Hybrid Nonsmooth Barrier Functions With Applications to Provably Safe and Composable Collision Avoidance for Robotic Systems

Abstract

Robots are entering an age of ubiquity, and to operate effectively, these systems must typically satisfy a series of constraints (e.g., collision avoidance, obeying speed limits, maintaining connectivity). In addition, modern applications hinge on the completion of particular tasks, such as driving to a certain location or monitoring a crop patch. The dichotomy between satisfying constraints and completing objectives creates a need for constraint-satisfaction frameworks that are composable with a pre-existing primary objective. Barrier functions have recently emerged as a practical and the composable method for constraint satisfaction, and prior results demonstrate a system of Boolean logic for nonsmooth barrier functions as well as a composable controller-synthesis framework; however, this prior work does not consider dynamically changing constraints (e.g., a robot sensing and avoiding an obstacle). Consequently, the main theoretical contribution of this letter extends nonsmooth barrier functions to time-varying barrier functions with jumps. In a practical instantiation of the theoretical main results, this letter revisits a classic problem by formulating a collision-avoidance framework and composing it with a nominal controller. Experimental results show the efficacy of this framework on a light detection and ranging (LIDAR)-equipped differential-drive robot in a real-time obstacle-avoidance scenario.