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

## TL;DR

This paper develops robust control barrier functions for second-order, sampled-data mechanical systems with uncertainties, and applies them to robotic grasping to ensure safety and task constraints are met.

## Contribution

It introduces novel control barrier functions for relative degree two, sampled-data systems with uncertainties, and demonstrates their effectiveness in robotic grasping tasks.

## Key findings

- Validated through simulations and experiments
- Ensures no slip, over-extension, or fingertip roll-off during grasping
- Compatible with existing manipulation controllers

## Abstract

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.