沈阳工业大学学报2025，Vol.47Issue(5)：575-583,9.DOI:10.7688/j.issn.1000-1646.2025.05.04
基于虚拟弹簧的hp自适应伪谱法在无人机编队航迹规划中的应用
Application of virtual spring-based hp adaptive pseudospectral method in UAV formation trajectory planning
摘要
Abstract
[Objective]With the increasing demand for application of unmanned aerial vehicles(UAVs)in complex scenarios such as power grid inspection and emergency rescue,the limitations of single UAV in task execution have become increasingly prominent.Multi-UAV formation can effectively improve inspection efficiency and expand operation coverage,but significant challenges remain in formation maintenance,collaborative trajectory optimization,and environmental adaptability to complex environments during practical application.An optimal control method that integrated virtual spring forces with the hp-adaptive pseudospectral method was proposed to address the difficulties of formation maintenance and path optimization during large planar maneuvers of UAV swarms,thus enhancing the stability,flexibility,and disturbance resistance of collaborative flight of UAV formations and providing technical support for high-demand scenarios for UAVs such as power grid inspection.[Methods]First,a multi-UAV system dynamics model was built,and a virtual spring mechanism was incorporated into the formation control system to realize flexible constraints and elastic self-adjustment between UAVs.By combining the virtual spring method with the traditional leader-follower method,a formation strategy that could balance rigid support and adaptive adjustment ability of formations was designed.On this basis,the hp-adaptive pseudospectral method was then applied to solve the optimal control problem of UAV formations.By discretizing state and control variables at Legendre-Gauss nodes and constructing global interpolation polynomials,the trajectory optimization problem was transformed into a nonlinear programming(NLP)problem,with constraints such as dynamics,energy consumption,and velocity combined to conduct a high-precision numerical solution.In simulation experiments,a typical four-UAV diamond formation was set up,and the algorithm's adaptability to different terrains,wind disturbances,and mission requirements was comprehensively explored.[Results]Simulation results show that the proposed virtual spring-based hp-adaptive pseudospectral method can realize smooth formation turning and velocity control.During a 90° large maneuver,UAVs can not only satisfy multiple constraints such as path deflection and speed change,but also maintain a stable formation.Compared with traditional leader-follower and artificial potential field methods,the new method demonstrates significant advantages in position error,formation maintenance,and wind resistance.Under 10 m/s strong wind,the formation stability of the proposed method exceeds 70％,showing significant advantages over its competing algorithms.3D terrain simulations and real flight tests further validate the algorithm's adaptability and robustness,and the method still maintains lower formation deformation rates and trajectory tracking error under multiple terrains such as hills,mountains,and canyons,with the features of reasonable energy consumption control and strong engineering practicability.[Conclusion]By innovatively integrating the virtual spring elastic constraint with the hp-adaptive pseudospectral method,an optimal control technique for UAV formation trajectory planning in complex environments was proposed.The rigidity constraint limitations of traditional formation methods are overcome,flexible maintenance and adaptive adjustment of formations are realized,and the accuracy and efficiency of collaborative trajectory optimization are significantly improved by the method.The research results provide an efficient and reliable technical path for collaborative flight of UAV swarms in demanding tasks such as power grid inspection and emergency rescue.Future studies may further increase the method's application potential in multi-formation collaboration and complex obstacle environments,promoting the intelligent and practical development of UAV formations.关键词
无人机/集群编队/航迹规划/虚拟势场/领航跟随法/最优控制方法/伪谱法/协同控制Key words
unmanned aerial vehicle/swarm formation/trajectory planning/virtual potential field/leader-follower method/optimal control method/pseudospectral method/collaborative control分类
信息技术与安全科学引用本文复制引用
李翔,罗望春,石志彬,张兴华,刘洪驿..基于虚拟弹簧的hp自适应伪谱法在无人机编队航迹规划中的应用[J].沈阳工业大学学报,2025,47(5):575-583,9.基金项目
国家自然科学基金项目(12202384) （12202384）
中国南方电网超高压输电公司项目(CGYKJXM20220111). （CGYKJXM20220111）
