A Comparison Between Quadrotor Flight Configurations

This paper compares a quadcopter operating in the plus and cross configurations. Using mutli-rotor controls (Ω0 collective, ΩP pitch, ΩR roll, and ΩY yaw control), the plus-configuration generates a yaw moment when a pitch or roll control input is introduced; but for the cross-configuration, pitch and roll control is decoupled from yaw. While the collective control, 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 since 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 these modes are stable and their poles are coincident in hover. In forward flight, these modes separate, and the frequency and damping of both modes increases. The nature of the lateral phugoid mode in forward flight is very similar to hover, but the longitudinal phugoid mode begins to include altitude changes (in addition to longitudinal translation and pitch attitude). Over a certain airspeed range, a couple of real poles (corresponding to heave and pitch subsidence) combine to result in an oscillatory short-period mode. No significant difference is seen in the autonomous flight dynamic characteriscs (pole locations) between the plus- and cross-configurations. A comparison of the control authority available between the plus- and cross-configuration quadcopters shows that while collective and yaw control authority is identical, pitch and roll control authority is up to about 30% greater for the cross-configuration since all four (as opposed to only two) rotors are used.

Reference

Niemiec, R., and Gandhi, F., "A Comparison Between Quadrotor Flight Configurations ,"

Proceedings of the 42nd European Rotorcraft Forum, Lille, France, Sept. 5-8, 2016.