# Landmark Guided Probabilistic Roadmap Queries

## TL;DR

This paper introduces a landmark-based heuristic for probabilistic roadmap motion planning that precomputes minimum spanning trees to accelerate query times, especially beneficial in multi-query scenarios.

## Contribution

The paper proposes a novel heuristic using precomputed spanning trees to reduce query time in PRM motion planning, trading off preprocessing time and memory for faster queries.

## Key findings

- The heuristic outperforms Dijkstra's and A* algorithms in multi-query environments.
- Preprocessing increases initial computation but significantly speeds up subsequent queries.
- Effective in both randomized environments and practical manipulator simulations.

## Abstract

A landmark based heuristic is investigated for reducing query phase run-time of the probabilistic roadmap (\PRM) motion planning method. The heuristic is generated by storing minimum spanning trees from a small number of vertices within the \PRM graph and using these trees to approximate the cost of a shortest path between any two vertices of the graph. The intermediate step of preprocessing the graph increases the time and memory requirements of the classical motion planning technique in exchange for speeding up individual queries making the method advantageous in multi-query applications. This paper investigates these trade-offs on \PRM graphs constructed in randomized environments as well as a practical manipulator simulation.We conclude that the method is preferable to Dijkstra's algorithm or the ${\rm A}^*$ algorithm with conventional heuristics in multi-query applications.