Adaptive Controller Based on Estimated Parameters for Quadcopter Trajectory Tracking

Abstract

This paper presents a trajectory control system design for a quadcopter, an unmanned aerial vehicle (UAV), which is based on estimated parameters that are assumed to exhibit random walk behavior. Initially, the rotational dynamic model of the UAV is formulated using the Newton Euler method in terms of angular velocity about the x, y, and z axes. This model is then simplified into three separated-first-order linear differential equations, with coefficients derived from the combined effects of inertia, aerodynamic drag, and gyroscopic effects, referred to as lumped parameters. A Proportional-Integral (PI) controller with feed-forward design is then developed to control this simplified model. To adapt the controller to the lumped parameters that exhibit random walk behavior, each simplified equation is restructured into a processing and measurement model. The states of these models are estimated by using the Unscented Kalman Filter (UKF). These estimated values are then utilized to adjust the PI gains and compensate the signal of the designed angular velocity controller, transforming it into an adaptive controller. The entire UAV controller comprises two main parts, an inner loop for adaptive angular rate control and an outer loop serving as an attitude-thrust controller. The proposed controller is simulated using Simulink, with circular and square trajectories. The simulation results demonstrate that the quadcopter successfully follows the desired circular and square paths. The steady-state error for the x and y axes in the square trajectory is less than 0.05 meters within 5 seconds, and for the z axis, it is less than 0.02 meters within 2.5 seconds. The controller gains do not require adjustment when changing trajectories. Moreover, the estimated parameters remain nearly constant at steady state.