Characterization of the Aerodynamic Ground Effect and Its Influence in Multirotor Control

Research Article Characterization of the Aerodynamic Ground Effect and Its Influence in Multirotor Control Pedro Sanchez-Cuevas, Guillermo Heredia, and Anibal Ollero Robotics,VisionandControlGroup,UniversityofSeville,Seville,Spain Correspondence should be addressed to Guillermo Heredia; gui[email protected] Received 14 February 2017; Revised 6 July 2017; Accepted 13 July 2017; Published 17 August 2017 Academic Editor: Kenneth M. Sobel Copyright © 2017 Pedro Sanchez-Cuevas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper analyzes the ground effect in multirotors, that is, the change in the thrust generated by the rotors when flying close to the ground due to the interaction of the rotor airflow with the ground surface. This effect is well known in single-rotor helicopters but has been assumed erroneously to be similar for multirotors in many cases in the literature. In this paper, the ground effect for multirotors is characterized with experimental tests in several cases and the partial ground effect, a situation in which one or some of the rotors of the multirotor (but not all) are under the ground effect, is also characterized. The influence of the different cases of ground effect in multirotor control is then studied with several control approaches in simulation and validated with experiments in a test bench and with outdoor flights. 1. Introduction In the last years, there has been a growing interest in Unmanned Aerial Vehicles (UAVs) [1]. UAVs of different sizes have been used in applications such as exploration, detection, precise localization, monitoring, and measuring the evolution of natural disasters. However, in most of these applications, the aerial robots are mainly considered as platforms for environment sensing. Then, the aerial robots do not modify the state of the environment and there are no physical interactions between the UAV and the environment. Furthermore, the interactions between the UAVs themselves are essentially information exchanges, without physical couplings between them. Recently, the development of autonomous aerial robots with integrated robotic manipulators is catching much interest in robotic research [2, 3]. These aerial manipulators [4– 6], as they are usually known, extend the range of possible applications of UAVs. For instance, aerial manipulators can be used for the inspection and maintenance of industrial plants and infrastructures [7], aerial power lines, and moving objects [8] and taking samples of material from areas that are difficult to access. Aerial robotic manipulation with multirotors usually involves flying near objects, structures, and other obstacles, for example, to grasp or manipulate objects that are on the ground, over surfaces, near walls, or even under a surface. In all these cases, the multirotors will operate in hover or low speed near these horizontal or vertical surfaces. This paper studies the control of multirotor platforms under the influence of close ground surfaces on multirotors rotor thrust. Thus, for example, in the AEROARMS European project [9], aerial manipulators with multiple arms are used for inspection and maintenance in industrial settings and flying close to horizontal surfaces, and in the ARCAS European project [10], aerial robotic manipulation for assembly over a surface is considered (see Figure 1). The wake of a rotorcraft can be greatly affected when the rotor is close to obstacles that disturb its free development. The most common of these effects is the one produced by the ground surface. This phenomenon, usually known as ground effect, is more pronounced in rotorcraft operating in hover and low speed. For rotorcraft hovering close to the ground, therotorwakemustrapidlyexpandasitapproachesthe surface, transitioning from the almost vertical downwash to radial outwash parallel to the ground. This alters the velocity Hindawi International Journal of Aerospace Engineering Volume 2017, Article ID 1823056, 17 pages https://doi.org/10.1155/2017/1823056 2 International Journal of Aerospace Engineering Figure 1: Structure assembly in the ARCAS project. of the slipstream and the induced velocity, which then affects the rotor thrust and power. The ground effect in helicopters has been well researched in literature [11, 12] and has been studied for take-off, landing, and hovering near the ground [13–15]. However, for multirotors, it has not received much attention yet, although these platforms are being increasingly used in multiple applications. The influence of ground effect in helicopters has been studied through the use of an underlying aerodynamic model or empirically. A classical analytical