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：在复杂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通行时间，同时满足飞行器各电机推力的约束。现有方法要么依赖无法保证动力学可行性的凸松弛技术，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，该算法显式集成了四旋翼刚体动力学及约束条件，包括对输入（含电机转速）和飞行器状态（含位姿、线速度、角速度及加速度）的限制。相比采用弱化动力学可行性概念的多种规划器，我们展示了该规划器能生成更快速且符合机器人硬件约束的轨迹。此外，我们还演示了如何利用TOPPQuad规划采用双向电机的四旋翼飞行器轨迹。总体而言，所提方法为在保障自主微型飞行器安全性的前提下最大化其效能开辟了新途径。