SDRE Flight Control For X-Cell and R-Max Autonomous Helicopters

Abstract — This paper presents a state-dependent Riccati equation (SDRE) flight control approach and its application to autonomous helicopters. For our experiments, we used two different vehicles: an X-Cell-90 small hobby helicopter and a larger vehicle based on the Yamaha R-Max. The control design uses a 6-DOF nonlinear dynamic model that is manipulated into a pseudo-linear form where system matrices are given explicitly as a function of the current state. A standard Riccati equation is then solved numerically at each step of a 50 Hz control loop to design the nonlinear state feedback control law on-line. In addition, a static nonlinear compensator is designed to address issues with the mismatch between the original nonlinear dynamics and its pseudo-linear transformation. I. NOMENCLATURE u, v, w vehicle velocities along X, Y and Z fuselage axes p, q, r vehicle angular (roll, pitch, yaw) velocities φ, θ, ψ Euler angles: roll, pitch and yaw x, y, z vehicle position in inertial frame ulon, ulat longitudinal and lateral cyclic control inputs ucol, utcol main and tail rotors collective control inputs uw, vw, ww wind velocities along X, Y, and Z fuselage axes m helicopter mass Ixx, Iyy, Izz main moments of inertia T rotor thrust λ0 inflow ratio µ advance ratio µz Vtip normal airflow component speed of the rotor blade tip a rotor blade lift curve slope CT rotor thrust coefficien