Control Barrier Functions in Sampled-Data Systems

Joseph Breeden, Kunal Garg, Dimitra Panagou

Published 2021-03-05Version 1

This paper presents conditions for ensuring forward invariance of safe sets under sampled-data system dynamics with piecewise-constant controllers and fixed time-steps. First, we introduce two different metrics to compare the conservativeness of sufficient conditions on forward invariance under piecewise-constant controllers. Then, we propose three approaches for guaranteeing forward invariance, two motivated by continuous-time barrier functions, and one motivated by discrete-time barrier functions. All proposed conditions are control affine, and thus can be incorporated into quadratic programs for control synthesis. We show that the proposed conditions are less conservative than those in earlier studies. The advantages of the new approaches are demonstrated via simulations on an obstacle-avoidance problem for a unicycle agent and on a spacecraft attitude reorientation problem, in which the new approaches achieve the mission objectives for cases where the existing methods fail.