# Control Barrier Functions for Mechanical Systems: Theory and Application to Robotic Grasping

arXiv: https://arxiv.org/abs/1903.09816 · HTML: https://mlsanity.com/paper/1903.09816/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2019.

## Built on by (most cited first, 8 of 8)

- [VLSA: Vision-Language-Action Models with Plug-and-Play Safety Constraint Layer](https://mlsanity.com/paper/2512.11891/) (2025)
- [VoicePilot: Harnessing LLMs as Speech Interfaces for Physically Assistive Robots](https://mlsanity.com/paper/2404.04066/) (2024)
- [Exact Verification of ReLU Neural Control Barrier Functions](https://mlsanity.com/paper/2310.09360/) (2023)
- [CBF-LLM: Safe Control for LLM Alignment](https://mlsanity.com/paper/2408.15625/) (2024)
- [Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach](https://mlsanity.com/paper/2208.02319/) (2022)
- [Scalable Verification of Neural Control Barrier Functions Using Linear Bound Propagation](https://mlsanity.com/paper/2511.06341/) (2025)
- [Optimal Parameter Adaptation for Safety-Critical Control via Safe Barrier Bayesian Optimization](https://mlsanity.com/paper/2503.19349/) (2025)
- [Control Barrier Function for Aligning Large Language Models](https://mlsanity.com/paper/2511.03121/) (2025)

## Abstract (arXiv)

Control barrier functions have been demonstrated to be a useful method of ensuring constraint satisfaction for a wide class of controllers, however existing results are mostly restricted to continuous time systems of relative degree one. Mechanical systems, including robots, are typically second-order systems in which the control occurs at the force/torque level. These systems have velocity and position constraints (i.e. relative degree two) that are vital for safety and/or task execution. Additionally, mechanical systems are typically controlled digitally as sampled-data systems. The contribution of this work is two-fold. First, is the development of novel, robust control barrier functions that ensure constraint satisfaction for relative degree two, sampled-data systems in the presence of model uncertainty. Second, is the application of the proposed method to the challenging problem of robotic grasping in which a robotic hand must ensure an object remains inside the grasp while manipulating it to a desired reference trajectory. A grasp constraint satisfying controller is proposed that can admit existing nominal manipulation controllers from the literature, while simultaneously ensuring no slip, no over-extension (e.g. singular configurations), and no rolling off of the fingertips. Simulation and experimental results validate the proposed control for the robotic hand application.