# Growing Convex Collision-Free Regions in Configuration Space using Nonlinear Programming

arXiv: https://arxiv.org/abs/2303.14737 · HTML: https://mlsanity.com/paper/2303.14737/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2023.

## Built on by (most cited first, 4 of 4)

- [Constant-time Motion Planning with Anytime Refinement for Manipulation](https://mlsanity.com/paper/2311.00837/) (2023)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Constant-Time Planning for Chaining Collision-free Motion to Manipulation Behaviors](https://mlsanity.com/paper/2512.00939/) (2025)
- [Unified Branch-and-Bound Search for the Steiner Traveling Salesman Problem on Graphs of Convex Sets](https://mlsanity.com/paper/2608.21319/) (2026)

## Abstract (arXiv)

One of the most difficult parts of motion planning in configuration space is ensuring a trajectory does not collide with task-space obstacles in the environment. Generating regions that are convex and collision free in configuration space can separate the computational burden of collision checking from motion planning. To that end, we propose an extension to IRIS (Iterative Regional Inflation by Semidefinite programming) [5] that allows it to operate in configuration space. Our algorithm, IRIS-NP (Iterative Regional Inflation by Semidefinite & Nonlinear Programming), uses nonlinear optimization to add the separating hyperplanes, enabling support for more general nonlinear constraints. Developed in parallel to Amice et al. [1], IRIS-NP trades rigorous certification that regions are collision free for probabilistic certification and the benefit of faster region generation in the configuration-space coordinates. IRIS-NP also provides a solid initialization to C-IRIS to reduce the number of iterations required for certification. We demonstrate that IRIS-NP can scale to a dual-arm manipulator and can handle additional nonlinear constraints using the same machinery. Finally, we show ablations of elements of our implementation to demonstrate their importance.