Journal of Graphics ›› 2024, Vol. 45 ›› Issue (3): 505-515.DOI: 10.11996/JG.j.2095-302X.2024030505
• Computer Graphics and Virtual Reality • Previous Articles Next Articles
JIA Mingchao1(
), FENG Bin2, WU Peng1, ZHANG Kun1, SANG Shengju2(
)
Received:2023-08-31
Accepted:2023-11-27
Online:2024-06-30
Published:2024-06-11
Contact:
SANG Shengju (1965-), professor, Ph.D. His main research interests cover robotics, embedded technology, etc. E-mail:About author:JIA Mingchao (1998-), master student. His main research interest covers path planning. E-mail:1216135454@qq.com
Supported by:CLC Number:
JIA Mingchao, FENG Bin, WU Peng, ZHANG Kun, SANG Shengju. A path planning for cultural tourism service robot combining improved A* algorithm and improved dynamic window approach[J]. Journal of Graphics, 2024, 45(3): 505-515.
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URL: http://www.txxb.com.cn/EN/10.11996/JG.j.2095-302X.2024030505
| α | 舍弃的搜索方向 |
|---|---|
| 0 | n1,n4,n6 |
| (0,90°) | n4,n6,n7 |
| 90° | n6,n7,n8 |
| (90°,180°) | n5,n7,n8 |
| 180°或-180° | n3,n5,n8 |
| (-180°,-90°) | n2,n3,n5 |
| -90° | n1,n2,n3 |
| (-90°,0) | n1,n2,n4 |
Table 1 Search neighborhood selection strategy
| α | 舍弃的搜索方向 |
|---|---|
| 0 | n1,n4,n6 |
| (0,90°) | n4,n6,n7 |
| 90° | n6,n7,n8 |
| (90°,180°) | n5,n7,n8 |
| 180°或-180° | n3,n5,n8 |
| (-180°,-90°) | n2,n3,n5 |
| -90° | n1,n2,n3 |
| (-90°,0) | n1,n2,n4 |
| 向量A方向 | 向量B方向 | 半径R | 圆心点Ox | 圆心点Oy | 起始弧度F | 终止弧度S |
|---|---|---|---|---|---|---|
| ↑ | ↗ | R | x1+R | (y1+y2)/2 | π | 3π/4 |
| ↑ | ↖ | R | x1-R | (y1+y2)/2 | 0 | π/4 |
| → | ↗ | R | (x1+x2)/2 | y1+R | -π/2 | -π/4 |
| → | ↘ | R | (x1+x2)/2 | y1-R | π/2 | π/4 |
| ↓ | ↘ | R | x1+R | (y1+y2)/2 | -π | -3π/4 |
| ↓ | ↙ | R | x1-R | (y1+y2)/2 | 0 | -π/4 |
| ← | ↙ | R | (x1+x2)/2 | y1-R | π/2 | 3π/4 |
| ← | ↖ | R | (x1+x2)/2 | y1+R | -π/2 | -3π/4 |
| ↗ | ↑ | R | x2-R | (y3+y2)/2 | -π/4 | 0 |
| ↗ | → | R | (x3+x2)/2 | y2-R | 3π/4 | π/2 |
| ↘ | → | R | (x3+x2)/2 | y2+R | -3π/4 | -π/2 |
| ↘ | ↓ | R | x2-R | (y3+y2)/2 | π/4 | 0 |
| ↙ | ↓ | R | x2+R | (y3+y2)/2 | 3π/4 | π |
| ↙ | ← | R | (x3+x2)/2 | y2+R | -π/4 | -π/2 |
| ↖ | ↑ | R | x2+R | (y3+y2)/2 | -3π/4 | -π |
| ↖ | ← | R | (x3+x2)/2 | y2-R | π/4 | π/2 |
| ↑ | → | 1/2 | (x1+x3)/2 | (y1+y3)/2 | π | π/2 |
