In this paper, we propose an alternating optimization method to address a time-optimal trajectory generation problem. Different from the existing solutions, our approach introduces a new formulation that minimizes the overall trajectory running time while maintaining the polynomial smoothness constraints and incorporating hard limits on motion derivatives to ensure feasibility. To address this problem, an alternating peak-optimization method is developed, which splits the optimization process into two sub-optimizations: the first sub-optimization optimizes polynomial coefficients for smoothness, and the second sub-optimization adjusts the time allocated to each trajectory segment. These are alternated until a feasible minimum-time solution is found. We offer a comprehensive set of simulations and experiments to showcase the superior performance of our approach in comparison to existing methods. A collection of demonstration videos with real drone flying experiments can be accessed at https://www.youtube.com/playlist?list=PLQGtPFK17zUYkwFT-fr0a8E49R8Uq712l .

翻译：本文提出了一种交替优化方法，用于解决时间最优轨迹生成问题。与现有方案不同，我们的方法引入了一种新的公式，在保持多项式平滑约束的同时，最小化整体轨迹运行时间，并融入运动导数的硬限制以确保可行性。为解决此问题，我们开发了一种交替峰值优化方法，将优化过程分为两个子优化：第一个子优化对多项式系数进行平滑性优化，第二个子优化调整每个轨迹段分配的时间。这两个子优化交替进行，直到找到可行的最小时间解。我们提供了一系列全面的仿真和实验，以展示我们的方法相较于现有方法的优越性能。实际无人机飞行实验的演示视频合集可通过以下链接访问：https://www.youtube.com/playlist?list=PLQGtPFK17zUYkwFT-fr0a8E49R8Uq712l。