Rigid Body Path Planning using Mixed-Integer Linear Programming

TL;DR

This paper introduces a scalable three-stage algorithm for rigid body path planning in crowded environments, combining workspace decomposition and MILP to improve efficiency over existing methods.

Contribution

It proposes a novel approach that decomposes the free workspace into convex polytopes and uses small MILPs for path generation, enhancing scalability and computation speed.

Findings

Shorter online computation times compared to baseline methods.

Better scalability with environment size and tunnel width.

Effective in both 2D and 3D environments.

Abstract

Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP) formulations, suffer from limited scalability with respect to either the size of the workspace or the number of obstacles. In order to address the scalability issue, we propose a three-stage algorithm that first generates a graph of convex polytopes in the workspace free of collision, then poses a large set of small MILPs to generate viable paths between polytopes, and finally queries a pair of start and end configurations for a feasible path online. The graph of convex polytopes serves as a decomposition of the free workspace and the number of decision variables in each MILP is limited by restricting the subproblem within two or three free polytopes rather than the entire free region. Our simulation results demonstrate shorter online computation time compared to baseline methods and scales better with the size of the environment and tunnel width than sampling-based planners in both 2D and 3D environments.