基于微分平坦性，实现固定翼无人机快速轨迹规划
Differential Flatness-based Fast Trajectory Planning for Fixed-wing Unmanned Aerial Vehicles
- 利用微分平坦性构建参数化轨迹，消除等式约束
- 实现线性时间复杂度优化，单次计算耗时不足1秒
- 适合实时规划需求，尤其在复杂障碍环境
由于固定翼无人机具有强非线性与非完整动力学特性，尽管已有多种通用轨迹优化方法，但多数难以兼顾计算效率与物理可行性。本文提出一种基于微分平坦性的固定翼无人机轨迹优化方法（DFTO-FW）。通过分析微分平坦特性并采用多项式参数化，设计定制化轨迹表示，消除等式约束，避免求解复杂动力学带来的高计算负担。通过设计积分型性能代价函数并推导解析梯度，将原问题转化为轻量级、无约束、可解析梯度的优化问题，实现线性时间复杂度，显著提升效率。仿真结果表明，DFTO-FW在个人桌面环境下生成随机障碍环境中的轨迹仅需亚秒级CPU时间，相较其他方法提升数量级。
原文摘要 · Abstract (English)
Due to the strong nonlinearity and nonholonomic dynamics, despite the various general trajectory optimization methods presented, few of them can guarantee efficient computation and physical feasibility for relatively complicated fixed-wing UAV dynamics. Aiming at this issue, this paper investigates a differential flatness-based trajectory optimization method for fixed-wing UAVs (DFTO-FW). The customized trajectory representation is presented through differential flat characteristics analysis and polynomial parameterization, eliminating equality constraints to avoid the heavy computational burdens of solving complex dynamics. Through the design of integral performance costs and derivation of analytical gradients, the original trajectory optimization is transcribed into a lightweight, unconstrained, gradient-analytical optimization with linear time complexity to improve efficiency further. The simulation experiments illustrate the superior efficiency of the DFTO-FW, which takes sub-second CPU time (on a personal desktop) against other competitors by orders of magnitude to generate fixed-wing UAV trajectories in randomly generated obstacle environments.
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