âunifiedâ in the sense that a single controller is being used for all flight modes: hover, transition and level flight and for. 3D aircraft dynamics. The tail-sitter VTOL ...
A Unified Control Method for Quadrotor Tail-sitter UAVs in All Flight Modes: Hover, Transition, and Level Flight* Jinni Zhou, Ximin Lyu, Zexiang Li, Shaojie Shen and Fu Zhang Abstract— This paper presents a unified control framework for controlling a quadrotor tail-sitter UAV. The most salient feature of this framework is its capability of uniformly treating the hovering and forward flight, and enabling continuous transition between these two modes, depending on the commanded velocity. The key part of this framework is a nonlinear solver that solves for the proper attitude and thrust that produces the required acceleration set by the position controller in an online fashion. The planned attitude and thrust are then achieved by an inner attitude controller that is global asymptotically stable. To characterize the aircraft aerodynamics, a full envelope wind tunnel test is performed on the full-scale quadrotor tail-sitter UAV. In addition to planning the attitude and thrust required by the position controller, this framework can also be used to analyze the UAV’s equilibrium state (trimmed condition), especially when wind gust is present. Finally, simulation results are presented to verify the controller’s capacity, and experiments are conducted to show the attitude controller’s performance.
I. INTRODUCTION Unmanned aerial vehicles (UAVs) are being used for a wide variety of missions, such as search and rescue, line inspection, surveying, surveillance and reconnaissance (ISR), and in agriculture. To meet the ever increasing variety of missions and operation environments, a UAV that is both maneuverable (e.g. capability of vertical takeoff, landing, hovering) and efficient (i.e. longer range or endurance) offers unique capabilities that are generally not possible for conventional fixed-wing airplanes or rotary-wing aircrafts. Vertical takeoff and landing (VTOL) wing UAVs combine the desirable capabilities of rotary-wing and fixed-wing aircraft configurations in a single platform. When compared to its fixed-wing counterparts, a VTOL UAV can take off and land vertically and hover in a stationary position. These capabilities are particularly promising in urban and constrained environments where there is limited access to a runway, catapult or loiter space [1]. Moreover, by nature of its design, a fixed-wing airplane needs additional facilities and human involvement for safe takeoff or landing, which significantly limits its fully automated operation. When compared to its rotary-wing counterparts, a VTOL UAV can achieve longer flight endurance and range, which can reduce the frequency of battery replacement and extend the mission range and efficiency. As a consequence, VTOL UAVs are very suitable for a wide variety of missions and environments. Among the various implementations of VTOL aircraft [2], a tail-sitter aircraft is perhaps the simplest one since it does *Supported by Hong Kong Innovation Technology Fund (ITS/334/15FP). All with the Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST). {jzhouao,
xlvaa, eezxli, eeshaojie, eefzhang}@ust.hk
Fig. 1.
The tail-sitter VTOL UAV prototype
not require any extra actuators (e.g., tilting mechanisms) for the VTOL maneuver. Being simple is particularly useful for small and micro scale UAVs in order to save weight and manufacturing complexity. As such, a number of research teams have actively explored tail-sitter VTOL UAVs, such as the twin-engine configuration described in [3], the configuration with coaxial contra-rotating propellers in [4], and the quadrotor tail-sitter UAVs developed by Oosedeo et al. [5] and Wang et al. [6], to name a few. In order to achieve both hovering and level flight without any additional actuators, a tail-sitter VTOL UAV switches between these two distinct flight modes by tilting the whole aircraft pitch angle by 90 degrees. This maneuver is usually referred to as transition flight. The transition flight should be performed in a stable, reliable, and fully controlled manner without significant altitude drop or gain in order to avoid potential collisions. Yet all tail-sitter UAVs possess a common transition flight that is aerodynamically unstable as a stall usually occurs on the wing during the transition. There is a large amount of literature on the VTOL transition control. For the twin-engine T-wing tail-sitter UAV developed by Stone et al. [7], the flight dynamics were decoupled into longitudinal and lateral directions, and a gainscheduled LQR controller was used to control the vertical and forward flights. The transition was achieved by sending a step pitching angle command to the vertical controller. Meanwhile, the throttle was either specified open-loop via a pitch-angle schedule or controlled with a velocity controller to match a pre-specified velocity schedule with the pitchangle. Such a scheme is essentially open-looped, yielding uncontrolled lateral motion and altitude drop or gain during the transition. This effect was partially mitigated by an offline optimization process, which aimed to minimize the transition time while restricting the variation range of altitude
by utilizing an aerodynamic database of the aircraft [8]. However, the off-line optimization process did not consider any disturbances, such as wind gust, that could occur during real operation and, as a consequence, the reliability and robustness of such an open-loop transition strategy is questionable. The same issue applies to the work by Kita et al. [10] and Oosedo et al. [11] where a similar offline optimization process was used, and Frank et al. [1] where the transition was achieved by sending a series of well-chosen way-points (as opposed to the pitch command) to the hover controller and then switching to the level flight controller once the pitch angle dropped below some prescribed value. In [4], the pitch angle command was linearly interpolated during the transition. This can soften the transition process and avoid pitch angle overshoot, as pointed out by the author. However, this improvement did not address any drawbacks of the original strategy where the pitch angle was commanded as a step signal. In [9], three transition controllers were investigated on a model Convair XFY-1 Pogo, a simple controller based on a vector-thrust model, feedback linearization controller and model reference adaptive controller (MRAC). All these three controllers were designed based on two-dimensional (i.e., the longitudinal direction) flight dynamics and the lateral motion remained uncontrolled. In addition, the author did not consider the aerodynamic force as a function of the pitch angle, which is the virtual control action to be determined, in designing the feedback linearization controller. More theoretical work on the transition control of two-dimensional tail-sitter VTOL UAVs model can be found in [12]-[18]. In [12], two optimal transition problems (minimum time and minimum energy) were presented and solved numerically, and the effectiveness of this method was validated in simulation. In [13], a hybrid control strategy for autonomous transition between hover to level flights was developed for a fixed-wing aircraft, by dividing the flight envelope into four different regions: hover, transition, level and recovery flight, and utilizing either linear optimal control or nonlinear control techniques for each region. Pucci et al. [14] proposed to transform the original system dynamics, whose aerodynamic forces typically depend on the aircraft orientation, into one that is independent of the aircraft orientation, by changing of thrust control input. This equivalent transformation, which is later referred to as spherical equivalence [15], enables to compute the orientation (i.e. transition angle) and thrust separately, thus significantly easing the transition controller design and analysis. The author also derived the conditions on airfoil aerodynamic characteristics for which such spherical equivalence holds. The author further examined the effect of stall in [17], and proved that a class of transition maneuvers are not tractable due to equilibrium bifurcation and control singularities. In [16], a novel approach to the control of scale model airplanes was shown, this approach is an extension of the study in [18]. When compared to other work on aircraft nonlinear control, Hua et al. [16] didn’t make small angle of attack assumption, enlarging the controller’s operating domain.
