Three-dimensional path planning for UAVs considering flight energy consumption: An approach based on improved elliptic tangent maps

Aiming to address the problem of insufficient optimization of energy consumption in unmanned aerial vehicle (UAV) path planning, a three-dimensional (3D) path planning method based on a tangent map and considering energy consumption is proposed.

First, to ensure safe UAV flight, an ellipsoidal obstacle modeling approach is introduced. This approach represents irregular obstacles using a safety envelope, ensuring a minimum safe distance between the UAV and obstacles. Unlike conventional envelope-based methods, the proposed approach eliminates path redundancy, thereby lowering computational complexity and enhancing planning efficiency and flight safety. Second, the traditional elliptic tangent graph method is improved by incorporating a bidirectional search strategy and a node screening mechanism. These enhancements generate optimized two-dimensional (2D) reference path points, notably reducing the number of turning points along the path and shortening the overall path length. Finally, the proposed method integrates the 2D reference path points with an energy consumption model to enable 3D path planning. The 3D reference path points are derived from their 2D counterparts. When the start and end points of the UAV lie at the same altitude, a dimensionality reduction strategy is applied to convert the 3D planning problem into a 2D planar one, which is then solved using the elliptic tangent graph method. In cases involving height differences between the start and end points, an energy evaluation model is used to compare the energy costs of two strategies (horizontal flyover and vertical climb). The path point with the lowest energy consumption is selected, and cubic B-spline curves are applied to smooth the path. Aiming to evaluate the performance of the proposed method, three test scenarios with varying obstacle densities and layouts are designed. Comparative experiments are conducted against four benchmark algorithms: A^*, rapidly-exploring random trees (RRT), particle swarm optimization (PSO), and the vector field histogram (VFH).

Results demonstrate that, in 2D environments, the improved elliptic tangent graph method consistently generates the shortest paths with the fewest turns, regardless of obstacle distribution. Its performance advantage becomes increasingly evident as environmental complexity rises. In complex 3D environments, the method not only delivers shorter and smoother flight paths but also substantially reduces the overall energy consumption of UAV operations. Specifically, compared with the A^*, RRT, PSO, and VFH algorithms, the proposed method achieves average reductions in path length of 8.7%, 18.7%, 13.4%, and 4.1%, respectively; reductions in the number of turns of 68.8%, 82.1%, 82.8%, and 75.0%; and reductions in energy consumption of 51.6%, 34.0%, 59.1%, and 55.3%. Additionally, comparative experiments conducted with varying safety distances (2, 4, and 6 m) reveal that appropriately increasing the safety distance can improve flight safety without compromising path optimality. However, excessively large safety distances may lead to inefficient use of free space and reduced planning efficiency.

These improvements effectively overcome the traditional tradeoffs between path length, motion smoothness, and energy efficiency, offering a solution that combines theoretical innovation with engineering practicality to enhance UAV mission endurance and operational safety.