# Safe Navigation and Obstacle Avoidance Using Differentiable Optimization Based Control Barrier Functions

arXiv: https://arxiv.org/abs/2304.08586 · HTML: https://mlsanity.com/paper/2304.08586/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2023.

## Built on by (most cited first, 5 of 5)

- [Efficient Motion Planning for Manipulators with Control Barrier Function-Induced Neural Controller](https://mlsanity.com/paper/2404.01184/) (2024)
- [SafeSwarm: Decentralized Safe RL for the Swarm of Drones Landing in Dense Crowds](https://mlsanity.com/paper/2501.07566/) (2025)
- [T-CBF: Traversability-based Control Barrier Function to Navigate Vertically Challenging Terrain](https://mlsanity.com/paper/2503.06083/) (2025)
- [Constraint-Aware Reinforcement Learning via Adaptive Action Scaling](https://mlsanity.com/paper/2510.11491/) (2025)
- [Differentiable Optimization Layered Safety-Critical Control for Risk-Aware Navigation via Conformal Prediction](https://mlsanity.com/paper/2605.16327/) (2026)

## Abstract (arXiv)

Control barrier functions (CBFs) have been widely applied to safety-critical robotic applications. However, the construction of control barrier functions for robotic systems remains a challenging task. Recently, collision detection using differentiable optimization has provided a way to compute the minimum uniform scaling factor that results in an intersection between two convex shapes and to also compute the Jacobian of the scaling factor. In this letter, we propose a framework that uses this scaling factor, with an offset, to systematically define a CBF for obstacle avoidance tasks. We provide theoretical analyses of the continuity and continuous differentiability of the proposed CBF. We empirically evaluate the proposed CBF's behavior and show that the resulting optimal control problem is computationally efficient, which makes it applicable for real-time robotic control. We validate our approach, first using a 2D mobile robot example, then on the Franka-Emika Research 3 (FR3) robot manipulator both in simulation and experiment.