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Grupo Profissional

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Raymond Castillo
Raymond Castillo

Rotor - Rotos 2.1 (Rainy Day)


In most of the application scenarios, the multi-rotor platforms are required to localize themselves in the environment, namely to estimate their position with respect to an a priori fixed reference frame. Due to its high pervasiveness, such an issue constitutes a well-studied problem within the aerial robotic community and several solutions have been proposed in the literature. Most of the existing works focus on the outdoor localization of UAV, where the principal challenge rests on the global navigation satellite system (GNSS) signal (temporary) loss and/or degradation (see, e.g., [10,11,12]). Localization in indoor environments is, instead, less investigated, as it turns out to be a difficult issue per se, which contributes to hindering the spread of UAVs indoor applications. The indoor environment represents one of the main cases of GNSS-denied areas, mainly because the satellite signals are blocked or corrupted by physical barriers. As a consequence, multi-rotor UAVs are required to rely on a different data source to compute a position estimation, and thus they need to be equipped with other alternative (and possibly lightweight) sensors. In addition, a higher level of accuracy is generally required for position estimation when flying in physically limited and possibly cluttered areas. Despite these challenging aspects, recent IoT-inspired technological trends boost the employment of autonomous aerial vehicles to perform different tasks in indoor scenarios, especially in the emerging smart domestic and industrial contexts. These include, for instance, cooperative monitoring [13], ground robots tracking [14], infrastructures contact inspection [15], people and objects detection [16], items transportation [17].




Rotor - Rotos 2.1 (Rainy Day)



Taking into account these facts, in this work we describe a VIO localization method based on fiducial markers, which aims at ensuring the navigation of any multi-rotor UAV vehicle in an indoor environment. In particular, motivated by the increasing number of industrial applications involving aerial platforms, we account for a quasi-static context whose topology allows the presence of a wide planar map placed either on the ground or on the ceiling. One of the original aspects of the proposed navigation solution, indeed, consists in the design of a map of fiducial markers having the following features:


The first feature is justified by the intent of limiting as much as possible the loss of updated position information during UAV flight to cope with the complex dynamics of the aerial platforms and to ensure a certain level of safety. The employment of markers with different sizes is, instead, motivated by the purpose of proposing a localization method valid for (different) multi-rotor platforms flying at various altitudes, guaranteeing high estimation quality. In this sense, the designed positioning method also allows us to cope with take-off and landing maneuvers during which the UAV altitude changes quite rapidly. In this sense, as compared to most of the state-of-the-art works, we provide a localization system that turns out to be suitable for the whole UAV navigation task, ensuring the same level of positioning accuracy for the take off, landing and more complex maneuvers.


Independently of their number, while spinning the propellers of any star-shaped multi-rotor generate some thrust forces and a drag torques. The combination of those quantities then results in the total control force and control torque exerted on the vehicle CoM. More formally, taking into account a global fixed reference frame (world frame FW) and a local frame centered in the vehicle CoM (body frameFB), the dynamics of any star-shaped multi-rotor can be described through the Newton-Euler approach. Thus, we have the following model:


Star-shaped multi-rotor UAVs used for validation: (a) a small-size quadrotor having mass approximately 0.5 kg and (b) a medium size hexarotor having mass approximately 3.5 kg.


accounting for the cumulative results of all the trials wherein T1 is executed by QR01 (Figure 10) and HR01 (Figure 11). For the hexarotor platform, we observe that for all the phases the error does not exceed 0.2 m in terms of absolute value (as confirmed by the amplitude of the total range), and it is generally less than 0.1 m (as confirmed by the amplitude of the interquartile range). We remark that this last value corresponds to the 5% of the total traveled distance during each phase since it is equal to 1.8 m. We also note that the error mean (red point) and median (blue line) approximately correspond and their value is very low in correspondence to the R phase: this can be justified by the payload distribution which can determine a preferential movement in terms of vibration. On the other side, for the quadrotor platform, the boxplots reveal both higher total range and interquartile range which are under 0.3 m and 0.18 m, respectively. The highest error occurs in correspondence to the R phase: this behavior is opposite to the one observed before and it highlights the mechanical differences between the two platforms. We also observe that the gap between the error mean and median is higher, confirming the presence of higher peaks in the signal trend, coherent with the vibrating QR01 dynamics.


