analytic expression is also provided. Computer simulations support the derived results.