# A Model-Free Online Learning Control for Attitude Tracking of Quadrotors
###### Abstract  
This paper investigates the problem of attitude tracking in quadrotor unmanned aerial vehicles (UAVs) using a model-free online learning control (MFOLC) scheme. The attitude system, which is represented by unit quaternions, is considered in the presence of uncertain and unknown inertia parameters, time-varying external disturbances, and angular velocity measurement noise. A computationally low-cost control scheme consisting of a model-free baseline controller and a module capable of learning from previous control input is designed. The proposed controller does not require precise inertial parameters and does not involve feedforward terms that use these parameters and true system states. This ensures that the approach can protect the control effort from sensor noise as well as parameter uncertainty. We also show that all the signals in the closed-loop system are uniformly ultimately bounded. Comparative simulations and real-world experiments  
scheme was developed for a quadrotor. In addition, the sliding-mode technique was also used to establish observers to estimate the external disturbances within the appointed settling time [11]. To improve the accuracy of the disturbance estimation, neural networks were integrated into controllers to provide a more accurate estimation of the external disturbances [12; 13]. However, neural networks require a large amount of training data, while their generalization abilities in different environments also need to be validated. The idea of disturbance estimation-based control has also been applied to the case of model parameter uncertainty. In such a case, one first designs a baseline controller using a set of nominal parameters, and then estimates and compensates for the parameter uncertainties as external disturbances. Once the output of the estimation component can approximate the true disturbances, the stability of the closed loop system can be theoretically guaranteed. However, when the sensor noise is significant, it is difficult for the estimated disturbances to converge to the true value, and thus it is hard to ensure the stability of the system. Furthermore, the disturbance estimation component requires additional computational consumption and prior information on the quadrotor to build a nominal model. To address the issue of unknown model parameters, learning-based control has been widely utilized in recent years. This includes offline learning methods such as reinforcement learning and deep reinforcement learning. These methods learn control policies directly from flight data and thus avoid having to use a UAV model [14; 15]. However, their generalization remains difficult to ensure, and their performance and stability should be further verified when the scene that generates the data for training differs greatly from the actual scene. Because of this, offline learning methods have only achieved good performance in some static scenarios, such as drone racing [16]. In contrast, online learning approaches combine a model-based controller with a model online-learning mechanism, which can cope with uncertain model parameters or unknown situations [17; 18]. This is very similar to disturbance estimation-based methods, which are also essentially a data-based method, and therefore control performance may be hard to guarantee when the measurements are noisy. In addition, the online learning mechanism increases computational consumption. To achieve accurate and robust attitude control with compact computational power, [PERSON] et al. [19] proposed an online learning control (OLC) algorithm. This approach achieves robust attitude control for spacecraft by adding the online learning of previous control outputs to a baseline controller. However, a feedforward term that compensates for the gyroscopic moments requires knowing the exact inertia matrix, which is difficult to accomplish in practice.