An Interior Point Method Solving Motion Planning Problems with Narrow Passages

TL;DR

This paper introduces an interior point method grounded in differential geometry to effectively solve motion planning problems with narrow passages, addressing non-convexity issues in high-dimensional spaces.

Contribution

It presents a novel interior point approach that explicitly models the Riemannian manifold of the configuration space for motion planning.

Findings

Efficiently solves 3 Dofs and 6 Dofs narrow passage problems

Outperforms traditional sampling-based methods in complex scenarios

Demonstrates the effectiveness of differential geometry in motion planning

Abstract

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.