# Differentiable Optimization Layered Safety-Critical Control for Risk-Aware Navigation via Conformal Prediction

arXiv: https://arxiv.org/abs/2605.16327 · HTML: https://mlsanity.com/paper/2605.16327/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 15 of 15)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Perception-Based Control under Stochastic Sensor Uncertainty using Conformal Prediction](https://mlsanity.com/paper/2304.00194/) (2023)
- [Safe Navigation and Obstacle Avoidance Using Differentiable Optimization Based Control Barrier Functions](https://mlsanity.com/paper/2304.08586/) (2023)
- [Perceive With Confidence: Statistical Safety Assurances for Navigation with Learning-Based Perception](https://mlsanity.com/paper/2403.08185/) (2024)
- [Conformalized Reachable Sets for Obstacle Avoidance With Spheres](https://mlsanity.com/paper/2410.09924/) (2024)
- [Collision Avoidance for Convex Primitives via Differentiable Optimization Based High-Order Control Barrier Functions](https://mlsanity.com/paper/2410.19159/) (2024)
- [Optimization-free Smooth Control Barrier Function for Polygonal Collision Avoidance](https://mlsanity.com/paper/2502.16293/) (2025)
- [Safe Multi-Robotic Arm Interaction via 3D Convex Shapes](https://mlsanity.com/paper/2503.11791/) (2025)
- [Small-Gain Theorem for Safety Verification under High-Relative-Degree Constraints](https://mlsanity.com/paper/2204.04376/) (2022)
- [Feasible Space Monitoring for Multiple Control Barrier Functions with application to Large Scale Indoor Navigation](https://mlsanity.com/paper/2312.07803/) (2023)
- [Visibility-Aware RRT* for Safety-Critical Navigation of Perception-Limited Robots in Unknown Environments](https://mlsanity.com/paper/2406.07728/) (2024)
- [Polytope Volume Monitoring Problem: Formulation and Solution via Parametric Linear Program Based Control Barrier Function](https://mlsanity.com/paper/2503.12546/) (2025)
- [Robust Safety Critical Control Under Multiple State and Input Constraints: Volume Control Barrier Function Method](https://mlsanity.com/paper/2503.13996/) (2025)

## Abstract (arXiv)

Risk-aware navigation in unknown environments is a fundamental challenge for autonomous vehicles operating in complex urban systems. To address this issue, this paper presents a differentiable optimization layered safety-critical control method based on conformal prediction. First, to handle uncertainties arising from sensor noise, the conformal prediction method is employed to generate risk-aware obstacle ellipsoids around an elliptical-shaped robot. Second, two nested differentiable optimization layers are introduced to build the control barrier functions for obstacle avoidance and feasibility guarantee, respectively. Then, a quadratic program based safety-critical control law is proposed to integrate the above control barrier function constraints as well as input constraints. In the end, the effectiveness of the proposed framework is demonstrated through numerical simulations.