MASP: Scalable Graph-Based Planning Towards Multi-UAV Navigation
Abstract
1. Introduction
- Proposing a hierarchical multi-UAV navigation planner, Multi-UAV Scalable Graph-based Planner (MASP), to decompose a large exploration space into multiple goal-conditioned subspaces, enhancing sample efficiency in a large exploration space.
- Representing drones and goals as graphs and applying an attention-based mechanism and a group division mechanism to ensure scalability to arbitrary numbers of drones and promote effective cooperation.
- Compared to planning-based competitors, enhancing task efficiency by over 19.12% in MPE with 50 drones and 27.92% in OmniDrones with 20 drones (referred to Section 5.5.1), and achieving at least a 47.87% enhancement across varying team sizes (referred to Section 5.5.2).
2. Related Work
2.1. Multi-UAV Navigation
2.2. Goal-Conditioned HRL
2.3. Graph Neural Networks
3. Problem Formulation
4. Methodology
4.1. Overview
4.2. The High-Level Policy: Goal Matcher
4.3. The Low-Level Policy: Coordinated Action Executor
- A complete bonus for successfully reaching the assigned goal, , which is 1 if agent k reaches its assigned goal, otherwise 0.
- A distance penalty for task efficiency, , which is the negative L2 distance between agent k and its assigned goal.
- A collision penalty for collision avoidance, , computed based on the number of collisions at each time step.
4.4. Multi-UAV Scalable Graph-Based Planner Training
Algorithm 1 Training Procedure of MASP |
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5. Experiments
5.1. Testbeds
5.2. Implementation Details
5.3. Evaluation Metrics
- Success Rate (SR): This metric measures the average ratio of goals reached by the drones to the total goals per episode.
- Steps: This metric represents the average timesteps required to reach 100% Success Rate per episode.
- Collisions: This metric denotes the average number of collisions per step.
- Execution Time: This metric represents the time required for evaluation, measured in milliseconds (ms).
- Memory Usage: This metric represents the memory size required for evaluation, measured in Gigabyte (GB).
- Network Parameters: This metric refers to the number of network parameters needed for each RL-based method.
5.4. Baselines
- ORCA [7]: ORCA is an obstacle avoidance algorithm that excels in multi-UAV scenarios. It predicts the movements of surrounding obstacles and other drones, and then infers a collision-free velocity for each drone.
- Voronoi [9]: A Voronoi diagram comprises a set of continuous polygons, with a vertical bisector of lines connecting two adjacent points. By partitioning the map into Voronoi units, a safe path can be planned from the starting point to the destination.
- MAPPO [12]: MAPPO is a straightforward extension of PPO in the multi-agent setting, where each agent is equipped with a policy with a shared set of parameters. MAPPO is updated based on the aggregated trajectories from all drones. Additionally, an attention mechanism is applied to enhance the model’s performance.
- (H)MAPPO [12]: (H)MAPPO adopts a hierarchical framework, with the Hungarian algorithm as the high-level policy for goal assignment and MAPPO as the low-level policy for goal achievement.
- DARL1N [25]: DARL1N is under an independent decision-making setting for large-scale agent scenarios. It breaks the curse of dimensionality by restricting the agent interactions to one-hop neighborhoods. This method is extended to multi-UAV navigation tasks.
- HTAMP [38]: This is a hierarchical method for task and motion planning via reinforcement learning, integrating high-level task generation with low-level action execution.
- MAGE-X [14]: This is a hierarchical approach applied in multi-UAV navigation tasks. It first centrally allocates target goals to the drones at the beginning of the episode and then utilizes GNNs to construct a subgraph only with important neighbors for higher cooperation.
5.5. Main Results
5.5.1. Training with a Fixed Team Size
5.5.2. Varying Team Sizes Within an Episode
5.6. Robustness Evaluation in Noisy and Realistic Environments
5.7. Computational Cost
5.8. Sensitivity Analysis
5.9. Ablation Studies
- MASP w. RG: GM is replaced by random sampling, assigning each drone a random yet distinct goal.
- GM w.o. Graph: An MLP layer is adopted as an alternative to GM for assigning goals to drones at each high-level step. For drone k, the MLP layer takes in the concatenated position information of all drones and goals, with the position information of drone k listed first.
- CAE w.o. Graph: An MLP layer is employed as an alternative to CAE to capture the correlation between drones and goals. The input for drone k comprises the position of all drones and the assigned goal for drone k.
- MASP w. GraphSAGE: GM and Group Information Fusion module in CAE are replaced with GraphSAGE [54]. GraphSAGE generates embeddings by sampling and aggregating features from a node’s local neighborhood.
