Backpropagating Constraints-Based Trajectory Tracking Control of a Quadrotor with Constrained Actuator Dynamics and Complex Unknowns

In this paper, a backpropagating constraints-based trajectory tracking control (BCTTC) scheme is addressed for trajectory tracking of a quadrotor with complex unknowns and cascade constraints arising from constrained actuator dynamics, including saturations and dead zones. The entire quadrotor system including actuator dynamics is decomposed into five cascade subsystems connected by intermediate saturated nonlinearities. By virtue of the cascade structure, backpropagating constraints (BCs) on intermediate signals are derived from constrained actuator dynamics suffering from nonreversible rotations and nonnegative squares of rotors, and decouple subsystems with saturated connections. Combining with sliding-mode errors, BC-based virtual controls are individually designed by addressing underactuation and cascade constraints. In order to remove smoothness requirements on intermediate controls, first-order filters are employed, and thereby contributing to backstepping-like subcontrollers synthesizing in a recursive manner. Moreover, universal adaptive compensators are exclusively devised to dominate intermediate tracking residuals and complex unknowns. Eventually, the closed-loop BCTTC system stability can be ensured by the Lyapunov synthesis, and trajectory tracking errors can be made arbitrarily small. Simulation studies demonstrate the effectiveness and superiority of the proposed BCTTC scheme for a quadrotor with complex constrains and unknowns.