Smooth UAV Path Planning Based on Composite-Energy-Minimizing Bézier Curves

Huanxin Cao (), Zhanhe Du (), Gang Hu, Yi Xu and Lanlan Zheng
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Huanxin Cao: School of Economics and Administration, Xi’an University of Technology, Xi’an 710054, China
Zhanhe Du: School of Economics and Administration, Xi’an University of Technology, Xi’an 710054, China
Gang Hu: Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China
Yi Xu: School of Economics and Administration, Xi’an University of Technology, Xi’an 710054, China
Lanlan Zheng: School of Economics and Administration, Xi’an University of Technology, Xi’an 710054, China

Mathematics, 2025, vol. 13, issue 14, 1-20

Abstract: Path smoothing is an important part of UAV (Unmanned Aerial Vehicle) path planning, because the smoothness of the planned path is related to the flight safety and stability of UAVs. In existing smooth UAV path planning methods, different characteristics of a path curve are not considered comprehensively, and the optimization functions established based on the arc length or curvature of the path curve are complex, resulting in low efficiency and quality of path smoothing. To balance the arc length and smoothness of UAV paths, this paper proposes to use energy-minimizing Bézier curves based on composite energy for smooth UAV path planning. In order to simplify the calculation, a kind of approximate stretching energy and bending energy are used to control the arc length and smoothness, respectively, of the path, by which the optimal path can be directly obtained by solving a linear system. Experimental validation in multiple scenarios demonstrates the methodology’s effectiveness and real-time computational viability, where the planned paths by this method have the characteristics of curvature continuity, good smoothness, and short arc length. What is more, in many cases, compared to path smoothing methods based solely on bending energy optimization, the proposed method can generate paths with a smaller maximum curvature, which is more conducive to the safe and stable flight of UAVs. Furthermore, the design of collision-free smooth path for UAVs based on the piecewise energy-minimizing Bézier curve is studied. The new method is simple and efficient, which can help to improve UAV path planning efficiency and thus improve UAV reaction speed and obstacle avoidance ability.

Keywords: UAV path planning; path smoothing; deformable curve; energy-minimizing curve; Bézier curve (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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