5.10. Strategies Analysis
6. Conclusions
7. Limitation
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Agents | Metrics | (H)ORCA | (H)RRT* | (H)Voronoi | (H)MAPPO | MAPPO | DARL1N | HTAMP | MAGE-X | MASP |
---|---|---|---|---|---|---|---|---|---|---|
N = 5 | Steps↓ | 16.38(0.53) | 7.58(1.49) | 8.86(1.27) | 8.04(1.53) | 8.69(1.24) | ∖ | ∖ | 14.75(0.60) | 7.54(1.37) |
SR↑ | 0.72(0.01) | 0.99(0.01) | 0.98(0.01) | 1.00(0.00) | 1.00(0.00) | 0.74(0.02) | 0.65(0.05) | 1.00(0.00) | 1.00(0.00) | |
Collisions↓ | 0.57(0.03) | 3.41(0.14) | 3.44(0.25) | 0.42(0.02) | 1.32(0.38) | 2.80(0.53) | 1.63(0.43) | 0.45(0.02) | 0.47(0.01) | |
N = 20 | Steps↓ | 34.28(3.22) | 26.86(2.27) | 28.72(2.68) | 27.43(2.49) | ∖ | ∖ | ∖ | ∖ | 24.41(2.66) |
SR↑ | 0.95(0.03) | 0.99(0.01) | 1.00(0.00) | 1.00(0.00) | 0.71(0.02) | 0.62(0.03) | 0.05(0.01) | 0.75(0.02) | 1.00(0.00) | |
Collisions↓ | 0.49(0.04) | 1.69(0.05) | 1.80(0.03) | 0.75(0.05) | 2.53(1.02) | 3.22(1.23) | 1.54(0.05) | 1.78(0.14) | 0.14(0.01) | |
N = 50 | Steps↓ | 60.66(4.76) | 58.68(3.89) | 57.88(5.43) | 51.88(4.06) | ∖ | ∖ | ∖ | ∖ | 47.46(5.93) |
SR↑ | 0.97(0.01) | 0.99(0.01) | 0.99(0.01) | 0.99(0.01) | 0.01(0.01) | 0.49(0.02) | 0.02(0.01) | 0.23(0.01) | 0.99(0.01) | |
Collisions↓ | 0.30(0.02) | 1.39(0.14) | 1.31(0.42) | 0.42(0.75) | 0.78(0.26) | 1.14(0.34) | 1.35(0.21) | 1.69(0.37) | 0.23(0.01) |
Agents | Metrics | (H)ORCA | (H)RRT* | (H)Voronoi | (H)MAPPO | MAPPO | DARL1N | HTAMP | MAGE-X | MASP |
---|---|---|---|---|---|---|---|---|---|---|
N = 5 | Steps↓ | 260.10(10.02) | 236.10(9.47) | 173.89(12.91) | 185.34(7.14) | ∖ | ∖ | ∖ | 231.26(19.32) | 138.35(13.57) |
SR↑ | 0.98(0.03) | 0.97(0.01) | 0.99(0.02) | 1.00(0.00) | 0.50(0.09) | 0.68(0.02) | 0.32(0.08) | 0.99(0.01) | 1.00(0.00) | |
Collisions↓ | 0.00(0.00) | 0.01(0.01) | 0.02(0.01) | 0.01(0.01) | 0.01(0.01) | 0.01(0.01) | 0.01(0.01) | 0.01(0.01) | 0.00(0.00) | |
N = 20 | Steps↓ | 449.10(14.86) | 438.23(11.02) | 437.43(14.24) | 335.74(13.07) | ∖ | ∖ | ∖ | ∖ | 315.31(14.52) |
SR↑ | 0.97(0.03) | 0.97(0.01) | 0.93(0.01) | 0.96(0.01) | 0.15(0.03) | 0.15(0.01) | 0.14(0.03) | 0.14(0.03) | 0.97(0.01) | |
Collisions↓ | 0.01(0.03) | 0.03(0.03) | 0.01(0.03) | 0.01(0.01) | 0.03(0.02) | 0.05(0.01) | 0.04(0.02) | 0.08(0.02) | 0.01(0.01) |
Agents | Metrics | (H)ORCA | (H)RRT* | (H)Voronoi | MASP |
---|---|---|---|---|---|
Steps↓ | 43.64(3.86) | 40.68(3.37) | 40.18(3.41) | 22.38(3.04) | |
SR↑ | 0.89(0.01) | 0.92(0.01) | 0.93(0.01) | 1.00(0.00) | |
Collisions↓ | 0.18(0.02) | 0.72(0.14) | 0.86(0.13) | 0.16(0.03) | |
Steps↓ | ∖ | 89.18(4.88) | 88.73(4.27) | 46.49(4.49) | |
SR↑ | 0.86(0.01) | 0.91(0.01) | 0.91(0.02) | 1.00(0.00) | |
Collisions↓ | 0.15(0.03) | 0.56(0.05) | 0.67(0.03) | 0.15(0.01) |
Agents | Metrics | (H)ORCA | (H)RRT* | (H)Voronoi | MASP |
---|---|---|---|---|---|
Steps↓ | ∖ | ∖ | 490.35(15.63) | 426.73(18.50) | |
SR↑ | 0.68(0.04) | 0.61(0.04) | 0.85(0.03) | 0.94(0.01) | |
Collisions↓ | 0.00(0.00) | 0.01(0.01) | 0.01(0.01) | 0.01(0.01) |
Agents | Metrics | (H)ORCA | (H)RRT* | (H)Voronoi | MASP |
