Real-time trajectory optimization under input constraints for a flatness-controlled laboratory helicopter

A fast receding horizon scheme for trajectory optimization under input constraints is presented and applied to a laboratory helicopter with three degrees-of-freedom (3DOF). The approach utilizes saturation functions to transform the underlying input-constrained optimal control problem into an unconstrained one. The numerical solution of the optimality conditions is based on the classical gradient method, which is easy to implement and allows a time and memory efficient computation of the single iterations. Although the receding horizon trajectories are calculated in a suboptimal way to guarantee real-time feasibility, simulation studies of flight maneuvers for the 3DOF helicopter reveal the computational speed and performance of the presented method. To prove the practical applicability, the method is used in experiments to generate the reference trajectories for a flatness-based tracking controller of the 3DOF helicopter with a sampling time of 1 ms on a standard real-time hardware.