Optimal control for power-off landing of a small-scale helicopter a pseudospectral approach

We derive optimal power-off landing trajectories, for the case of a small-scale helicopter UAV. These open-loop optimal trajectories represent the solution to the minimization of a cost objective, given system dynamics, controls and states equality and inequality constraints. The plant dynamics features a 3-D nonlinear helicopter model, including dynamics from the rigid body, the main rotor Revolutions Per Minute (RPM), and the actuators. The novel part of this paper is threefold. First, we provide a new cost functional which, during the flight, maximizes helicopter performance and control smoothness, while minimizing roll-yaw cross-coupling. Second, and aside from the standard state and control bounds, we provide a trajectory constraint on tail rotor blade tip, to avoid ground strike when the helicopters pitches up, just before touch-down. Third, we apply the pseudospectral collocation discretization scheme, through a direct optimal control method, to solve our problem. The advantage of the pseudospectral method, compared to other direct optimal control approaches, lies in its exponential convergence, implying increased computational efficiency, provided the functions under considerations are sufficiently smooth. Finally, we conclude by a discussion of several simulation examples.