model for the ground effect is provided by [11], using potential flow with a single source to model the rotor airflow and the method of images to account for the ground effect. Other authors have provided empirical expressions for the rotor thrust increment in ground effect for large [16] and small UAV helicopters [17]. The model in [11] has been widely used because it has a simple analytical form and has been experimentally shown to accurately capture the relationship between rotor thrust in ground effect and rotor height over the ground surface. The ground effect in multirotors has received much less attention. Several papers deal with the aerodynamic models of multirotors [18], which are used for navigation [19] or even for power control [20]. Disturbance observers have become popular in the last years for estimating external wrench in multirotors[21,22].Inmostcases,itisassumedthatthe external disturbance source is unique, mainly contact forces [23, 24] or wind. In [25], the simultaneous online estimation ofaerodynamicandcontactforcesisstudiedtodiscriminate between them and compute the wind velocity by means of model inversion. However, disturbance observers have not been used for ground effect estimation. The influence of ground effect has been considered in the development of controllers for low-altitude flight in [26] using an adaptive controller and a height estimator that works well in the experiments, although false measurement from the ultrasonic sensor can destabilize the system. A takeoff and landing controller that uses an ant colony filter for estimation of the ground effect is presented in [27]. The algorithm is tested in simulation with PID and sliding modes controllers, and in both cases the consideration of the ground effect improves significantly the controller performance. In [28], a PID landing controller with a ground effect robust compensator has been presented. The experimental tests show that accounting for the ground effect improves the controller behavior. Also, ground effect estimation using a vision sensor to estimate distance to obstacles and learning from previous flights have also been proposed [29]. A dynamic controller for rotorcraft landing and hovering in ground effect using feedback control based on flow field estimationhasalsobeendevelopedandtestedinsimulation [30]. However, in almost all cases, the model of the ground effect in [11] is assumed or evaluated for a single rotor. The only experimental results that have been reported, making experiments with a small quadrotor flying in hover over the ground at different heights [31] and using a test bench [32], suggest that the ground effect in multirotors may be larger than predicted by [11], although the issue has not been further analyzed. This paper studies the influence of the ground effect in multirotor control, considering the full multirotor and not only an isolated rotor. Then, the effects of all the rotors of the multirotor being under the ground effect are analyzed. Furthermore, a phenomenon that we have called multirotor partial ground effect is described and analyzed. It appears only in multirotors when flying close to surfaces or objects in the environment, in situations where some of the rotors experiment the ground effect but not all. To the authors’ knowledge, this is the first time that the aerodynamic partial ground effect is reported in the literature. A test bench has been built to determine experimentally theinfluenceofproximitytothesesurfacesoftheindividual rotors in a multirotor and of the whole multirotor. In the paper, the results of these experiments are presented. The organization of the rest of the paper is as follows: Section 2 presents the analysis of the ground effect for a single rotor and the full multirotor and when only some of the rotors are under the ground effect, using experimental results in the test bench. Section 3 studies the implications of flying near surfaces for multirotor control, presenting simulations of different control strategies in ground effect. These control strategies include a standard linear controller, whosebehaviorisusedasbaselineforcomparison,andtwo controllers that consider the ground effect: a controller that uses an external wrench disturbance observer for ground effect estimation and a controller that estimates ground effect from the model of the environment. Section 4 presents several experiments with multirotors in a test stand and flying International Journal of Aerospace Engineering 3 outdoors which show the ground effect and the performance of the controllers. 