Motion planning, formation control and obstacle avoidance for multi-agent systems

In this paper we investigate the problem of navigating, in a centralized manner, a team of unicycle-like robots in a known environment avoiding obstacles and, at the same time, steering them to patrol an assigned path in controlled formation. Such a goal is pursued by combining algorithms that use tools borrowed from algebraic geometry with some methods inspired by classical navigation functions. The former allows to automatically construct Lyapunov functions that certify the convergence to the desired formation and to the desired path, if obstacles are absent, while the latter allow to avoid collisions among agents and with fixed obstacles. Simulations are reported throughout all the paper to illustrate the theoretical results.