A Two-Stage Path Planning Algorithm Based on Rapid-Exploring Random Tree for Ships Navigating in Multi-Obstacle Water Areas Considering COLREGs
Abstract
:1. Introduction
2. Literature Review
2.1. Global Path Planning
2.2. Local Path Planning
2.3. RRT Algorithm
3. Methodologies
3.1. The RRT Algorithm
Algorithm 1: RRT algorithm expand spanning tree | |
Input: Start point Pstart; Goal point Pgoal; Set of static obstacles Osta; Distance step Dp; Samples probability Pr | |
Output: The RRT tree Ar | |
1: | Create an array Ar as RRT tree and put the start point Pstart as its head node; |
2: | While Pgoal not in Ar |
3: | Generated a random number Rn between (0,1); |
4: | If Rn > Pr |
5: | Sample a sampling point Xrand in free space; |
6: | Else |
7: | Set goal point Pgoal as sampling point; |
8: | End If |
9: | Get nearest point form the sampling point Xnearest; |
10: | Generate new node Xnew with distance step Dp form Xnearest; |
11: | If no risk from Xnearest to Xnew with Osta |
12: | Append Xnew to Ar; |
13: | Else |
14: | Go to line 2; |
15: | End If |
16: | If distance between Xnew and Pgoal < Dp & no risk from Xnew to Pgoal with Osta |
17: | Append Pgoal to Ar; |
18: | End If |
19: | End While |
20: | Return Ar |
3.2. Global Path Planning Based on RRT Algorithm
3.2.1. Navigable Map Construction Considering Grounding Risk
3.2.2. Sampling Space and Iterative Optimization
3.2.3. Global Path Planning Algorithm Based on RRT Algorithm
Algorithm 2: Global path planning algorithm based on RRT algorithm | |
Input: Start point Pstart; Goal point Pgoal; Set of static obstacles Osta; Distance step Dp; Samples probability Pr; Origin path Pathrrt; Optimized path Patho; Iterative time N | |
Output: The result of global path planning Pathg | |
1: | Calculate the path length of Pathrrt (Lp), Lse and Ld |
2: | For i = 1,2,…N do |
3: | Construct or update elliptic sampling space |
4: | Pathi generation based on RRT algorithm and ellipse sampling space |
5: | Sent Pathi to smooth optimization |
6: | Calculate the length Ls of Pathi after smooth optimization |
7: | If Ls < Lp |
8: | Assign Ls to the major axis Lp and update Ld; |
9: | Set Pathi as the optimized path Patho; |
10: | End If |
11: | End For |
12: | Return Pathg = Patho |
3.3. Local Path Planning under Dynamic Collision Risk
3.3.1. Dynamical Collision Risk Detection Based on Ship Domain
3.3.2. The Restriction of Ship Manoeuvrability and COLREGs
- 1.
- Ship manoeuvrability restriction
- 2.
- Sampling space selection considering COLREGs restriction
3.3.3. Local Path Planning Algorithm
Algorithm 3: Local path planning algorithm under ship dynamic collision risk | |
Input: OS position Xown; Next waypoint Xnp; static obstacles Osta; Distance step Dp; Dynamic obstacles Odyn; Samples probability Pr; Iterative time M; maximum turning angle Amax | |
Output: Local planned path Pathl | |
1: | Create an array Al to store Local planned path Pathl |
2: | Set Xown and Xnp as the start and end point in local path planning; |
3: | Calculate the distance don between Xown and Xnp; |
4: | While Xnp not in Al |
5: | Constructed the elliptic sampling space, Lp = 3 * don, Lse = don; |
6: | Update the sampling space according to the ship encounter situation |
7: | Generated a random number Rn between (0, 1); |
8: | If Rn > Pr |
9: | Sample a sampling point Xrand in free space; |
10: | Else |
11: | Set goal point Xnp as sampling point; |
12: | End If |
