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This manuscript considers the problem of ensuring stability and safety during formation control with distributed multi-agent systems in the presence of parametric uncertainty in the dynamics and limited communication. We propose an integrative approach that combines Control Barrier Functions, Adaptive Control, and connected graphs. A reference model is designed so as to ensure a safe and stable formation control strategy. This is combined with a provably correct adaptive control design that includes a use of a CBF-based safety filter that suitably generates safe reference commands, and employs error-based relaxation (EBR) of Nagumo's Invariance Theorem. Together, it is shown to lead to a guarantee of boundedness, formation control, and forward invariance. Numerical examples are provided to support the theoretical derivations.
Solano-Castellanos et al. (Fri,) studied this question.