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 actuation bounds 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 thrusts) 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 planners with relaxed notions of dynamic feasibility in both simulation and hardware. 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.

The use of bidirectional propellers provides quadrotors with greater maneuverability which is advantageous in constrained environments. This paper addresses the development of a trajectory planning algorithm for quadrotors with bidirectional motors. Previous work has shown that the property of differential flatness can be leveraged for efficient trajectory planning. However, planners that leverage flatness for quadrotors fail at points where the acceleration of the center of mass is equal to gravity, i.e., when the vehicle experiences free fall. The central contribution of this paper is a flatness-based trajectory planning method that allows quadrotors to use bidirectional propellers and pass through the so-called free-fall singularity. We model our system as a differentially flat hybrid system with the aid of coordinate charts derived from the Hopf fibration and develop an algorithm that computes forward and reverse thrusts for each propeller, resulting in smooth trajectories everywhere in SE(3). We demonstrate the planner's versatility by planning knife-edge maneuvers and trajectories passing through the free-fall singularity, while transitioning from forward to reverse thrust.