Tracking Control for a Tilt-rotor with Input Constraints by Robust Gaits

While the quantities of advanced control methods in the conventional quadrotor (with four inputs) surges to a plateau in the past two decades. Advanced with the lateral forces, controlling Ryll's tilt-rotor attracted increasing attentions recently. Ryll's tilt-rotor, mounted with the extra 4 motors to change the directions of the thrusts (with respect to its body-fixed frame), has eight inputs. The established control methods for stabilizing this vehicle are classified by the number of inputs determined by the controller; typical controllers calculate six or eight inputs to stabilize this vehicle. While these controllers can cause the over-intensive change in the tilting angles. The tilting angles can be expected to change in an over-wide range or over-rapidly, both of which are less expected in the application. With this concern, the controller in the most recent technique, augmented by the gait plan procedure, only determines four magnitudes of the thrusts. The four tilting angles are specified with time continuously during this gait plan procedure independently before the control procedure. It has been proved that if the gaits are planned on “Two Color Map” while following the relevant “Two Color Map Theorem”, the feedback linearization-based controller in the latter of this cascade structure is robustified. Obviously, these admissible gaits on Two Color Map Theorem correspond to unique dynamics, showing different hoverabilities and trackable trajectories, which have not been elucidated yet. Despite the sound proof of the existence of the invertible decoupling matrix based on Two Color Map Theorem, the singular decoupling matrix can also be introduced by the activation of the saturation restrictions of the inputs. The activation of the non-zero constraints or maximum thrusts constraints can destroy the further application of the feedback linearization (dynamic inversion). This paper bridges the dynamics of the tilt-rotor to the robust gaits for the first time. Based on this, the relationship between the time-specified tilting angles and the trackable trajectories for the tilt-rotor is to be explored, concentrating on the gaits following Two Color Map Theorem. Then, the dynamics of the tilt-rotor adopting several typical gaits, satisfying Generalized Two Color Map Theorem, are analyzed by the exploration of the admissible (trackable) trajectories. The tracking simulations are developed to verify the relationship found. These simulations are carried out by Simulink, MATLAB.