Safe trajectory tracking using closed-form controllers based on control barrier functions

This paper considers the problem of guaranteeing avoidance of critical state space regions during tracking of reference trajectories for systems with dynamics equivalent to r-th order decoupled integrators. The necessity to avoid those critical regions during trajectory tracking may arise during the transient phase or because the reference trajectory was planned without taking into account the presence of those critical regions. A typical problem in mobile robotics, taken as reference in this paper, is the avoidance of obstacles in the robot workspace during tracking of reference state space trajectories. The proposed controller ensures a safety clearance from the forbidden regions by filtering out, when appropriate, the component of the tracking command that would eventually lead the system to enter the critical region. The method relies on the construction of first-order control barrier functions and closed-form controllers, with formal proof of safety and stability, and its effective application to wheeled mobile robots and quadrotors is demonstrated through simulation.