2. The Ground Effect in Rotary Wing UAVs 2.1. Ground Effect for Single Rotor. As mentioned before, the ground effect for single-rotor helicopters has been extensively studied in the literature [11–16]. When the rotor is under the ground effect, there is an increment in the thrust generated by the rotor for the same power, which is greater the closer the rotor is to the ground. In general, the ground effect in helicopters has been found to be significant when the rotor is at a vertical distance to the ground of up to one rotor diameter. A simple analytical model that is used to model thegroundeffectinhelicoptersusespotentialflowwitha single source to model the rotor airflow and the method of images to model the ground effect (potential flow with the method of images (PFI)) [11]. Other authors have presented empirical expressions for the increment of rotor thrust in groundeffectwhichshowsimilarresults[16,17],although the PFI model in [11] has been widely used because it has a simple analytical form and has been experimentally shown to accurately capture the relationship between rotor thrust in ground effect and rotor height over the ground surface. The PFI model represents the rotor as a threedimensional potential source, which has a strength of 𝑠=𝑅2VIGE/4,whereRis the radius of the rotor and VIGE is the induced velocity at the rotor. The velocity potential of a source placed at (𝑥0,𝑦0,𝑧0)canbeexpressedas 𝜙=− 𝑠 √(𝑥−𝑥0)2+(𝑦−𝑦0)2+(𝑧−𝑧0)2.(1) Theeffectofthegroundplaneismodelledasamirrorimage source to enforce that the flow does not pass through the ground plane. Thus, placing two sources in 𝑥0=0,𝑦0=0, and ±𝑧and obtaining the ratio of air velocities in-ground- effect (IGE) and out-of-ground-effect (OGE), the following expression for the rotor thrust increment due to the ground effect can be derived [11]: 𝑇IGE 𝑇OGE =1 1−(𝑅/4𝑧)2,(2) where 𝑇OGE is the thrust generated by the rotor flying out of the ground effect, 𝑇IGE is the thrust when the rotor is under the ground effect, 𝑅is the radius of the rotor, and zis the vertical distance of the rotor to the ground. In order to check the validity of this model for multirotor rotors, a series of tests have been performed in a specially designed test bench, which has been built for experimental motor/rotor characterization close to surfaces. This test bench,showninFigure2,isabletomeasurerotorthrust, rotor speed, and motor PWM input, controlled from a computer with a data acquisition card and a graphic user interface. The test bench allows making tests with different distance/inclination angle of the rotor plane with respect to surfaces. (a) (b) Figure 2: Test bench developed at GRVC for testing the ground effect. The “ground plane” (vertical white panel) can be placed at different distances from the rotor plane: (a) test with a single rotor and (b) test with a complete multirotor. Tests with several combinations of motor and rotor have been made using the test bench. Figure 3 shows the results of two of them, which correspond to two multirotors of different size.ThefirstoneisthePQUADquadrotorwithfourrotorsof 12cmradiusandatotalweightof1,4Kg,andthesecondoneis the AMUSE multirotor [6], which has eight rotors of 20,5 cm radius and a total weight of 12 Kg. The ground plane has been placed at different distances from the rotor and a set of nine tests have been performed for each distance. The results are displayedinFigure3asthemeanvalueoftheincrementin thrust with respect to the case when there is no ground effect (𝑇IGE/𝑇OGE)andanerrorbarshowingthestandarddeviation. The results in Figure 3 show that the PFI model that is used in helicopters for modelling the ground effect predicts alsowelltheinfluenceofthegroundformultirotorrotors, which are much smaller. A functional interpretation of the ground effect as seen in Figure 3 is that the ground “pushes the rotorcraft up” as the 4 International Journal of Aerospace Engineering Ground effect 1 1.05 1.1 1.15 1.2 1.25 T）＇％/T／＇％ 31.5 2.5 3.50.5 1 2 4 z/R Figure 3: Ground effect for a single rotor: experimental and theoretical results of the increment in the thrust generated by a single rotor as a function of the distance to the ground plane. Black dashes lines represent the results of the PFI model. Blue error bar is the experimental result for PQUAD and orange error bar is the experimental result for AMUSE. rotor approaches the surface. For the same transmitted power to the motor, the rotor develops more thrust caused only by thepresenceoftheground,whichdeviatestheairflowradially and parallel to the ground, generating new fields of velocity and pressure around the rotor. 