Zero-order Control Barrier Functions for Sampled-Data Systems with State and Input Dependent Safety Constraints

2024-11-26

arXiv.org

AI Summary

This work addresses the challenge of real-time safety-critical control for sampled-data systems subject to high relative-degree safety constraints and state-input coupling. We propose Zero-Order Control Barrier Functions (ZOCBFs), which eliminate reliance on Lie derivatives or higher-order time derivatives; instead, safety conditions are formulated solely via finite differences of barrier function values between consecutive sampling instants—achieving the first zero-order discrete-time CBF formulation. The method unifies treatment of coupled state and input constraints, accommodates arbitrary relative-degree safety requirements, and provides three efficient implementation strategies: quadratic programming, numerical root-finding, and lookup-table-based evaluation. Evaluated on collision avoidance and rollover prevention over uneven terrain, ZOCBFs guarantee rigorous safety enforcement while significantly reducing computational overhead, enabling real-time, scalable safety-critical control.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

We propose a novel zero-order control barrier function (ZOCBF) for sampled-data systems to ensure system safety. Our formulation generalizes conventional control barrier functions and straightforwardly handles safety constraints with high-relative degrees or those that explicitly depend on both system states and inputs. The proposed ZOCBF condition does not require any differentiation operation. Instead, it involves computing the difference of the ZOCBF values at two consecutive sampling instants. We propose three numerical approaches to enforce the ZOCBF condition, tailored to different problem settings and available computational resources. We demonstrate the effectiveness of our approach through a collision avoidance example and a rollover prevention example on uneven terrains.

Problem

• Ensures safety in sampled-data systems using ZOCBF
• Handles state and input dependent safety constraints
• Avoids differentiation by using difference of ZOCBF values

Innovation

• Zero-order control barrier functions for safety
• Handles state and input dependent constraints
• Three numerical approaches for enforcement