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.