2.2. Ground Effect for the Full Multirotor. Unlike helicopters thathaveasinglemainrotor,inmultirotors,thepresenceof multiple coplanar rotors may induce different behavior with respect to the single-rotor case, since the airflows from the different rotors may interfere with each other. An analytical model of the ground effect obtained using potential flow and the method of images for a full multirotor has been derived, following the same assumptions of the PFI for a single rotor shownintheprevioussubsection.Thepotentialflowmodel uses one source located at the geometric center of each rotor and its corresponding image source to represent the ground boundary conditions. So, the four rotors and four images will be modelled, placing three dimensional sources in the same way as the previous section. For the case of a quadrotor with four coplanar rotors with a separation dfrom each rotor axis to its adjacent rotor axes, the sources of the rotors and itsimageswillbe𝜙1,5 : (0,0,±𝑧),𝜙2,6 : (0,𝑑,±𝑧),𝜙3,7 : (𝑑,0,±𝑧),and𝜙4,8 : (𝑑,𝑑,±𝑧),where𝜙𝑖,𝑖+4 represents the velocity potentials of the rotor 𝑖and its rotor image (𝑖+4). Thus, the resultant expression of the increment in thrust due to the ground effect is the following: 𝑇IGE 𝑇OGE =1 1−(𝑅/4𝑧)2−𝑅2(𝑧/√(𝑑2+4𝑧2)3)−(𝑅2/2)(𝑧/√(2𝑑2+4𝑧2)3).(3) Figure 4 shows the increment in thrust for a quadrotor due to the ground effect with a dashed line and for a single rotor with a solid line for comparison. It can be seen that the effect is significantly larger for a quadrotor due to the aerodynamic interference of the other rotors (the additional terms in the denominator of (3)). Furthermore, experimental tests with a full quadrotor have also been performed using the test bench described above. In this case, the tests have been done with the PQUAD quadrotor shown in Figure 2(b), and the results can be seen in Figure 4. Similar to the single-rotor case, five tests have been done at each distance to the ground, and the average values are marked with a red circle and a blue error bar represents the standard deviation. The experimental results inFigure4givevaluesforthegroundeffectthrustincrease which are significantly larger than the predicted ones with the PFI quadrotor model (dashed line) and the results for a single rotor. A possible explanation for this larger effect in the full multirotor is what is known as the fountain effect,which arises when a pair of rotors are flying close to the ground. This can lead to strong flow interactions of the slipstream flow between the rotors. The airflow of each rotor splays out radially in all directions when it encounters the ground plane, but in the area between the rotors it interacts with the flow of the other rotor and the flow reverses back up through the rotors, impinging on the central part of the quadrotor body, increasing the upward force acting on the aerial vehicle due to the ground effect. This effect has been reported for tandem helicopters [33] and has been suggested also for quadrotors [32]. Figure 5 shows a CFD simulation that illustrates this fountain effect. This simulation has been done using a simplified model of a quadrotor hovering at adistanceof2R(with a rotor radius Rof 12 cm for the simulation) from the ground plane. The rotors have been modelled as a constant velocity source on the rotor area, that is, the rotation of the propeller is not being simulated. The velocity of the constant velocity source is the mean value of the airspeed measured experimentally under the rotors of the PQUAD quadrotor flying in hover. The central part of the quadrotor body has been modelled with a solid box. Figure 5 shows the velocity field in a vertical plane cut along the quadrotor diagonal. It can be seen in this figure that the airflow coming out from the rotors, instead of spreading parallel to the ground in all directions as in the outer part of rotors 1 and 3, interacts with the ground and the central body in the central area between both rotors, forming a vortex ring that causes the fountain effect with the increase of the thrust duetothegroundeffect. The PFI quadrotor model of (3) does not reproduce the behavior observed in the experiments. Since it is very useful to have a simplified model of the ground effect in multirotors International Journal of Aerospace Engineering 5 that can be used for simulations and controller development, an additional term has been included in the equation to account for flow recirculation and the central body lift that it generates. This additional term uses the velocity of the air atthecentralpointofthebodyandadjustsitsinfluencewith an empirical coefficient 𝐾𝑏, which takes a value close to 2 in the experiments performed. Then the expression of the thrust increment due to the ground effect takes the following form: 𝑇IGE 𝑇OGE =1 1−(𝑅/4𝑧)2−𝑅2(𝑧/√(𝑑2+4𝑧2)3)−(𝑅2/2)(𝑧/√(2𝑑2+4𝑧2)3)−2𝑅2(𝑧/√(𝑏2+4𝑧2)3)𝐾𝑏,(4) where bis the distance between two opposite rotor axes (diagonal) and 𝐾𝑏is the empirical body lift coefficient. Figure 6 shows the thrust