论文标题
平滑时间为无人机的最佳轨迹生成
Smooth time optimal trajectory generation for drones
论文作者
论文摘要
在本文中，我们解决了在重力存在下，在一组所需的航路点上以界定加速度建模为点质量的无人机转向问题。我们首先提供了一种方法来求解最小时间控制输入，该方法将基于连续时间问题公式的两个航路点之间的点质量，我们通过使用pontryagin的最低原理来解决。随后，我们通过在时间域中离散并将最小时间问题作为非线性程序（NLP）求解，从而在给定的路点上解决了时间 - 最佳轨迹。然后将通过离散域中求解NLP获得的每个路点的速度用作边界条件，以在这些多个路点上扩展我们的两点解决方案。我们应用这种计划方法来执行一项测量任务，以最大程度地减少探索目标区域或音量所花费的时间。提出了这种新计划方法的数值模拟和理论分析。我们的方法的结果也与传统多项式轨迹（如最低快照计划）进行了比较。
In this paper, we address a minimum-time steering problem for a drone modeled as point mass with bounded acceleration, across a set of desired waypoints in the presence of gravity. We first provide a method to solve for the minimum-time control input that will steer the point mass between two waypoints based on a continuous-time problem formulation which we address by using Pontryagin's Minimum Principle. Subsequently, we solve for the time-optimal trajectory across the given set of waypoints by discretizing in the time domain and formulating the minimum-time problem as a nonlinear program (NLP). The velocities at each waypoint obtained from solving the NLP in the discretized domain are then used as boundary conditions to extend our two-point solution across those multiple waypoints. We apply this planning methodology to execute a surveying task that minimizes the time taken to completely explore a target area or volume. Numerical simulations and theoretical analyses of this new planning methodology are presented. The results from our approach are also compared to traditional polynomial trajectories like minimum snap planning.
