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A Bresenham's line based global path planning algorithm. A recursive path planning algorithm was developed that operates on the grid maps represented by a masked array and solves potential looping problems using a state machine-based loop breaking mechanism.

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A Bresenham-based Global Path Planning Algorithm on Grid Maps

This repository contains supplementary code for the Paper.

Velikzhanin, Artem, and Inna Skarga-Bandurova. "A Bresenham-based Global Path Planning Algorithm on Grid Maps." 2023 13th International Conference on Dependable Systems, Services and Technologies (DESSERT). IEEE, 2023.

Abstract

This paper presents a novel global path planning algorithm adapted to grid maps extending the Bug algorithm family. During experiments with Bresenham’s line algorithm, it was found that this algorithm allows natural obstacle avoidance. Based on this observed property, a recursive path planning algorithm was developed that operates on the grid maps represented by a masked array and solves potential looping problems using a state machine-based loop breaking mechanism. BRP was compared with existing methods from the Bug family of algorithms as well as with more classical algorithms such as A*, D*, and Dijkstra. The Piano Movers problem was also touched upon. The time performance of the BLA algorithm for different line thicknesses was compared. Based on these experiments, future optimisation of the BRP algorithm for motion planning tasks is possible. Through experiments, BRP was found to show significant improvement in path planning time for certain map cases compared to existing algorithms while acknowledging a slight increase in route length, approximately 0.43% above the optimal path. The presented work improves the field of global path planning by providing efficient and adaptable solutions that can be applied to specific applications.

Illustrative animation depicting algorithmic processes

Applying the algorithm to a grid map

Perfomanse analysis

Testing was performed on 5,000 thousand randomly generated point pairs for the three maps. It is assumed that a route is always possible between any two points in the pair.

Used symbols: µ — mean; Th – thickness; OD – original distance; TE – execution time; OP – occupancy percentage; RE – successful goal-finding percentage; TD - total distance; SM – trajectory smoothness.

BRP algorithm perfomance comparision (MAP1)

Algorithm μ OD OP (%) μ TD μ SM μ TE RE (%)
Dijkstra 32.39 9.36 34.35 0.121 0.0225 100
A* 32.39 9.36 34.36 0.24 0.008 100
D* 32.39 9.36 33.32 0.126 0.055 100
Bug_0 32.33 9.36 36.42 0.152 0.0078 99.64
Bug_1 32.2 9.36 42.26 0.31 0.011 97.62
Bug_2 30.13 9.36 39.62 0.267 0.0062 52.6
BRP 32.39 9.36 34.51 0.366 0.0029 100

BRP algorithm perfomance comparision (MAP2)

Algorithm μ OD OP (%) μ TD μ SM μ TE RE (%)
Dijkstra 33.92 19.08 79.44 0.154 0.018 100
A* 33.92 19.08 79.44 0.215 0.03 100
D* 33.92 19.08 78.42 0.152 0.056 100
Bug_0 33.92 19.08 81.22 0.122 0.047 100
Bug_1 33.92 19.08 107.07 0.167 0.044 100
Bug_2 34.07 19.08 113.34 0.148 0.02 86.56
BRP 33.92 19.08 84.09 0.296 0.024 100

BRP algorithm perfomance comparision (MAP3)

Algorithm μ OD OP (%) μ TD μ SM μ TE RE (%)
Dijkstra 32.46 36.4 36.52 0.22 0.0138 100
A* 32.46 36.4 36.52 0.244 0.0071 100
D* 32.46 36.4 35.43 0.215 0.079 100
Bug_0 30.98 36.4 45.37 0.51 0.089 53.0
Bug_1 38.89 36.4 112.48 0.33 0.116 28.98
Bug_2 37.64 36.4 96.1 0.343 0.077 21.78
BRP 32.46 36.4 39.21 0.28 0.0219 100

Citation

@inproceedings{velikzhanin2023bresenham,
  title={A Bresenham-based Global Path Planning Algorithm on Grid Maps},
  author={Velikzhanin, Artem and Skarga-Bandurova, Inna},
  booktitle={2023 13th International Conference on Dependable Systems, Services and Technologies (DESSERT)},
  pages={1--8},
  year={2023},
  organization={IEEE}
}

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MIT

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A Bresenham's line based global path planning algorithm. A recursive path planning algorithm was developed that operates on the grid maps represented by a masked array and solves potential looping problems using a state machine-based loop breaking mechanism.

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