increment due to the ground effect given by the multirotor PFI with the body lift term, with 𝐾𝑏=2. As can be seen in the figure, expression (4) matches more closely the experimental values. As a conclusion, although the ground effect in multirotors (multiple coplanar rotors) has been assumed by most researchers to be the same as for helicopters (a single rotor) [18–29] and be significant up to distances to the ground of 2 rotor radii, the results presented in this section show clearly that this is not the case; the ground effect for multirotors is much larger, being significant for distances to the ground of up to 5 rotor radii. Although the PFI can be expanded toincludethecontributionsofalltherotorsofaquadrotor (see (3)), the addition of a body lift term with an empirical coefficient (see (4)) reproduces the experimental behavior and can be used in simulations and controller development. 2.3. Partial Ground Effect. A new phenomenon that appears in aerial manipulation with multirotors when approaching some locations in the environment to manipulate objects is what we called multirotor partial ground effect.Inthepartial ground effect (see Figure 7 for a quadrotor), which is unique tomultirotors,themultirotorisflyinginhoveroratlowspeed in a situation in which only one or several of its rotors (but not all) are under the influence of the ground effect. In this situation, rotor 3 in Figure 7 will experiment an increase in thrust Δ𝑇ge1which will generate a disturbing moment 𝑀ge1which tries to rotate the multirotor counterclockwise and then move apart from the object because of the tilting. This effect may induce an important disturbance, and its implications in multirotorcontrolwillbeanalyzedinthenextsections. If one of the rotors is under the ground effect, its characterization can be modelled as described in Section 2.1. However,thecasewhenthreeoftherotorsareclosetoa horizontal surface under the ground effect will be different. For this case, a similar analysis to the full multirotor has been made, including the PFI analytical model and the experimental tests in the test bench with a quadrotor with only three rotors switched on. The results are shown in Figure 8, where the ground effect is much larger than that for asinglerotorandfollowsthesametrendasthatforthefull multirotor, though with less intensity. 2.4. Response to Attitude Disturbances. Another consequence ofthegroundeffectwhichisalsouniquetomultirotorscomes from the way the rotor thrust forces vary with the distance to the ground. In Figure 9, a multirotor hovering in ground effect which experiments an attitude perturbation is shown. Since the increment in rotor thrust depends on the distance ofeachrotortothegroundandeachrotorhasadifferentdistance (𝑧1and 𝑧3inFigure9),adisturbancemoment𝑀ge2will be generated which tries to rotate the multirotor opposing the disturbance, and, thus, it is a stabilizing moment. Inpractice,however,ithasbeenfoundthatfortypical attitude disturbances of about 5–10∘this effect, although stabilizing, is not considerable unless the multirotor is very close to the ground, and then it is considered not significant for controller development. 3. Influence of Proximity to Surfaces in Multirotor Control Thissectionanalyzestheinfluenceofflyingclosetosurfaces on multirotor control. Partial ground effect is a special phenomenon that appears only in multirotors when flying closetosurfacesandcanbedefinedassituationsinwhich only some of the rotors (but not all) are under the ground effect. We study the control of the partial ground effect because it is the most related to the practice of aerial manipulation. The section includes a comparative study of the results obtained in simulation tests of different control strategies of a quadrotor model. The tests have been made simulating that the multirotor is under the influence of the ground effect and using the ground effect model presented in the previous section. 3.1. Multirotor Dynamic Model. The dynamic model of the multirotor can be obtained using the Euler-Lagrange formulation [34, 35]. This model is basically obtained by considering the multirotor as a rigid body evolving in 3D space and subject to one force (the total thrust generated by al the rotors) and three moments generated by the differences in speed and thrust of pairs of rotors. The dynamics of the electric motors are relatively fast and therefore they will be neglected as well as the flexibility of the blades. The generalized coordinates of the multirotor can be defined as 𝑞=(𝑥,𝑦,𝑧,𝜙,𝜃,𝜓), (5) where 𝜉=(𝑥,𝑦,𝑧)denote the position of the center of mass of the multirotor relative to the inertial frame and 6 International Journal of Aerospace Engineering Ground effect, complete quadrotor 1 1.1 1.2 1.3 1.4 T）＇％/T／＇％ 365214 z/R Figure 4: Ground effect for a full multirotor (quadrotor): experimental and theoretical results of the increment in the thrust generated by a quadrotor as a function of the distance to the ground plane in green error bar compared to the results for a single rotor in red error bar. The PFI approximations are represented in blue and black dashed lines, respectively. 