First, focusing on Figure 12d and Figure 13d, one can observe that for both the aerial platforms all the hovering phases envisaged in the considered trajectory are characterized by some drifts on the (x,y)-plane of the world frame. This is confirmed by the trend of the position components px and py in Figure 12a,b (for QR01) and Figure 13a,b (for HR01). In particular, such oscillations with respect to the imposed way-points are wider for the quadrotor platform that drifts till 0.4 m from the desired position, both along the x- and y-axis of the world frame. This fact is still attributable to its light mass (and inertia) making this platform more prone to vibrations during flight. However, note that the outputs of VIO and VICON system are very closed besides the presence of this oscillatory behavior of the UAVs.


The Rain Bird 5000 Series Rotor is designed to deliver superior water distribution and larger water droplets, eliminating tough dry spots. The 5000 Series Rotor is a rugged mid-range gear-drive rotary sprinkler, offering durability, great performance, and the convenience of arc adjustment from the top. This versatile rotor offers a standard rubber cover and the convenience of reversing full-and part-circle operation (up to 360 degrees) in one unit. And, with a tree of Rain Curtain nozzles, the 5000 Series Rotor offers excellent distribution for top-notch efficiency. All of this and proven gear-driven design is what makes the 5000 Series Rotor one head that will "Take Performance to the Top."


A reliable nonlinear dynamic model of the quadrotor is presented. The nonlinear dynamic model includes actuator dynamic and aerodynamic effect. Since the rotors run near a constant hovering speed, the dynamic model is simplified at hovering operating point. Based on the simplified nonlinear dynamic model, the PID controllers with feedback linearization and feedforward control are proposed using the backstepping method. These controllers are used to control both the attitude and position of the quadrotor. A fully custom quadrotor is developed to verify the correctness of the dynamic model and control algorithms. The attitude of the quadrotor is measured by inertia measurement unit (IMU). The position of the quadrotor in a GPS-denied environment, especially indoor environment, is estimated from the downward camera and ultrasonic sensor measurements. The validity and effectiveness of the proposed dynamic model and control algorithms are demonstrated by experimental results. It is shown that the vehicle achieves robust vision-based hovering and moving target tracking control.


The main contributions of this paper are the following. First, a reliable nonlinear dynamic model is presented based on the analysis of actuator dynamic, aerodynamic effect, and rigid body dynamic. The gyroscope effect of the rotors is considered by dividing the quadrotor into body part and rotor part. It makes the dynamic model more reliable to take actuator dynamic and aerodynamic effect into account. Second, the PID controllers with feedback linearization and feedforward control are proposed to control both the attitude and position of the quadrotor. The dynamic model is explicitly expressed as a cascade system of three subsystems to be suitable for the backstepping method. The control algorithms are realized on a fully custom quadrotor and vision-based autonomous indoor moving target tracking flight is achieved.


This paper is structured as follows. In Section 2, we first analyze the actuator dynamic and aerodynamic effect. The actuator dynamic is the derivation of the Kirchhoff laws and the law of rotation. The aerodynamic effect is mainly about blade flapping which has a significant effect on attitude tracking control. Then, a reliable nonlinear dynamic model is addressed using Newton-Euler method. The dynamic model is a combination of actuator dynamic, aerodynamic effect, and rigid body dynamic. In Section 3, a general PID controller with feedforward control is proposed. Then, based on the simplified nonlinear dynamic model, decoupling nonlinear control laws are presented using feedback linearization and the backstepping control strategy is applied to the position control. Section 4 describes the system design of our fully custom quadrotor and discusses the experimental results. The fully custom quadrotor is equipped with an IMU, a downward camera, and a downward ultrasonic sensor. Full control experiments are executed in the order of attitude control, altitude control, hovering control, and tracking control. At last, we outline the conclusion in Section 5.


Most researchers used to regard the whole quadrotor as a rigid model [24], neglecting the propeller gyroscope effect and aerodynamic effect. Moreover, models containing actuator dynamic are rarely investigated. However, studies show that aerodynamic effect is obvious even with moderate speed [7] and that actuator dynamic has a strong influence on the attitude stabilization [6]. Thus, a detailed analysis of those effects is necessary. 041b061a72


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    Gabriel Edwards
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    Joseph Murphy
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    Nicholas Hill
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    Raymond Castillo
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