Control Barrier Corridors: From Safety Functions to Safe Goal Sets

Abstract

Safe autonomy is a critical requirement and a key enabler for robots to operate in complex environments. Control barrier functions and safe motion corridors are two widely used but distinct safety methods, functional and geometric, respectively, for planning and control. Control barrier functions filter control inputs to limit the decay rate of safety, whereas safe motion corridors are geometrically constructed to define a local safe zone around the system state. This paper introduces a new notion of control barrier corridors, unifying these two approaches by converting control barrier functions into local safe goal regions for reference goal selection in feedback control systems. We show, with examples on fully actuated systems, kinematic unicycles, and linear output regulation systems, that individual state safety can be extended locally over control barrier corridors for convex barrier functions, provided the control convergence rate matches the barrier decay rate. Such safe control barrier corridors enable safely reachable persistent goal selection over continuously changing barrier corridors during motion, which we demonstrate for verifiably safe path following in autonomous exploration of unknown environments.