𝜂=(𝜙,𝜃,𝜓)are the three Euler angles (roll, pitch, and yaw) representing the orientation of a reference system attached to the multirotor body with respect to the inertial frame. If 𝑚is the total mass of the multirotor and 𝐽is the matrix of moments of inertia of the aerial vehicle in the inertial frame, the resultant Euler-Lagrange equations for the translational and rotational degrees of freedom are, respectively, 𝑚𝜉+(00 𝑚𝑔)=𝑅𝐹𝜉, 𝐽𝜂+𝐶1(𝜂, 𝜂) 𝜂=𝜏. (6) In (4), 𝐶1(𝜂, 𝜂)is referred to as the Coriolis terms and contains the gyroscopic and centrifugal effects, Ris the rotation matrix between the body and inertial systems, and 𝐹𝜉=(0,0,𝑇)and 𝜏=(𝜏𝜙,𝜏𝜃,𝜏𝜓)are the force and moments generated by the rotors. Both translational and rotational dynamic equations can be expressed in matrix form as 𝑀(𝑞)𝑞+𝐶(𝑞,𝑞) 𝑞+𝐺(𝑞)=𝐹, (7) where 𝐹=(𝐹𝜉,𝜏)are the generalized moments and M,C,and Gare the mass, Coriolis, and gravity matrix, respectively. The thrust generated by each rotor and the reaction torque due to rotor drag are generally accepted to be proportional to the square of the angular velocity of the rotor 𝜔𝑖when flying on free air: 𝑇𝑖=𝑘𝜔2 𝑖, 𝑄𝑖=𝑐𝜔2 𝑖.(8) The thrust and drag coefficients kand ccan be determined by static thrust tests. Then, for a quadrotor in which the distance of the geometric center to the axis of each rotor is d, there is a direct correspondence between the four generalized moments and the angular velocities of the rotors: [ [ [ [ [ [ 𝑇 𝜏𝜙 𝜏𝜃 𝜏𝜓 ] ] ] ] ] ]=[ [ [ [ [ [ 𝑘𝑘𝑘𝑘 0 𝑘𝑑 0 −𝑘𝑑 −𝑘𝑑0𝑘𝑑0 −𝑐 𝑐 −𝑐 𝑐 ] ] ] ] ] ] [ [ [ [ [ [ [ 𝜔2 1 𝜔2 2 𝜔2 3 𝜔2 4 ] ] ] ] ] ] ].(9) However, when the multirotor is flying close to the ground or other horizontal surfaces, the rotor thrust and drag model(8)arenolongervalid,ashasbeenshowninSection2. To account for the ground effect and partial ground effects in the simulator, the thrust model is modified as 𝑇𝑖=𝑘𝜔2 𝑖𝑓GE (𝑧𝑟,𝑖), (10) where 𝑓GE(𝑧𝑟)is the ground effect factor that accounts for the increment in thrust due to the ground effect and partial ground effect, which is obtained from the data in Sections 2.1–2.3. This ground effect factor, 𝑓GE(𝑧𝑟), depends on the relative distance of each rotor to the ground, 𝑧𝑟.Forthat purpose, a 3D map of the environment in which the aerial robot is flying has been included in the simulator (see Figure 10). Furthermore, in the simulator, we have considered thefactthattherotorthrustincrementvariesapproximately linearly with the rotor area that is under the ground effect, as has been reported with experiments with a helicopter rotor [36]. Then, the generalized dynamic model of the multirotor becomes 𝑀(𝑞)𝑞+𝐶(𝑞,𝑞) 𝑞+𝐺(𝑞)=𝐹+𝐹GE,(11) where 𝐹GE are the additional generalized moments due to the ground effect. Two different cases have been tested in order to analyze theinfluenceofthegroundeffectinmultirotorcontroland compare the different control approaches. (1)The multirotor flies over an obstacle (see Figure 11(a)), beginning in point A and ending in point B. In the reference trajectory, the 𝑦-coordinate remains constant, and the 𝑥coordinate varies from 𝑥=0(point A) to 𝑥=7(point B). The obstacle is between 𝑥=3and 𝑥=5. (2)The multirotor is commanded to go from point A to point B and hover on B, where it has to perform a manipulation operation (see Figure 11(b)). In point B, only one rotor is over the obstacle and then under the influence of the partial ground effect. In the reference trajectory, the 𝑦-coordinate remains constant, and the x-coordinate varies from 𝑥=0(point A) to 𝑥=2.8(point B). The obstacle is between 𝑥=3and 𝑥=5. Three different control alternatives have been analyzed in both scenarios: conventional control with cascaded linear controllers, estimated torque controller, and control with rotor height estimation (feedforward). The results obtained using the different control alternatives are shown below. A comparison between these alternatives will be shown at the end of this section. International Journal of Aerospace Engineering 7 Rotor 1 Rotor 3 Central body Ground plane Figure 5: CFD simulation of a quadrotor simplified model hovering in ground effect at a distance of 2Rof the ground plane. The rotors have been modelled as a constant velocity source on the rotor area, with the mean velocity measured experimentally on the PQUAD quadrotor flying in hover. Ground effect, complete quadrotor 638052147 z/R 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 T）＇％/T／＇％ Figure 6: Ground effect for a full multirotor (quadrotor): experimental and theoretical results of the increment in the thrust generated by a quadrotor as a function of the distance to the ground plane (green) compared to the results for a single rotor (red). Five experiments have been performed at each distance; the error bar represents the standard deviation. PFI approximations are represented in the blue dashed line for quadrotor with body lift term (see (4)) and black dashed line for one rotor (see (2)). 