Velocity-Free Horizontal Position Control of Quadrotor Aircraft via Nonlinear Negative Imaginary Systems Theory

Abstract

This paper presents a velocity-free position control strategy for quadrotor unmanned aerial vehicles based on nonlinear negative imaginary (NNI) systems theory. Unlike conventional position control schemes that require velocity measurements or estimation, the proposed approach achieves asymptotic stability using only position feedback. We establish that the quadrotor horizontal position subsystem, when augmented with proportional feedback, exhibits the NNI property with respect to appropriately defined horizontal thrust inputs. A strictly negative imaginary integral resonant controller is then designed for the outer loop, and robust asymptotic stability is guaranteed through satisfaction of explicit sector-bound conditions relating controller and plant parameters. The theoretical framework accommodates model uncertainties and external disturbances while eliminating the need for velocity sensors. Simulation results validate the theoretical predictions and demonstrate effective position tracking performance.