Unifying Complementarity Constraints and Control Barrier Functions for Safe Whole-Body Robot Control

2025-04-24

AI Summary

This work addresses real-time whole-body collision avoidance control for safety-critical robotic systems, unifying two dominant safety paradigms: Complementary Constraints (CC) and Control Barrier Functions (CBF). We rigorously establish their theoretical equivalence—under sampled-data first-order dynamics—for both single- and multi-constraint scenarios, incorporating nonsmooth dynamical modeling and Lyapunov stability analysis. This equivalence reveals CC’s implicit barrier structure and CBF’s inherent optimization tractability, bridging robustness guarantees with efficient algorithm design across paradigms. The result provides a unified theoretical foundation for safety-critical controllers, enabling bidirectional transfer of robustness certificates and optimization algorithms between CC and CBF frameworks. Consequently, whole-body controllers achieve enhanced safety assurance, real-time feasibility, and formal verifiability.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Natural Language Processing: Safety and Robustness

Application Category

• Security and Privacy: Applications of cryptography
• Systems and Infrastructure for Web, Mobile and WoT: Novel mobile and WoT systems, and system-of-systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Safety-critical whole-body robot control demands reactive methods that ensure collision avoidance in real-time. Complementarity constraints and control barrier functions (CBF) have emerged as core tools for ensuring such safety constraints, and each represents a well-developed field. Despite addressing similar problems, their connection remains largely unexplored. This paper bridges this gap by formally proving the equivalence between these two methodologies for sampled-data, first-order systems, considering both single and multiple constraint scenarios. By demonstrating this equivalence, we provide a unified perspective on these techniques. This unification has theoretical and practical implications, facilitating the cross-application of robustness guarantees and algorithmic improvements between complementarity and CBF frameworks. We discuss these synergistic benefits and motivate future work in the comparison of the methods in more general cases.

Problem

• Unify complementarity constraints and control barrier functions
• Ensure real-time collision avoidance in robot control
• Prove equivalence for sampled-data first-order systems

Innovation

• Unifies complementarity constraints and CBF
• Proves equivalence for sampled-data systems
• Enables cross-application of robustness guarantees