This paper addresses the problem of multi-agent coordination and control under multiple objectives, and presents a set-theoretic formulation which is amenable to Lyapunov-based analysis and control design. A novel class of Lyapunov-like barrier functions is introduced and used to encode multiple, non-trivial control objectives, such as collision avoidance, proximity maintenance and convergence to desired destinations. The construction is based on the concept of recentered barrier functions and on approximation functions. A single Lyapunov-like function encodes the constrained set of each agent, yielding simple, closed-form control solutions. The proposed construction allows also for distributed control design based on information locally available to each agent. The scenario considered here involves nonholonomic vehicles, while simulation results demonstrate the efficacy of the approach.