Adaptive Attitude Tracking of a Quad-Rotorcraft using Nonlinear Control Hierarchy Ranjan Dasgupta Embedded System and Robotics Innovation Lab Tata Consultancy Services Ltd Kolkata, India ranjan.dasgupta@tcs.com Abstract—Adaptive control of a quad-rotorcraft is designed to estimate unknown plant parameters online in order to improve the robustness of the system against parametric uncertainties. Using the hierarchical structure of a quadrotor a nonlinear position and an adaptive attitude control law is proposed that can asymptotically track a command signal without the knowledge of inertia matrix. A projection based adaptive law estimates the unknown inertia parameters and ensures that the estimate always stay inside a pre-defined compact set. Adaptive design obeys the underlying principle behind hierarchical control where the vehicle tracks the desired position and compute guided attitudes from a thrust input so that designed rotor torques drives the vehicle towards desired orientation. A rigorous stability analysis proves that the overall system is stable by considering the effect of strong nonlinear coupling between the position and attitude subsystem. Closed-loop error dynamics is asymptotically converging and ensure all signals are bounded in the cascaded control structure. Simulation results demonstrate the theoretical conjecture of the proposed controller. Index Terms—quad-rotorcraft, nonlinear, adaptive, hierarchi- cal, parameter estimation, regressor I. I NTRODUCTION Adaptive control design of a quad-rotorcraft addresses the problem of unknown model parameters and matched uncer- tainties associated with nonlinear and multivariate dynamics. A number of adaptive compensation methods [1]–[3], [5], [6], [9], [15] to estimate unknown mass, inertia matrix, aero- dynamic damping force and moment coefficients combining with Model Reference Adaptive Control (MRAC), filtered MRAC, feedback linearization, output feedback (OFB), slid- ing mode, higher-order sliding mode, back-stepping, integral back-stepping to control altitude, position and attitude of the quadrotor have widely been proposed. Most of the control algorithms can asymptotically track command signal and guarantee boundedness of tracking errors. Nonlinear dynamic inversion [7] is applied on an input-output linearized system where the physical model is dynamically inverted and MRAC is used to compensate for parameter uncertainties. In [10] an adaptive sliding back-stepping technique is proposed for atti- tude control which uses strict feedback form with matched un- certainties. The primary control law is divided into equivalent and switching control to achieve global asymptotic tracking of the desired attitude trajectory. Intelligent control methods presented in [1], [12] use neural networks to perform state and output feedback control of a quad-rotorcraft and achieve semi- globally or globally uniformly ultimately bounded (UUB) tracking errors. A new adaptive neural network control [8] is proposed to stabilize a quadrotor in the presence of modeling error and wind disturbance. Robust adaptive controllers are utilized in [8], [12] for the dynamics of a quad-rotorcraft in the presence of linear-in-the-parameter (LIP) uncertainties and bounded disturbances. In [4] an integral predictive and H ∞ nonlinear robust control strategy is used to solve tracking prob- lem in the presence of aerodynamic disturbance and parametric uncertainties. An L1 adaptive output feedback control [3] is designed to provide robustness against time-delay on the output measurement. Recently adaptive control algorithms [3], [14] start focusing on propeller damage, sensor faults and partial loss of rotational speed. The control scheme uses a group of on-line compensation techniques inside a closed loop system such that the transient performance of tracking errors can be improved in case of rotor failure. Classical works on hierarchical design [11], [13], uses orientation and thrust as control variables to stabilize the vehicle position. Exploiting the hierarchical structure a virtual control input is considered for the translational dynamics from which the desired attitude and thrust is acquired. Since the desired attitude is regarded as input of rotational dynamics the attitude tracking error introduces a nonlinear coupling between the position and attitude subsystem whose effect on stability of the overall system must be considered. A recent work in hierarchical control [11], of a quad tilt-wing unmanned aerial vehicle (UAV) applies nonlinear adaptive control approach for attitude inner-loop whereas MRAC is designed for the position outer-loop that uses linear dynamics to provide virtual control inputs to control the UAV position. It also investigates the error introduced by the inner loop controller that appears as disturbances in the outer loop controller producing UUB result. The proposed work designs a nonlinear position and an adaptive attitude control of a quad-rotorcraft that uses hierar- chical structure to compute guidance law from Euler-Lagrange (E-L) dynamics. A projection based adaptive law is derived based on Lyapunov analysis and control algorithm tracks the attitude command signal without the knowledge of inertia matrix. Lyapunov analysis shows that the overall closed- loop system is stable, tracking errors are bounded and error dynamics converges asymptotically by considering the effect of strong nonlinear coupling between the two subsystems.