High-Order Control Barrier Function Based Robust Collision Avoidance Formation Tracking of Constrained Multi-agent Systems

In this work, we propose a high-order control barrier functions (HOCBFs) based safe formation tracking controller for second-order multi-agent systems subject to input uncertainties and both velocity and input constraints (VICs). First, a nominal velocity and input constrained formation tracking controller is proposed which using sliding mode control theory to eliminate the effects of the uncertain dynamics. Then, the HOCBFs-based collision avoidance conditions are derived for the followers where both collision among the agents and between the agents and the obstacles are considered. Finally, the collision avoidance formation tracking controller for the constrained uncertain second-order multi-agent systems is constructed by formulating a local quadratic programming (QP) problem for each follower. It is shown that under proper initial conditions, there always exist feasible control inputs such that collision avoidance can be guaranteed under both VICs of the agents. Simulation examples illustrate the effectiveness of the proposed control strategy.