Robust Position Control of a Quadrotor Using Onboard Optical Flow Sensor

In this paper, the uncertainty and disturbance estimator (UDE)-based position controllers are developed to achieve the robust position control of a quadrotor using only onboard sensing. Firstly, in order to accurately estimate the positions of the quadrotor in GPS-denied environments, an open source high speed optical flow sensor PX4FLOW is adopted. Secondly, the UDE-based controllers are developed to handle the challenges brought by the highly nonlinear quadrotor position dynamics, including underactuation, coupling, nonaffine inputs, model uncertainties and external disturbances. Real flight experiments, including hover and disturbance rejection are carried out to demonstrate the effectiveness of the developed UDE-based controllers. INTRODUCTION In recent years, unmanned aerial vehicles (UAVs) have drawn considerable amount of attention from both research and industrial communities because of their wide field of applications, such as search and rescue, industrial inspection, precision agriculture, aerial photography, etc [1,2]. In order to accomplish the aforementioned tasks, the ability of the UAVs to navigate autonomously, maneuver sharply and hover precisely is very important. One of the popular UAVs that has been widely applied is the quadrotor since it has relatively simple mechanical structure and vertically taking off (landing) ability. The quadrotor has six degrees of freedom including three rotational (attitude) and three translational (position) motions with solely four independent control inputs (thrust and three torques along the body axes). The horizontal positions of the quadrotor are controlled by varying its attitude angles. The quadrotor is able to stabilize and control its attitude angles with the information from onboard inertia measurement unit (IMU), which consists of accelerometers, gyroscopes and magnetometers. Nevertheless, even with the attitude angles stabilized to zero degrees, due to the inaccurate measurements of the low-cost onboard IMU and other environmental disturbances, the quadrotor could not hover at a fixed point for a long time. Hence, the position control of a quadrotor is an essential step towards the quadrotor autonomy. The precise position control of a quadrotor requires the accurate estimation of the quadrotor positions followed by proper control actions [3, 4]. In order to have an accurate position estimation of the quadrotor, various position estimation sensors and methods have been investigated. The global positioning system (GPS) receiver is a common onboard device utilized for the navigation task of quadrotor UAVs [2, 5, 6]. However, the GPS receiver mainly has two constraints: 1) accuracy, and 2) a clear view of the sky. According to the National Coordination Office for Space-Based Positioning, Navigation, and Timing [7], the horizontal accuracy of the GPS receiver is about 3.5 meters. Furthermore, the requirement for a clear view of the sky has limited the GPS receiver mostly for outdoor applications. As for the GPS-denied navigation, one of the widely adopted methods for 1 Copyright c © 2016 by ASME quadrotor navigation is the motion capture system, which utilizes multiple external cameras and reflective markers to determine the positions of the quadrotor [8, 9]. However, it is not suitable for missions where the installation of such a system is not feasible. Therefore, for UAVs, how to extract their position information in GPS-denied environments solely from the onboard sensing is still a very challenging and open research topic [3]. The laser range finder [10] and onboard camera [3, 4, 11] seem to be two promising onboard solutions for the quadrotor navigation task. Compared to laser, the onboard camera has the advantage of lightweight and low cost. Recent studies have revealed that flying insects utilize optical flow to accomplish their dynamic navigation while keeping energy consumption at an unbelievable low level [12]. This biomimetic principle motivates a number of researchers exploring the idea of optical flow-based navigation [4,11]. In [4], an open source high speed optical flow sensor PX4FLOW is developed. The sensor weighs about 20 grams with the update rate about 120 Hz in low light conditions. The lightweight and fast update rate features make it especially suitable for quadrotor navigation task. Therefore, the PX4FLOW is utilized in this paper to accomplish the quadrotor position estimation task. Besides the difficulties of vehicle position estimation, another aspect of challenges for the position control of UAVs comes from its highly nonlinear system dynamics. First of all, the quadrotor is an underactuated multiple-input multiple-output (MIMO) system, which has six outputs while only four inputs. The horizontal positions (x, y) of the quadrotor are controlled by varying its attitude angles. Furthermore, the inputs of the horizontal position dynamics are in nonaffine forms. The coupling between the position subsystems and attitude subsystems also brings challenges to the controller design. Finally, the quadrotor is very sensitive to the perturbations caused by model uncertainty and external disturbance, which could be generated from battery voltage dropping, aerodynamic effects or wind gusts. In order to deal with those challenges and to achieve good control performance, many control strategies have been reported in the literature. Backstepping is a well-known technique used for control of nonlinear systems and it is well suited for the cascaded structure of the quadrotor dynamics to solve the underactuation problem [13, 14]. In order to compensate the model uncertainties, adaptive control methods are widely used, such as the model reference adaptive control [15], the immersion and invariance-based adaptive control [16] and adaptation laws based on Lyapunov-like energy function [17]. The robustness is crucial to the UAVs, since they are constantly perturbed by external disturbances, specially in outdoor applications [17]. Hence, the robust control of a quadrotor is still an active field, such as sliding mode control [18], H∞ control [19] and disturbance observer based control [20]. Compared to the aforementioned robust control methods, the uncertainty and disturbance estimator (UDE)-based controller, which was proposed in [21], has a relatively simple structure and it is computationally efficient. The basic idea of the UDE method is that in the frequency domain an engineering signal (the model uncertainty and external disturbance) can be approximated by putting it through a filter with the appropriate bandwidth. The remarkable performance of the UDE strategy has been demonstrated in recent years through both theories [22, 23, 24] and practical applications [25, 26, 27, 28]. In this paper, in response to the aforementioned challenges, the UDE-based controllers are developed for the position control of a quadrotor. The major contributions of this paper include: 1. The PX4FLOW optical flow sensor is integrated to accomplish the onboard position estimation in GPS-denied environment. 2. In order to to achieve the position control of a quadrotor while dealing with the problem of underactuation, coupling, nonaffine inputs, model uncertainties and external disturbances, a robust tracking control scheme based on the UDE is developed. 3. The effectiveness of the developed control strategy is demonstrated through real flight experiment studies. Compared with previous UDE works on quadrotor attitude and height control [25,28], this paper mainly focuses on the horizontal position controller development. This paper evolves along the following lines. In Section 2, the mathematical model of a quadrotor is presented and the control problem is formulated. The details of the UDE-based controller design are discussed in Section 3. In Section 4, real flight experiments, including hover at fixed point and step disturbance rejection, are carried out to demonstrate the effectiveness of the proposed approach. Conclusions are made in Section 5. PRELIMINARIES AND PROBLEM FORMULATION