Planning time-optimal trajectories for quadrotors in cluttered environments is a challenging, non-convex problem. This paper addresses minimizing the traversal time of a given collision-free geometric path without violating bounds on individual motor thrusts of the vehicle. Previous approaches have either relied on convex relaxations that do not guarantee dynamic feasibility, or have generated overly conservative time parametrizations. We propose TOPPQuad, a time-optimal path parameterization algorithm for quadrotors which explicitly incorporates quadrotor rigid body dynamics and constraints such as bounds on inputs (including motor speeds) and state of the vehicle (including the pose, linear and angular velocity and acceleration). We demonstrate the ability of the planner to generate faster trajectories that respect hardware constraints of the robot compared to several planners with relaxed notions of dynamic feasibility. We also demonstrate how TOPPQuad can be used to plan trajectories for quadrotors that utilize bidirectional motors. Overall, the proposed approach paves a way towards maximizing the efficacy of autonomous micro aerial vehicles while ensuring their safety.

翻译：在杂乱环境中为四旋翼飞行器规划时间最优轨迹是一个具有挑战性的非凸问题。本文旨在最小化给定无碰撞几何路径的穿越时间，同时不违反飞行器单个电机推力的约束。以往的方法要么依赖无法保证动态可行性的凸松弛，要么生成过于保守的时间参数化方案。我们提出TOPPQuad——一种针对四旋翼飞行器的时间最优路径参数化算法，该算法明确融入了四旋翼刚体动力学以及输入（包括电机转速）和飞行器状态（包括位姿、线速度、角速度及加速度）等约束。我们证明，与采用松弛动态可行性概念的若干规划方案相比，该规划器能够生成更快的轨迹，同时满足机器人的硬件约束。此外，我们还展示了如何利用TOPPQuad为采用双向电机的四旋翼飞行器规划轨迹。总体而言，所提出的方法为在确保自主微型飞行器安全性的同时最大化其效能奠定了基础。