Multi-rotor Coordinate Transforms for Orthogonal Primary and Redundant Control Modes for Regular Hexacopters and Octocopters

This study develops the multi-rotor coordinate transformation, and for hexacopters and octocopters identifies primary and redundant controls in multi-rotor coordinates. For hexacopters, the control modes in multi-rotor coordinates comprise of four primary control modes (the collective, roll, pitch and yaw modes), and two redundant modes (twist and lift-share modes). For octocopters, in addition to the four primary control modes, there are four redundant modes. Two of the redundant modes are twisting modes, the third and fourth are roll-share and pitch-share modes. For both hexacopters and occtocopters, the paper discusses the differences in the control modes between the vertex-first and edge-first orientations. Trim results over the 0-10m/s airspeed range indicate that minimum power flight corresponds to the use of only the primary control modes (with zero redundant controls). The use of certain redundant controls can result in significant changes to the primary controls. The paper also examines the flight dynamic characteristics of hexacopters and octocopters. At moderate forward speed, use of the lift-share redundant control mode was seen to improve the phugoid mode damping of the hexacopter by 10% (at a 1% power penalty cost).