---|---|---|---|---|---|
Steps↓ | 228.05(14.52) | 269.20(13.78) | 203.65(10.71) | 146.38(10.83) | |
SR↑ | 0.94(0.02) | 0.87(0.03) | 0.93(0.02) | 0.98(0.02) | |
Collisions↓ | 0.01(0.01) | 0.02(0.01) | 0.01(0.01) | 0.01(0.01) | |
Steps↓ | 408.10(10.40) | 484.50(16.95) | 453.35(13.38) | 334.62(11.53) | |
SR↑ | 0.98(0.02) | 0.92(0.02) | 0.91(0.03) | 0.96(0.01) | |
Collisions↓ | 0.01(0.01) | 0.01(0.01) | 0.01(0.01) | 0.01(0.01) | |
Steps↓ | ∖ | ∖ | ∖ | 439.62(13.02) | |
SR↑ | 0.75(0.02) | 0.57(0.02) | 0.85(0.02) | 0.90(0.01) | |
Collisions↓ | 0.02(0.01) | 0.01(0.01) | 0.01(0.01) | 0.01(0.01) |
Agents | Metrics | GM | CAE | MASP |
---|---|---|---|---|
N = 100 | Memory Usage↓ | 1.28 | 0.72 | 2 |
Execution Time↓ | 11(1) | 7(1) | 18(2) |
Methods | ORCA | RRT* | Voronoi | MAPPO | DARL1N | HTAMP | MAGE-X | MASP |
---|---|---|---|---|---|---|---|---|
Execution Time↓ | 39(6) | 456(10) | 44(5) | 13(4) | 16(3) | 14(3) | 20(5) | 14(2) |
Agents | Metrics | 2 | 3 | 5 |
---|---|---|---|---|
N = 20 | Steps↓ | 28.85(2.12) | 24.41(2.66) | 23.78(2.35) |
SR↑ | 1.00(0.00) | 1.00(0.00) | 1.00(0.00) | |
Collisions↓ | 0.15(0.01) | 0.14(0.01) | 0.14(0.01) | |
Network Parameters↓ | P | ~2P | ~5P |
Agents | Metrics | 1 | 3 | 10 |
---|---|---|---|---|
N = 20 | Steps↓ | 24.23(2.11) | 24.41(2.66) | 29.59(2.43) |
SR↑ | 1.00(0.00) | 1.00(0.00) | 1.00(0.00) | |
Collisions↓ | 0.12(0.01) | 0.14(0.01) | 0.16(0.01) | |
Execution Time↓ | 45(7) | 13(4) | 4(2) |
Agents | Metrics | 8 | 32 | 64 |
---|---|---|---|---|
N = 20 | Steps↓ | 28.66(2.73) | 24.41(2.66) | 24.82(2.00) |
SR↑ | 1.00(0.00) | 1.00(0.00) | 1.00(0.00) | |
Collisions↓ | 0.18(0.01) | 0.14(0.01) | 0.13(0.01) | |
Network Parameters↓ | P | ~4P | ~9P |
Agents | Metrics | MASP w. RG | GM w.o. Graph | CAE w.o. Graph | MASP w. GraphSAGE | MASP w. GATv2 | MASP |
---|---|---|---|---|---|---|---|
N = 20 | Steps↓ | 35.91(2.73) | ∖ | 28.25(3.21) | 38.97(3.22) | 28.17(2.40) | 24.41(2.66) |
SR↑ | 1.00(0.00) | 0.04(0.01) | 1.00(0.00) | 0.85(0.04) | 0.98(0.03) | 1.00(0.00) | |
Collisions↓ | 0.25(0.02) | 3.32(0.02) | 0.17(0.01) | 1.26(0.03) | 0.83(0.02) | 0.14(0.01) |
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Share and Cite
Yang, X.; Yang, X.; Yu, C.; Chen, J.; Ding, W.; Yang, H.; Wang, Y. MASP: Scalable Graph-Based Planning Towards Multi-UAV Navigation. Drones 2025, 9, 463. https://doi.org/10.3390/drones9070463
Yang X, Yang X, Yu C, Chen J, Ding W, Yang H, Wang Y. MASP: Scalable Graph-Based Planning Towards Multi-UAV Navigation. Drones. 2025; 9(7):463. https://doi.org/10.3390/drones9070463
Chicago/Turabian StyleYang, Xinyi, Xinting Yang, Chao Yu, Jiayu Chen, Wenbo Ding, Huazhong Yang, and Yu Wang. 2025. "MASP: Scalable Graph-Based Planning Towards Multi-UAV Navigation" Drones 9, no. 7: 463. https://doi.org/10.3390/drones9070463
APA StyleYang, X., Yang, X., Yu, C., Chen, J., Ding, W., Yang, H., & Wang, Y. (2025). MASP: Scalable Graph-Based Planning Towards Multi-UAV Navigation. Drones, 9(7), 463. https://doi.org/10.3390/drones9070463