3.2. Conventional Control. A standard control scheme with cascaded PID linear controllers in each channel has been considered to analyze the response of the system to a conventional controller which does not take the ground effect into account. This control scheme is widely used as baseline in multirotor autopilots [37], and it is a good reference for the comparison with other methods. The multirotor is moving forward along the xglobal axis and the yaw angle is maintained constant in the simulations, and so the relevant variables that are presented in the plots as a function of the time are the pitch angle, 𝜃,andtheglobalcoordinateinthe direction of motion, 𝑥. The results obtained in the simulation using the PID controller in the two experiments are shown in Figure 12 (case 1: flying over obstacle) and Figure 13 (case 2: hovering T1 MＡ？1 T3+ΔT Ａ？1 Figure 7: Multirotor under partial ground effect. in partial ground effect). In the figures, a broken line has been included to mark the x-coordinate of the final destination of the multirotor (point B in both cases). Furthermore, the values of the x-coordinates that are over the obstacle are highlighted with green background. Several simulations are presented in each plot for comparison: “OGE,” which is the simulation of the multirotor flying high above the obstacle, so that no ground effect is present, and two simulations flying close to the obstacle (“IGE”) at two different heights normalized with the rotor radius R. Figure 12 shows the evolution of the x-coordinate and the pitch angle for the first case: flying over an obstacle. It can be observed that the ground effect disturbance produces a torque that affects the system in attitude and position. This torque is more significant when the vehicle is closer to the obstacle. In fact, the results for 𝑧/𝑅 = 2.0show how this torque pushed the vehicle away from the obstacle repeatedly and it cannot fly over it with this controller. 8 International Journal of Aerospace Engineering Three rotors, ground effect 32514 z/R 1 1.05 1.1 1.15 1.2 1.25 T/T／＇％ Figure 8: Red error bar: experimental and theoretical results of the increment in the thrust generated by three rotors as a function of the distance to the ground plane. Black dashed line: theoretical results of the PFI method for a single rotor. Blue dashed line: theoretical results of the PFI method for three rotors. T1 MＡ？2 T3+ΔT Ａ？2  z1z3 Figure 9: Response of a multirotor in ground effect to attitude disturbance. 0 5 0.5 5 1 1.5 0 2 0 −5−5 Figure 10: Example of environment map for simulation. In the second case (Figure 13), the multirotor tries to hover with only one rotor over the obstacle, but it is unable to do it in the 𝑥reference and keeps flying in a maintained oscillation going in and out of the ground effect. The simulations presented in Figures 12 and 13 were performed with the quadrotor flying at a velocity of 0.2 m/s. In order to assess the behavior at different translational velocities, the simulations have been done at a maximum speed of 1 m/s. Figure 14(a) shows the results of the hovering in partial ground effect test case, and it can be seen that thebehaviorissimilartotheonepresentedinFigure13. Figure 14(b) shows the simulation of case 2: flying over obstacle. In this case, although there is a strong perturbation in the pitch angle, the inertia of the multirotor moving at 1 m/s allows it to surpass the obstacle unlike when flying at 0.2 m/s. Since moving at a slow speed is more restrictive and also is more appropriate for aerial manipulation tasks, the rest of the simulations will be done with the multirotor flying at 0.2 m/s. Other simulations have been done considering sensor noise. Figure 15 shows the simulation of the quadrotor in case 1: hovering in partial ground effect with a velocity of 1m/s and 𝑧/𝑅=2. A normal distribution with a standard deviation of 0.015 rad/s has been supposed for the noise in thegyroscopes.ItcanbeseeninFigure15thatthepresence of noise in the sensors amplifies the oscillations, although the qualitative behavior is similar. In the rest of the paper, only the noise-free simulations will be presented. 