Multirotor Controls, Trim, and Autonomous Flight Dynamics of Plus- and Cross-Quadcopters

This paper examines a quadcopter operating in the plus and cross configurations. The plus configuration generates a yaw moment when a pitch/roll control input is introduced; but, for the cross configuration, the pitch/roll control is decoupled from yaw. Although the collective revolutions-per-minute control requirement, pitch attitude, and power requirement versus flight speed are identical for both configurations, in forward flight, the plus configuration requires a larger pitch control input because it uses only two rotors and a compensatory yaw control input. Quadcopters display two oscillatory modes in hover, a longitudinal phugoid mode (coupling longitudinal translation and pitch), and a lateral phugoid mode (coupling lateral translation and roll). Both modes are stable, and their poles are coincident in hover. In forward flight, the modes are distinct, and the frequency and damping of both modes increase. The nature of the lateral phugoid mode in forward flight is very similar to hover, but the longitudinal phugoid mode now includes altitude change. Over a certain airspeed range, a couple of real poles combine to produce an oscillatory short-period mode. No significant difference is seen in the autonomous flight dynamic characteristics between the plus and cross configurations. Maximum pitching and rolling moments produced by the cross configuration are √2 greater than those produced by the plus configuration because all four rotors are used.