A Differential Flatness-based Trajectory Planner for Endpoint Control

Abstract

For increasing the safety of quadcopters the development of recovery control algorithms is crucial. A common cause of quadcopter crashes is collisions. To validate recovery control algorithms on collisions, the quadcopter has to reach the post-collision state.
For this, the principle of 'endpoint control' is introduced, bringing the quadcopter to a specific state with a specified position, velocity, attitude, and angular velocity. A differential flatness-based endpoint control trajectory planner is presented that guarantees feasible trajectories. The planner is based upon a novel quaternion-based differential flatness transformation without singularities using quaternion multiplication. To guarantee feasible trajectories, an iterative method is proposed to limit the angular acceleration by adding acceleration constraints to the differential flat trajectory. The planner is able to optimize over multiple variables: minimizing velocity and snap. A method is proposed to combine these position derivatives in a cost function, creating a tunable trajectory planner. To test the trajectory planner a large number of endpoints are given to the algorithm. It is verified by looking at the feasibility of the trajectories generated and validated by determining what endpoints the trajectory planner can reach.