TOPPQuad: Dynamically-Feasible Time Optimal Path Parametrization for Quadrotors

TL;DR

TOPPQuad is proposed, a time-optimal path parameterization algorithm for quadrotors which explicitly incorporates quadrotor rigid body dynamics and constraints, such as bounds on inputs and state of the vehicle, and 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.

Abstract

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.

Figures (11)

• Figure 1: A time-optimal Lissajous curve trajectory computed with the TOPPQuad algorithm and tracked by a CrazyFlie quadrotor with the SE(3) Geometric Controller 5717652 in a Vicon motion capture system. TOPPQuad is able to plan trajectories at speeds otherwise infeasible by conventional trajectory planners.
• Figure 2: The distribution of maximum (top) and minimum (bottom) thrusts over 200 randomized trajectories for three sets of planners: minimum snap (left), minimum jerk (middle), and minimum acceleration (right). In each set, we compare a flatness-based planner at $v=5m/s$ (blue), a TOPP planner subject to velocity constraints (orange), and a TOPP planner subject to velocity and thrust constraints (green). No planner consistently plans trajectories that stay within motor thrust bounds.
• Figure 3: The distribution of maximum (top) and minimum (bottom) thrusts over 200 randomized trajectories for three sets of $\alpha$-scaled planners: minimum snap (left), minimum jerk (middle), and minimum acceleration (right). In each set, we compare against an $\alpha$-scaled flatness-based planner (blue), an $\alpha$-scaled TOPP planner subject to velocity constraints (orange), and an $\alpha$-scaled TOPP planner subject to velocity and thrust constraints (green). Only TOPPQuad (red) is able to take full range of the quadrotor's inputs.
• Figure 4: The distribution of traversal times over 200 randomized trajectories for three sets of $\alpha$-scaled planners: minimum snap (left), minimum jerk (middle), and minimum acceleration (right). In each set, we compare the traversal time for a $\alpha$-scaled flatness-based planner (blue), an $\alpha$-scaled TOPP planner subject to velocity constraints (orange), an $\alpha$-scaled TOPP planner subject to velocity and thrust constraints (green), and our TOPPQuad algorithm (red).
• Figure 5: The distribution of traversal time improvement over the four dynamically feasible planners when refined with TOPPQuad: min snap $v=1m/s$ (top left), $\alpha$-scaled $v=5m/s$ min snap (top right), $\alpha$-scaled TOPP w/velocity constraints (bottom left), and $\alpha$-scaled TOPP w/acceleration constraints (bottom right). Values are computed against the initial $v=1m/s$ trajectory guess. Our algorithm consistently sees improvements in total traversal time, even against other time-optimal methods.