Trajectory generation using sub-Riemannian curves for quadrotor UAVs

In this paper a semi-analytical technique for generating quadrotor trajectories using the projection of sub-Riemannian curves on SE(3) onto R3 is presented. The benefits of using these trajectories are that they have constant speed and acceleration magnitude, are smooth and analytically defined in terms of standard functions. Also, they are sub-optimal with respect to a weighted quadratic cost function of the translational and angular velocities. This paper shows, through simulation, that these curves are also dynamically feasible. In addition, a method for changing the velocity profile along these curves using time parametrisation, allowing for smooth rest-to-rest manoeuvres, is shown. An obstacle avoidance strategy using these analytically defined curves is demonstrated by producing multiple trajectories of different shapes. This is achieved by adding a final velocity perturbation to the error function that is minimised when generating the trajectory.