# Differentiable Collision-Free Parametric Corridors

**Authors:** Jon Arrizabalaga, Zachary Manchester, Markus Ryll  
**arXiv:** [2407.12283](https://arxiv.org/abs/2407.12283)  
**Date:** 2024-07-17  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2407.12283v1/

## Key points

- Authors Jon Arrizabalaga, Zachary Manchester, and Markus Ryll introduce a novel method for computing smooth and differentiable collision-free parametric corridors.
- The method improves upon existing approaches by generating continuous corridors compatible with various numerical techniques.
- Collision-free corridors are represented as path-parametric off-centered ellipses with a polynomial basis, a key innovation of the approach.
- The problem of maximizing corridor volume is formulated as convex, leading to an efficient solution approach.
- The effectiveness of the method is validated through thorough evaluation in both synthetic and real-world scenarios sourced from the KITTI dataset.
- The research has been accepted for publication at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) in Abu Dhabi, UAE in October 2024.
- Authors have shared their code repository on GitHub (https://github.com/jonarriza96/corrgen) and a video demonstration (https://youtu.be/MvC7bPodXz8) showcasing the practical implementation of their technique.

## Summary

In their paper titled "Differentiable Collision-Free Parametric Corridors," authors Jon Arrizabalaga, Zachary Manchester, and Markus Ryll introduce a novel method for computing smooth and differentiable collision-free parametric corridors. This approach is a significant improvement over existing methods that divide obstacle-free spaces into multiple convex sets. The corridors generated by this method are continuous and compatible with various numerical techniques used in learning and optimization processes. The key innovation lies in representing these collision-free corridors as path-parametric off-centered ellipses with a polynomial basis. By formulating the problem of maximizing the volume of these corridors as convex, the authors demonstrate an efficient solution approach. To validate the effectiveness of their method, they conduct a thorough evaluation through a synthetic case study and further test its applicability in a real-world scenario sourced from the KITTI dataset. This research has been accepted for publication at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) in Abu Dhabi, UAE, scheduled for October 2024. The authors have also provided access to their code repository on GitHub (https://github.com/jonarriza96/corrgen) and a video demonstration (https://youtu.be/MvC7bPodXz8), showcasing the practical implementation of their proposed technique.