# Safety-Critical Kinematic Control of Robotic Systems

arXiv: https://arxiv.org/abs/2009.09100 · HTML: https://mlsanity.com/paper/2009.09100/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2020.

## Built on by (most cited first, 7 of 7)

- [Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.15512/) (2023)
- [Efficient Action-Constrained Reinforcement Learning via Acceptance-Rejection Method and Augmented MDPs](https://mlsanity.com/paper/2503.12932/) (2025)
- [Efficient Motion Planning for Manipulators with Control Barrier Function-Induced Neural Controller](https://mlsanity.com/paper/2404.01184/) (2024)
- [Aligning Perception, Reasoning, Modeling and Interaction: A Survey on Physical AI](https://mlsanity.com/paper/2510.04978/) (2025)
- [Safe Uncertainty-Aware Learning of Robotic Suturing](https://mlsanity.com/paper/2505.16596/) (2025)
- [FlowHijack: A Dynamics-Aware Backdoor Attack on Flow-Matching Vision-Language-Action Models](https://mlsanity.com/paper/2604.09651/) (2026)
- [Constraint-Enhanced Reinforcement Learning Based on Dynamic Decoupled Spherical Radial Squashing](https://mlsanity.com/paper/2605.04185/) (2026)

## Abstract (arXiv)

Over the decades, kinematic controllers have proven to be practically useful for applications like set-point and trajectory tracking in robotic systems. To this end, we formulate a novel safety-critical paradigm for kinematic control in this paper. In particular, we extend the methodology of control barrier functions (CBFs) to kinematic equations governing robotic systems. We demonstrate a purely kinematic implementation of a velocity-based CBF, and subsequently introduce a formulation that guarantees safety at the level of dynamics. This is achieved through a new form CBFs that incorporate kinetic energy with the classical forms, thereby minimizing model dependence and conservativeness. The approach is then extended to underactuated systems. This method and the purely kinematic implementation are demonstrated in simulation on two robotic platforms: a 6-DOF robotic manipulator, and a cart-pole system.