Unifying Complementarity Constraints and Control Barrier Functions for Safe Whole-Body Robot Control
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915257071435776 |
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| author | Muchacho, Rafael I. Cabral Laha, Riddhiman Pokorny, Florian T. Figueredo, Luis F. C. Chakraborty, Nilanjan |
| author_facet | Muchacho, Rafael I. Cabral Laha, Riddhiman Pokorny, Florian T. Figueredo, Luis F. C. Chakraborty, Nilanjan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unifying Complementarity Constraints and Control Barrier Functions for Safe Whole-Body Robot Control Muchacho, Rafael I. Cabral Laha, Riddhiman Pokorny, Florian T. Figueredo, Luis F. C. Chakraborty, Nilanjan Robotics Systems and Control 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. |
| title | Unifying Complementarity Constraints and Control Barrier Functions for Safe Whole-Body Robot Control |
| topic | Robotics Systems and Control |
| url | https://arxiv.org/abs/2504.17647 |