3.3. Estimated Torque Controller. This control alternative includes a torque disturbance observer that is used to estimate thetorqueinducedbythepartialgroundeffect,causedbythe different aerodynamic thrust generated by the rotors when the multirotor is in partial ground effect. Several approaches have been used to estimate external force and torque disturbances in multirotors [22–24, 38]. In this paper, a nonlinear torque disturbance observer has been implemented [24]. If the multirotor dynamic equations are expressed in compact form (11), the nonlinear observer is able to estimate the forces andtorquesduetothegroundeffect𝐹GE: 𝐹GE =𝐿(𝑞,𝑞)(𝐹GE − 𝐹GE) =−𝐿(𝑞,𝑞) 𝐹GE +𝐿(𝑞,𝑞)(𝑀(𝑞) 𝑞+𝐶(𝑞,𝑞) 𝑞+𝐺(𝑞)−𝐹), (12) where  𝐹GE is the vector of estimated force and torque disturbances due to the ground effect and 𝐿(𝑞, 𝑞)is the observer matrix that has to be designed in order to assure convergence of the observer. Figure 16 shows the control scheme of this strategy. The results obtained with this control approach are shown in Figure 17 (flying over an obstacle) and Figure 18 (hovering in partial ground effect). In these figures, it can be observed thattheobtainedresultsarebetterthanusingaconventional PID-based controller, as was expected. In the first test case (as defined in Figure 11(a)), the response of the system is faster than with the baseline controller. Moreover, the multirotor is able to avoid being International Journal of Aerospace Engineering 9 yb zb xb yi zi xi A B (a) yb zb xb yi zi xi A B (b) Figure 11: (a) Case 1: flying over an obstacle under the influence of the ground effect. (b) Case 2: hovering at a point with only one rotor under the influence of ground effect. x Obstacle Reference x OGE x IGE (z/R = 3.0) x IGE (z/R = 2.0) 4010 15 20 25 30 35 500455 Time (s) 0 2 4 6 8 x (m) 4010 15 20 25 30 35 500455 Time (s)  OGE IGE (z/R = 3.0) IGE (z/R = 2.0) −1 0 1 2 3 (∘) Figure 12: PID controller: flying over obstacle. pushed away from the obstacle when 𝑧/𝑅=3.0,anditisable to arrive to its destination at point B (𝑥=7)whenitisflying closer to the obstacle at 𝑧/𝑅=2.0. The results of simulations in the second case (Figure 18) show that this control alternative can eliminate the aggressive oscillations in pitch angle. OGE IGE (z/R = 3.0) IGE (z/R = 2.0)  −1 0 1 2 3  20 25 30 35 4015 Time (s) x Obstacle Reference x OGE x IGE (z/R = 3.0) x IGE (z/R = 2.0) 20 25 30 35 4015 Time (s) 1.5 2 2.5 3 x (m) (∘) Figure 13: PID controller: hovering in partial ground effect. The estimated torque controller can improve the response of the system because the disturbances are partially cancelled atthesametimetheyarebeingproduced. 3.4. Control with Rotor Height Estimation (Feedforward). The last alternative that has been studied is based on a feedforward concept.Ashasbeenseenintheprevioussections,theground 16 International Journal of Aerospace Engineering [5] S. Kim, H. Seo, and H. J. Kim, “Operating an unknown drawer using an aerial manipulator,” in Proceedings of the 2015 IEEE International Conference on Robotics and Automation, ICRA 2015,pp.5503–5508,May2015. 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Bruyninckx, “A hybrid pose/ wrench control framework for quadrotor helicopters,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA),2012. ,QWHUQDWLRQDO-RXUQDORI $HURVSDFH (QJLQHHULQJ +LQGDZL3XEOLVKLQJ&RUSRUDWLRQ KWWSZZZKLQGDZLFRP 9ROXPH Robotics Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Active and Passive Electronic Components Control Science and Engineering Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 International Journal of Rotating Machinery Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Hindawi Publishing Corporation http://www.hindawi.com Journal of (QJLQHHULQJ Volume 201 Submit your manuscripts at https://www.hindawi.com VLSI Design Hindawi Publishing Corporation http://www.hindawi.com Volume 201- Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Shock and Vibration Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Civil Engineering Advances in Acoustics and Vibration Advances in Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Electrical and Computer Engineering Journal of Advances in OptoElectronics Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 The Scientific World Journal Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Sensors Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Modelling & Simulation in Engineering Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Chemical Engineering International Journal of Antennas and Propagation International Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Navigation and Observation International Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Distributed Sensor Networks International Journal of