| ↑ | ← | 1/2 | (x1+x3)/2 | (y1+y3)/2 | 0 | π/2 |
| → | ↑ | 1/2 | (x1+x3)/2 | (y1+y3)/2 | -π/2 | 0 |
| → | ↓ | 1/2 | (x1+x3)/2 | (y1+y3)/2 | π/2 | 0 |
| ↓ | → | 1/2 | (x1+x3)/2 | (y1+y3)/2 | -π | -π/2 |
| ↓ | ← | 1/2 | (x1+x3)/2 | (y1+y3)/2 | 0 | -π/2 |
| ← | ↑ | 1/2 | (x1+x3)/2 | (y1+y3)/2 | -π/2 | -π |
| ← | ↓ | 1/2 | (x1+x3)/2 | (y1+y3)/2 | π/2 | π |
Table 2 Arc optimization calculation result table
| 向量A方向 | 向量B方向 | 半径R | 圆心点Ox | 圆心点Oy | 起始弧度F | 终止弧度S |
|---|---|---|---|---|---|---|
| ↑ | ↗ | R | x1+R | (y1+y2)/2 | π | 3π/4 |
| ↑ | ↖ | R | x1-R | (y1+y2)/2 | 0 | π/4 |
| → | ↗ | R | (x1+x2)/2 | y1+R | -π/2 | -π/4 |
| → | ↘ | R | (x1+x2)/2 | y1-R | π/2 | π/4 |
| ↓ | ↘ | R | x1+R | (y1+y2)/2 | -π | -3π/4 |
| ↓ | ↙ | R | x1-R | (y1+y2)/2 | 0 | -π/4 |
| ← | ↙ | R | (x1+x2)/2 | y1-R | π/2 | 3π/4 |
| ← | ↖ | R | (x1+x2)/2 | y1+R | -π/2 | -3π/4 |
| ↗ | ↑ | R | x2-R | (y3+y2)/2 | -π/4 | 0 |
| ↗ | → | R | (x3+x2)/2 | y2-R | 3π/4 | π/2 |
| ↘ | → | R | (x3+x2)/2 | y2+R | -3π/4 | -π/2 |
| ↘ | ↓ | R | x2-R | (y3+y2)/2 | π/4 | 0 |
| ↙ | ↓ | R | x2+R | (y3+y2)/2 | 3π/4 | π |
| ↙ | ← | R | (x3+x2)/2 | y2+R | -π/4 | -π/2 |
| ↖ | ↑ | R | x2+R | (y3+y2)/2 | -3π/4 | -π |
| ↖ | ← | R | (x3+x2)/2 | y2-R | π/4 | π/2 |
| ↑ | → | 1/2 | (x1+x3)/2 | (y1+y3)/2 | π | π/2 |
| ↑ | ← | 1/2 | (x1+x3)/2 | (y1+y3)/2 | 0 | π/2 |
| → | ↑ | 1/2 | (x1+x3)/2 | (y1+y3)/2 | -π/2 | 0 |
| → | ↓ | 1/2 | (x1+x3)/2 | (y1+y3)/2 | π/2 | 0 |
| ↓ | → | 1/2 | (x1+x3)/2 | (y1+y3)/2 | -π | -π/2 |
| ↓ | ← | 1/2 | (x1+x3)/2 | (y1+y3)/2 | 0 | -π/2 |
| ← | ↑ | 1/2 | (x1+x3)/2 | (y1+y3)/2 | -π/2 | -π |
| ← | ↓ | 1/2 | (x1+x3)/2 | (y1+y3)/2 | π/2 | π |
Fig. 6 Improved A* algorithm simulation experiment comparison ((a) Traditional A* algorithm; (b) Only improve the evaluation function; (c) Only improve the neighborhood selection strategy; (d) Only improved cubic polyline optimization; (e) Ours)
| 算法 | 路径长度/m | 路径节点数目 | 拐点数目 | 遍历节点数目 | 运行时间/s | 密集区域 | 减速程度 | 禁止区域 |
|---|---|---|---|---|---|---|---|---|
| 传统A*算法 | 30.727 9 | 28 | 9 | 826 | 0.050 5 | 穿越 | 不适当 | 穿越 |
| 仅改进评价函数 | 33.313 7 | 31 | 10 | 410 | 0.007 3 | 否 | 适当 | 否 |
| 仅改进搜索策略 | 30.727 9 | 28 | 8 | 488 | 0.011 8 | 穿越 | 不适当 | 穿越 |
| 仅改进折线优化 | 30.213 9 | 8 | 6 | 826 | 0.059 5 | 穿越 | 不适当 | 穿越 |
| 本文算法 | 32.570 6 | 9 | 7 | 253 | 0.008 4 | 否 | 适当 | 否 |
