Control Barrier Corridors: From Safety Functions to Safe Goal Sets
Omur Arslan, Nikolay Atanasov
AI summary
Problem
Control barrier functions and safe motion corridors are traditionally separate functional and geometric safety methods that can interfere with stability or lack intuitive geometric representations for goal selection in feedback control.
Approach
The authors unify these approaches by defining control barrier corridors as local geometric safe goal sets derived from CBF constraints, allowing safe reference goals to be selected for pre-stabilized feedback controllers.
Key results
- Generic construction of control barrier corridors for goal-parametrized feedback systems
- Proof that convex CBFs with matched control gain and barrier decay rate yield locally safe goal neighborhoods
- Extension of safe corridor properties to kinematic unicycle and linear output regulation systems
- Demonstration of verifiably safe, persistent path following in autonomous exploration
Why it matters
Enables robotics researchers and control engineers to design stability-preserving, geometrically intuitive safety filters for safe navigation in complex environments.
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.