Provably safe coordinated navigation of cross-domain UAV-USV systems: extending the distributed guiding-vector-field framework to inter-vehicle collision avoidance, obstacle-dense and strongly heterogeneous settings, and coverage control

Hu, Zhang, Liu, Ding, Xu, Luo, and Cao (IEEE TCST 2024) proposed a distributed guiding-vector-field (DGVF) controller that makes heterogeneous unmanned aerial vehicles (UAVs) and unmanned surface vehicles (USVs) converge to prescribed paths and coordinate their formation, using only lightweight scalar communication, with asymptotic convergence proofs and real-lake experiments. The framework, however, assumes an obstacle-free environment and simplified vehicle models (second-order integrator UAVs, 3-DOF practical underactuated USV models), only sketches a control-barrier-function-based quadratic-program (CBF-QP) safety filter for inter-vehicle collision avoidance without any analysis, and addresses path navigation only. The open problem is to extend the DGVF coordinated-navigation framework so that its coordination and convergence guarantees survive the addition of provable safety guarantees and realistic constraints: (i) rigorous inter-vehicle collision-avoidance guarantees (e.g., via the CBF-QP construction the paper sketches) with joint safety and convergence analysis; (ii) operation in obstacle-dense environments; (iii) strongly heterogeneous vehicle dynamics beyond the simplified models; and (iv) a cross-domain coverage controller built on the same coordination technique. No existing work resolves any of these threads for cross-domain UAV-USV systems.

Background

A cross-domain unmanned system (CDUS) is a team of robots operating across physical domains — here, UAVs flying in 3D space and USVs moving on the 2D water surface — cooperating on maritime-air missions such as reconnaissance, detection, and rescue. Coordinating such teams is harder than coordinating a single-domain fleet: the vehicles obey different equations of motion, sense at different scales, and communicate over constrained wireless links. Guiding vector fields (GVFs) are a path-following technique in which a vector field is constructed from a desired path so that the field's integral curves converge onto the path; a vehicle that tracks the field's direction converges to the path. Hu et al. (IEEE Transactions on Control Systems Technology, vol. 32, no. 2, pp. 550-563, 2024; arXiv:2312.10946) introduced a distributed guiding-vector-field (DGVF) controller for CDUSs with a two-level architecture: an upper-level heterogeneous guidance-velocity controller that drives all vehicles to their prescribed paths while synchronizing their positions along the paths (formation coordination), and a lower-level tracking regulator that makes each vehicle follow its commanded guidance signals. The remarkable economy of the scheme is that coordination between neighboring UAVs and USVs is achieved by communicating only a single scalar per neighbor — the path parameter or 'virtual coordinate'. The vehicles are modeled, respectively, as second-order integrators (a point-mass model $\ddot{q}=\tau$ with acceleration input $\tau$, standard for UAVs whose fast inner-loop attitude control is abstracted away) and as 3-DOF underactuated surface vessels (surge, sway, and yaw velocities $u,v,r$, where the sway direction has no actuator). The paper proves asymptotic convergence of path-following errors and coordination variables, assuming the lower-level tracking errors vanish exponentially, and validates the controller in real-lake experiments with three UAVs and three USVs. Two limitations are explicit. First, the setting is obstacle-free, and inter-vehicle collision avoidance is not analyzed: Remark 9 of the paper sketches how the DGVF guidance signals could be filtered by a quadratic program (QP) using control barrier functions (CBFs) — functions $\phi$ of the state whose nonnegativity defines a safe set and whose constraint $\dot{\phi}\ge-\alpha(\phi)$ renders that set forward invariant, meaning trajectories that start safe remain safe — with candidate CBFs $\phi_{i,k}=\|q_i-q_k\|^2-R^2$ enforcing a minimum separation $R$ between vehicle pairs; but the paper states explicitly that 'for the rigorous technical analysis with additional inter-vehicle collision avoidances, it will be investigated in the future work'. Second, the conclusion lists further targets: coordinated navigation 'with strongly heterogeneous dynamics' (richer vehicle models than the simplified second-order UAV and underactuated USV dynamics, e.g., nonlinearities, higher-order actuator dynamics, or time delays) and 'in obstacle-dense environments', plus development of 'a cross-domain coordination coverage controller', i.e., extending the coordination technique from path following to cooperative coverage of a region of interest. Adjacent literature clarifies what is and is not known. For single vehicles and single-domain fleets, collision avoidance has been combined with vector-field guidance: collision-free vector-field guidance plus model predictive control (MPC) for one fixed-wing UAV (Pereira et al., ICRA 2021), vector-field-based collision-avoidance guidance for a USV (Chen et al., IEEE UT 2023), GVF plus CBF formation reconfiguration for multiple USVs (Gong et al., CCDC 2022), and a rule-based GVF collision-avoidance strategy for multiple USVs with boundedness proofs but simulation-only validation (Wei et al., Drones, 2025). For generic multi-agent systems (MASs), collision-free coordination under communication constraints is studied with command governors, artificial-potential-field-like safe commands, and barrier functions (Zhao, An, and Wang, IEEE TCST 2026; Zhao, An, and Zhang, IEEE TSMC 2026) — but these are not vector-field guidance schemes and not cross-domain. Follow-ups by the source group itself address a different cross-domain task, coordinated landing of multiple UAVs onto multiple USVs (Ding et al., ICRA 2024; IEEE TIE 2026), and a 2026 conference paper applies the DGVF hierarchy to air-sea clusters with environmental disturbance models but no safety certificates (Sun et al., AIEA 2026). For coverage, existing UAV-USV work is planning-level or application-level (Fu et al., IEEE TSMC 2025, trajectory homotopy for dynamic coverage; Santos et al., IEEE Access 2024, cooperative maritime coverage), not a DGVF-based distributed coverage controller. What remains unresolved is precisely the source paper's question: whether the DGVF framework's coordination and convergence guarantees can be extended to a setting with provable inter-vehicle and obstacle collision avoidance, more strongly heterogeneous dynamics, and coverage objectives.