Table 3 Improved A* algorithm simulation experimental data
| 算法 | 路径长度/m | 路径节点数目 | 拐点数目 | 遍历节点数目 | 运行时间/s | 密集区域 | 减速程度 | 禁止区域 |
|---|---|---|---|---|---|---|---|---|
| 传统A*算法 | 30.727 9 | 28 | 9 | 826 | 0.050 5 | 穿越 | 不适当 | 穿越 |
| 仅改进评价函数 | 33.313 7 | 31 | 10 | 410 | 0.007 3 | 否 | 适当 | 否 |
| 仅改进搜索策略 | 30.727 9 | 28 | 8 | 488 | 0.011 8 | 穿越 | 不适当 | 穿越 |
| 仅改进折线优化 | 30.213 9 | 8 | 6 | 826 | 0.059 5 | 穿越 | 不适当 | 穿越 |
| 本文算法 | 32.570 6 | 9 | 7 | 253 | 0.008 4 | 否 | 适当 | 否 |
| 组别 | X | K | 性能指标 |
|---|---|---|---|
| 1 | 0.30 | 79 | 穿越障碍物密集区域 |
| 2 | 0.30 | 80 | 穿越障碍物密集区域 |
| 3 | 0.30 | 81 | 穿越障碍物密集区域 |
| 4 | 0.10 | 79 | 穿越障碍物狭窄区域 |
| 5 | 0.10 | 80 | 穿越障碍物狭窄区域 |
| 6 | 0.10 | 81 | 穿越障碍物狭窄区域 |
| 7 | 0.06 | 79 | 穿越障碍物狭窄区域 |
| 8 | 0.06 | 80 | 穿越障碍物狭窄区域 |
| 9 | 0.06 | 81 | 穿越障碍物狭窄区域 |
| 10 | 0.05 | 79 | 穿越障碍物狭窄区域 |
| 11 | 0.05 | 80 | 路径质量优 |
| 12 | 0.05 | 81 | 路径质量较优 |
| 13 | 0.05 | 100 | 穿越减速慢行区域 |
| 14 | 0.04 | 80 | 路径拐点数目增多 |
| 15 | 0.03 | 80 | 路径拐点数目增多 |
Table 4 Parameter debugging experiment
| 组别 | X | K | 性能指标 |
|---|---|---|---|
| 1 | 0.30 | 79 | 穿越障碍物密集区域 |
| 2 | 0.30 | 80 | 穿越障碍物密集区域 |
| 3 | 0.30 | 81 | 穿越障碍物密集区域 |
| 4 | 0.10 | 79 | 穿越障碍物狭窄区域 |
| 5 | 0.10 | 80 | 穿越障碍物狭窄区域 |
| 6 | 0.10 | 81 | 穿越障碍物狭窄区域 |
| 7 | 0.06 | 79 | 穿越障碍物狭窄区域 |
| 8 | 0.06 | 80 | 穿越障碍物狭窄区域 |
| 9 | 0.06 | 81 | 穿越障碍物狭窄区域 |
| 10 | 0.05 | 79 | 穿越障碍物狭窄区域 |
| 11 | 0.05 | 80 | 路径质量优 |
| 12 | 0.05 | 81 | 路径质量较优 |
| 13 | 0.05 | 100 | 穿越减速慢行区域 |
| 14 | 0.04 | 80 | 路径拐点数目增多 |
| 15 | 0.03 | 80 | 路径拐点数目增多 |
| 算法 | 路径长度/ m | 路径节点 数目 | 是否有曲率 突变 |
|---|---|---|---|
| 传统A*算法 | 26.000 0 | 27 | 是 |
| 圆弧优化 | 24.258 1 | 54 | 否 |
Table 5 Smoothness optimization simulation data
| 算法 | 路径长度/ m | 路径节点 数目 | 是否有曲率 突变 |
|---|---|---|---|
| 传统A*算法 | 26.000 0 | 27 | 是 |
| 圆弧优化 | 24.258 1 | 54 | 否 |
Fig. 9 Complex environment fusion algorithm simulation experiment ((a) Initial global path; (b) Set up obstacles; (c) Get around dynamic obstacles; (d) Get around static obstacles one; (e) Get around static obstacles two; (f) The final path of the fusion algorithm)
Fig. 10 Narrow environment fusion algorithm simulation experiment ((a) Initial global path; (b) Get around obstacles; (c) The final path of the fusion algorithm)
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