13: | Get nearest point form the sampling point Xnearest; |
14: | Generate new node Xnew with distance step Dp form Xnearest; |
15: | Calculate the angle Anew between the Xnew and Xnearest |
16: | If Anew < Amax |
17: | If no risk from Xnearest to Xnew with Osta and Odyn //using dynamic risk detection model to judge |
18: | Append Xnew to Al; |
19: | Else |
20: | Go to line 7; |
21: | End If |
22: | Calculate the distance dng between Xnew and Xnp; |
23: | If dng < Dp & no risk from Xnew to Xnp with Osta and Odyn |
24: | Append Xnp to Al; |
25: | End If |
26: | Else |
27: | Go to line 7 |
28: | End If |
29: | End While |
30: | Return Pathl = Al |
4. Results and Discussion
4.1. The Experimental Situation
4.2. Result of Global Path Planning
4.3. Result of Local Path Planning
4.3.1. Overtaking Situation
4.3.2. Crossing Situation
4.3.3. Head-On Situation
4.4. Discussion and Analysis
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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No. | Nodes Position/n miles | |||||
---|---|---|---|---|---|---|
RRT | RRTe | RRTes | ||||
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
2 | 1.84 | 0.72 | 1.67 | 1.07 | 6.46 | 4.98 |
3 | 3.60 | 1.64 | 3.05 | 2.49 | 16.05 | 13.60 |
4 | 5.11 | 2.91 | 4.63 | 3.67 | 20.00 | 20.00 |
5 | 6.41 | 4.41 | 6.27 | 4.78 | The shortest path length: RRT: 29.01 n miles; RRTe: 28.73 n miles; RRTes: 28.57 n miles. | |
6 | 7.71 | 5.90 | 7.92 | 5.89 | ||
7 | 9.47 | 6.83 | 9.28 | 7.32 | ||
8 | 10.85 | 8.24 | 10.87 | 8.50 | ||
9 | 12.19 | 9.69 | 12.27 | 9.90 | ||
10 | 13.56 | 11.13 | 13.49 | 11.47 | ||
11 | 15.00 | 12.49 | 15.00 | 12.74 | ||
12 | 16.15 | 14.10 | 16.30 | 14.24 | ||
13 | 17.68 | 15.36 | 17.70 | 15.63 | ||
14 | 18.88 | 16.93 | 18.37 | 17.49 | ||
15 | 19.56 | 18.79 | 19.45 | 19.15 | ||
16 | 20.00 | 20.00 | 20.00 | 20.00 |
Own Ship (OS) | Target ship (TSs) | Distance /n Miles | Situation | ||||
---|---|---|---|---|---|---|---|
Position/n Miles | Heading/◦ | Speed/kn | Position/n Miles | Heading/◦ | Speed/kn | ||
(0.0, 0.0) | 52.4 | 12.6 | (1.43, 1.10) | 52.4 | 6.3 | 1.80 | Overtaking |
(6.46, 4.98) | 48.0 | (14.45, 4.56) | 318.0 | 12.6 | 8.00 | Crossing | |
(16.05, 13.60) | 31.7 | (20.0, 20.0) | 211.7 | 14.4 | 7.52 | Head-on |
Time/s | Global Path Planning | Local Path Planning | ||
---|---|---|---|---|
Overtaking | Crossing | Head-On | ||
Average | 77.73 | 37.48 | 43.18 | 34.24 |
Maximum | 162.73 | 50.61 | 57.53 | 54.81 |
Minimum | 36.73 | 27.90 | 31.25 | 14.88 |
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Zhang, J.; Zhang, H.; Liu, J.; Wu, D.; Soares, C.G. A Two-Stage Path Planning Algorithm Based on Rapid-Exploring Random Tree for Ships Navigating in Multi-Obstacle Water Areas Considering COLREGs. J. Mar. Sci. Eng. 2022, 10, 1441. https://doi.org/10.3390/jmse10101441
Zhang J, Zhang H, Liu J, Wu D, Soares CG. A Two-Stage Path Planning Algorithm Based on Rapid-Exploring Random Tree for Ships Navigating in Multi-Obstacle Water Areas Considering COLREGs. Journal of Marine Science and Engineering. 2022; 10(10):1441. https://doi.org/10.3390/jmse10101441
Chicago/Turabian StyleZhang, Jinfen, Han Zhang, Jiongjiong Liu, Da Wu, and C. Guedes Soares. 2022. "A Two-Stage Path Planning Algorithm Based on Rapid-Exploring Random Tree for Ships Navigating in Multi-Obstacle Water Areas Considering COLREGs" Journal of Marine Science and Engineering 10, no. 10: 1441. https://doi.org/10.3390/jmse10101441