Cat-Inspired Gaits for a Tilt-Rotor—From Symmetrical to Asymmetrical

Abstract

Among the tilt-rotors (quadrotors) developed in recent decades, Ryll’s model with eight inputs (four magnitudes of thrusts and four tilting angles) attracted great attention. Typical feedback linearization maneuvers all of the eight inputs with a united control rule to stabilize this tilt-rotor. Instead of assigning the tilting angles by the control rule, the recent research predetermines the tilting angles and leaves the magnitudes of thrusts with the only control signals. These tilting angles are designed to mimic the cat-trot gait while avoiding the singular decoupling matrix in feedback linearization. To complete the discussions of the cat-gait inspired tilt-rotor gaits, this research addresses the analyses on the rest of the common cat gaits, walk, run, transverse gallop, and rotary gallop. It is found that the singular decoupling matrix exists in walk gait, transverse gallop gait, and rotary gallop gait; the decoupling matrix can hardly be guaranteed to be invertible analytically. Further modifications (scaling) are conducted to these three gaits to accommodate the application of feedback linearization; the acceptable attitudes, leading to invertible decoupling matrix, for each scaled gait are evaluated in the roll-pitch diagram. The modified gaits with different periods are then applied to the tilt-rotor in tracking experiments, in which the references are uniform rectilinear motion and uniform circular motion with or without the equipment of the modified attitude-position decoupler. All the experiments are simulated in Simulink, MATLAB. The result shows that these gaits, after modifications, are feasible in tracking references, especially for the cases equipped with the modified attitude-position decoupler.