It is always a challenge to design a real-time optimal full flight envelope controller for a miniature helicopter due to the nonlinear, underactuated, uncertain, and highly coupled nature of its dynamics. This paper integrates the control of translational, rotational, and flapping motions of a simulated miniature aerobatic helicopter in one unified optimal control framework. In particular, a recently developed real-time nonlinear optimal control method, called the θ-D technique, is employed to solve the resultant challenging problem considering the full nonlinear dynamics without gain scheduling techniques and timescale separations. The uniqueness of the θ-D method is its ability to obtain an approximate analytical solution to the Hamilton–Jacobi–Bellman equation, which leads to a closed-form suboptimal control law. As a result, it can provide a great advantage in real-time implementation without a high computational load. Two complex trajectory tracking scenarios are used to evaluate the control capabilities of the proposed method in full flight envelope. Realistic uncertainties in modeling parameters and the wind gust condition are included in the simulation for the purpose of demonstrating the robustness of the proposed control law.
Efficient Methods for Flight Envelope Estimation through Reachability Analysis
