# A Motion Planning Algorithm in a lollipop graph

## TL;DR

This paper explores the topological complexity of robot motion planning on tracks modeled by graphs, providing explicit algorithms for collision-free movement, especially on a lollipop graph.

## Contribution

It introduces a method to compute the topological complexity of configuration spaces and presents an explicit collision-free motion planning algorithm for two robots on a lollipop graph.

## Key findings

- Calculated topological complexity for various graph tracks
- Developed an explicit collision-free motion planning algorithm for two robots
- Demonstrated the algorithm on a lollipop graph

## Abstract

This paper is concerned with problems relevant to motion planning in robotics. Configuration spaces are of practical relevance in designing safe control schemes for robots moving on a track. The topological complexity of a configuration space is an integer which can be thought of as the minimum number of continuous instructions required to describe how to move robots between any initial configuration to any final one without collisions. We calculate this number for various examples of robots moving in different tracks represented by graphs. We present and implement an explicit algorithm for two robots to move autonomously and without collisions on a lollipop track.