This chapter considers 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 control objectives, such as collision avoidance, proximity maintenance and convergence to desired destinations. The construction is based on recentered barrier functions and on maximum approximation functions. Thus, a single Lyapunov-like function is used to encode the constrained set of each agent, yielding simple, gradient-based control solutions. The derived control strategies are distributed, i.e., based on information locally available to each agent, which is dictated by sensing and communication limitations. The proposed coordination protocol dictates semi-cooperative conflict resolution among agents, as well as conflict resolution with respect to an agent (the leader) which is not actively participating in collision avoidance, except when necessary. The considered scenario is pertinent to surveillance tasks and involves nonholonomic vehicles. The efficacy of the approach is demonstrated through simulation results.
Comparative Analysis of Control Barrier Functions and Artificial Potential Fields for Obstacle Avoidance
