Differential flatness-based spatial-temporal hierarchical trajectory planning for fixed-wing UAVs in urban environments

The presence of dense irregular obstacles in complex urban environments and strong nonlinear dynamics of fixed-wing Unmanned Aerial Vehicle (UAV) cause low efficiency of trajectory planning and safety risks for fixed-wing UAVs. To address these issues, this paper investigates a spatial-temporal hierarchical trajectory planning method for fixed-wing UAVs based on differential flatness. A hierarchical planning framework of “path planning-safe corridors generation-trajectory optimization” is constructed. Firstly, heuristic graph search is utilized to obtain the reference path as the initial motion. Guided by the path planning results, safe flight corridors are generated through the iterative regional inflation method, which efficiently provides the initial values and feasible regions of trajectories. Subsequently, to reduce the complexity of trajectory optimization, a differential flatness-based spatial-temporal trajectory parameterization model for fixed-wing UAVs is established, enabling elimination of nonlinear dynamics, and terminal and safety constraints. Additionally, by designing penalty costs to handle flight performance constraints and deriving their analytical gradients, the original problem of trajectory planning is transformed into an unconstrained nonlinear optimization with analytical gradients. Finally, a Differential Flatness-Based Spatial-Temporal Hierarchical Trajectory Planning (STH-DFTP) algorithm is proposed to achieve efficient trajectory generation. The simulation results illustrate that the proposed STH-DFTP has superior efficiency, which only takes 10⁻²–10⁻¹ s to generate the flight trajectories for fixed-wing UAVs in complex urban environments, meeting the requirements for online trajectory planning in practice.