Robust Control Barrier Functions for Sampled-Data Systems

TL;DR

This paper introduces a novel control barrier function approach for ensuring safety in sampled-data systems with disturbances and measurement errors, validated through obstacle avoidance in robotic systems.

Contribution

It extends high-order control barrier functions to sampled-data systems with piecewise-constant controllers, providing safety guarantees under disturbances and measurement errors.

Findings

System remains safe under bounded disturbances and measurement errors.

Proposed method successfully applied to obstacle avoidance in robotic systems.

Ensures safety constraints are not violated in sampled-data control scenarios.

Abstract

This paper studies the problem of safe control of sampled-data systems under bounded disturbance and measurement errors with piecewise-constant controllers. To achieve this, we first propose the High-Order Doubly Robust Control Barrier Function (HO-DRCBF) for continuous-time systems where the safety enforcing constraint is of relative degree 1 or higher. We then extend this formulation to sampled-data systems with piecewise-constant controllers by bounding the evolution of the system state over the sampling period given a state estimate at the beginning of the sampling period. We demonstrate the proposed approach on a kinematic obstacle avoidance problem for wheeled robots using a unicycle model. We verify that with the proposed approach, the system does not violate the safety constraints in the presence of bounded disturbance and measurement errors.