# An Interior Point Method Solving Motion Planning Problems with Narrow Passages

arXiv: https://arxiv.org/abs/2007.04842 · HTML: https://mlsanity.com/paper/2007.04842/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2020.

## Built on by (most cited first, 2 of 2)

- [Resilient Legged Local Navigation: Learning to Traverse with Compromised Perception End-to-End](https://mlsanity.com/paper/2310.03581/) (2023)
- [Efficient Learning of High Level Plans from Play](https://mlsanity.com/paper/2303.09628/) (2023)

## Abstract (arXiv)

Algorithmic solutions for the motion planning problem have been investigated for five decades. Since the development of A* in 1969 many approaches have been investigated, traditionally classified as either grid decomposition, potential fields or sampling-based. In this work, we focus on using numerical optimization, which is understudied for solving motion planning problems. This lack of interest in the favor of sampling-based methods is largely due to the non-convexity introduced by narrow passages. We address this shortcoming by grounding the solution in differential geometry. We demonstrate through a series of experiments on 3 Dofs and 6 Dofs narrow passage problems, how modeling explicitly the underlying Riemannian manifold leads to an efficient interior-point non-linear programming solution.