Problem Statement

Extend the distributed guiding-vector-field (DGVF) coordinated-navigation framework of Hu et al. (IEEE TCST, 2024) for cross-domain unmanned systems (CDUSs) of heterogeneous UAVs and USVs so that its coordination guarantees hold under realistic safety constraints, dynamics, and tasks. The common objective uniting the requested results is a DGVF-class controller for cross-domain UAV-USV fleets in which provable safety and provable coordinated path navigation coexist. Concretely, the open problem, as stated by the source paper, comprises: (1) Rigorous inter-vehicle collision-avoidance guarantees integrated into the DGVF controller — e.g., completing the CBF-QP safety-filter construction sketched in Remark 9, where each vehicle solves a quadratic program that minimally modifies its DGVF guidance signal subject to inter-vehicle barrier constraints (written in the paper as $\dot{\phi}_{i,k}\le\phi_{i,k}$ with $\phi_{i,k}=\|q_i-q_k\|^2-R^2$ and safety radius $R$, and sketched there only for same-domain USV-USV and UAV-UAV pairs; note that this literal $\le$ constraint direction in the sketch differs from the standard invariance-producing CBF condition $\dot{\phi}\ge-\alpha(\phi)$ recalled in the Background and, as written, does not by itself prevent $\phi_{i,k}$ from crossing zero downward, so the sketch functions as a design starting point rather than a certified safety condition) — together with a closed-loop analysis proving, simultaneously, forward invariance of the safe separation set (the set of states with $\|q_i-q_k\|\ge R$) for all vehicle pairs, including the cross-domain UAV-USV pairs that the sketch omits, and the asymptotic path-following and coordination convergence that the obstacle-free framework establishes; (2) coordinated navigation in obstacle-dense environments, with static and/or dynamic obstacles, including guarantees that address feasibility of the filtered guidance and behavior in cluttered scenes; (3) coordinated navigation under strongly heterogeneous vehicle dynamics beyond the simplified models used in the source (second-order integrator UAVs and 3-DOF practical underactuated USV models), e.g., nonlinearities, higher-order actuator dynamics, or time delays; and (4) a cross-domain coordination coverage controller that uses the same coordination technique (lightweight virtual-coordinate communication) to make the heterogeneous UAV-USV team cooperatively cover, monitor, or explore a region of interest, with an explicit coverage objective and corresponding guarantees. An acceptable contribution may address a subset of these threads, provided it states which thread it resolves and preserves the source framework's essential feature — distributed coordination of cross-domain UAV-USV fleets with lightweight communication — without silently restricting the setting back to obstacle-free, single-domain, or nominally homogeneous cases; that is, any scope restriction relative to the declared thread must be explicitly declared, so a thread-(1) contribution may declare an obstacle-free environment (the setting of the source framework itself), whereas an undeclared removal of obstacles from a thread-(2) answer is not admissible.

References

1. Bin-Bin Hu, Hai-Tao Zhang, Bin Liu, Jianing Ding, Yifan Xu, Chuanshang Luo, Haosen Cao, 'Coordinated Navigation Control of Cross-Domain Unmanned Systems via Guiding Vector Fields', IEEE Transactions on Control Systems Technology, vol. 32, no. 2, pp. 550-563, 2024. DOI: 10.1109/TCST.2023.3323766; arXiv:2312.10946. https://arxiv.org/abs/2312.10946 (source paper)
2. Jianing Ding, Hai-Tao Zhang, Bin-Bin Hu, Bin Liu, Jiajie Huang, Yunfei Zhang, Hesheng Wang, 'Dual-Stage Coordinated Landing Control for Cross-Domain UAV-USV Fleets', IEEE Transactions on Industrial Electronics, vol. 73, pp. 11848-11860, 2026. DOI: 10.1109/TIE.2026.3670285. https://doi.org/10.1109/TIE.2026.3670285
3. Jianing Ding, Hai-Tao Zhang, Bin-Bin Hu, 'Coordinated Landing Control for Cross-Domain UAV-USV Fleets Using Heterogeneous-Feature Matching', 2024 IEEE International Conference on Robotics and Automation (ICRA), pp. 12041-12047. DOI: 10.1109/ICRA57147.2024.10611392. https://doi.org/10.1109/ICRA57147.2024.10611392
4. Bo Sun, Yangzhe Xie, Wenlong Jiang, Shuzhen Diao, Qingmei Cao, 'Distributed Guidance Vector Field Based Formation Control for Air-Sea Heterogeneous Clusters', 2026 7th International Conference on Artificial Intelligence and Electromechanical Automation (AIEA), pp. 72-79. DOI: 10.1109/AIEA70743.2026.11632466. https://doi.org/10.1109/AIEA70743.2026.11632466
5. Can Zhao, Liwei An, Jun-Sheng Wang, 'Collision/Obstacle Avoidance Cooperative Tracking Control for MASs With Network Constraints', IEEE Transactions on Control Systems Technology, vol. 34, pp. 330-342, 2026. DOI: 10.1109/TCST.2025.3610917. https://doi.org/10.1109/TCST.2025.3610917
6. Can Zhao, Liwei An, Lili Zhang, 'Collision-Free Output Feedback Distributed Coordination of MASs Under Unreliable Communication Topologies', IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 56, pp. 5388-5400, 2026. DOI: 10.1109/TSMC.2026.3697780. https://doi.org/10.1109/TSMC.2026.3697780
7. Junbao Wei, Jianqiang Zhang, Haiyan Li, Jiawei Xia, Zhong Liu, 'Guidance Method with Collision Avoidance Using Guiding Vector Field for Multiple Unmanned Surface Vehicles', Drones, vol. 9, no. 2, art. 105, 2025. DOI: 10.3390/drones9020105. https://doi.org/10.3390/drones9020105
8. Xiaoxuan Gong, Lu Liu, Haoliang Wang, Anqing Wang, Dan Wang, Zhouhua Peng, 'Multi-USV Formation Reconfiguration Based on Guiding Vector Fields and Control Barrier Functions', 2022 34th Chinese Control and Decision Conference (CCDC), pp. 3529-3534. DOI: 10.1109/CCDC55256.2022.10034039. https://doi.org/10.1109/CCDC55256.2022.10034039
9. Leonardo A. A. Pereira, Arthur H. D. Nunes, Adriano M. C. Rezende, Vinicius M. Goncalves, Guilherme V. Raffo, Luciano C. A. Pimenta, 'Collision-free vector field guidance and MPC for a fixed-wing UAV', 2021 IEEE International Conference on Robotics and Automation (ICRA), pp. 176-182. DOI: 10.1109/ICRA48506.2021.9560850. https://doi.org/10.1109/ICRA48506.2021.9560850
10. Qing-Da Chen, Sheng-Wei Huang, Ming-Hsin Ho, Feng-Yeang Chung, Chun-Han Chu, Chi-Min Liao, Jenhwa Guo, 'Vector Field-Based Guidance Method for Collision Avoidance of Unmanned Surface Vehicles', 2023 IEEE Underwater Technology (UT), pp. 1-7. DOI: 10.1109/UT49729.2023.10103386. https://doi.org/10.1109/UT49729.2023.10103386
11. Jinyu Fu, Ye Li, Yulei Liao, Kai Zhang, Hong Zhu, Shuo Xu, 'Mission-Driven Trajectory Homotopy to Explore Dynamic Coverage of USV-UAV Systems', IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 55, no. 12, pp. 8877-8888, 2025. DOI: 10.1109/TSMC.2025.3613395. https://doi.org/10.1109/TSMC.2025.3613395
12. Matheus C. Santos, Ben Bartlett, Vincent E. Schneider, Fiachra Ó. Brádaigh, Benjamin Blanck, Phillipe C. Santos, Petar Trslic, James Riordan, Gerard Dooly, 'Cooperative Unmanned Aerial and Surface Vehicles for Extended Coverage in Maritime Environments', IEEE Access, vol. 12, pp. 9206-9219, 2024. DOI: 10.1109/ACCESS.2024.3353046. https://doi.org/10.1109/ACCESS.2024.3353046
13. Hai-Tao Zhang, Bin-Bin Hu, Bin Liu, Jianing Ding, Jin Zhao, Housheng Su, Yunfei Zhang, Cheng Zhu, Ye Yuan, Yang Shi, 'Aerial-Marine Cross-Domain Uncrewed Systems: An Overview of Cyberphysical Coordination Frameworks for Marine Applications', IEEE Control Systems, vol. 45, no. 4, pp. 28-45, 2025. DOI: 10.1109/MCS.2025.3576275. https://doi.org/10.1109/MCS.2025.3576275