In this paper, we propose a unified control method for a quadrotor tail-sitter UAV. The proposed control method is “unified” in the sense that a single controller is being used for all flight modes: hover, transition and level flight and for 3D aircraft dynamics. The tail-sitter VTOL UAV considered in this paper, shown in Fig. 1, uses four rotors and control surfaces, if available, for full attitude and altitude control. While the detailed design and modeling process of the UAV is presented in [27], [28] and [29], this paper will focus on the control strategy of the aircraft, especially the transition control. When compared to the other transition strategies summarized above, the method presented in this paper enables the full flight dynamics of the UAV to be actively controlled during the transition. Moreover, it is capable of uniformly treating the hovering and forward flight modes, and enabling continuous transition between them. As such, the tail-sitter UAV can achieve stable flight at various pitch angles from 0 to 90 degrees without significant altitude drop or gain. Although flying at these intermediate pitch angle may not necessarily achieve minimal power consumption, it enables the UAV to fly at a wide range of speeds. Such a feature sometimes benefit applications such as surveillance and reconnaissance (ISR). A key part of the proposed method is a nonlinear solver that solves for the proper attitude and thrust that achieve the required acceleration put by an outer loop position or velocity controller in an online fashion. As the nonlinear solver needs to know the aerodynamic force of the UAV at a given airspeed, a full envelope wind tunnel experiment is performed on the full-scale quadrotor tail-sitter UAV. Besides planning the attitude and thrust required by the position controller in an online fashion, this framework could also be used off-line to analyze the UAV’s equilibrium state (trimmed condition), especially when wind gust is present. The remainder of this paper is organized as follows. Section II will present a full dynamic model of the UAV. The control architecture in detail will follow in section III, with numerical verification provided in section IV and experimental verification in section V. Finally, conclusions will be drawn in section VI. II. S YSTEM M ODELING A. Flight dynamics Coordinate systems used in this paper will follow conventions from conventional fixed-wing aircraft [19]. As seen in Fig. 2, the earth frame denoted by Fe (Oe , Xe ,Ye , Ze ) is in the convention of North, East and Down, while the body frame, denoted by Fb (CG, Xb ,Yb , Zb ), is referred to in terms of the front, right and down directions. The body orientation is denoted as R ∈ SO(3). Let vector p = [x, y, z]T denote the position of the center of mass of the UAV expressed in the earth frame Fe (Oe , Xe ,Ye , Ze ), vector v = [vx , vy , vz ]T denotes the linear velocity of the UAV expressed in the earth frame, ω is the UAV angular rate expressed in the body frame, m denotes the UAV total mass, and I denotes the inertia matrix of the UAV. Applying Newton’s equations of motion to the
airframe yields the following dynamic model: = v
2
mv˙ = mge3 + R (Te1 + faero ) b R˙ = Rω I ω˙ = −ω × (Iω) + τ + Maero ,
(2) (3) (4)
b denotes the skew-symmetric matrix such that where the ω b ωx = ω ×x for any vector x ∈ R3 and × being the cross product, e1 = [1, 0, 0]T , e3 = [0, 0, 1]T , T is the total thrust generated on all motors, τ is the moment vector produced by the differential motor thrust, faero and Maero respectively denote the aerodynamic force and moment vectors expressed in the body frame and will be discussed in detail in the next section. Other terms such as the motor acceleration/deceleration and the motor gyroscopic effects are neglected in Eq. (4) because their values are too small.
CL
(1)
0
-2 100
200
0
0 -100
Y: β
Fig. 3.
-200
X: α
Full envelope lift coefficient CL
2
CD
p˙
1 0
-1 100
200
0
0 -100
Y: β
-200
X: α
L Fig. 4.
D
Xb
Zb Xe
Ye
0.5
ux CY
Yb Y
uz
Full envelope drag coefficient CD
0 -0.5 100
200
0
Ze
u
Y: β
uy Fig. 5.
Fig. 2.
0 -100
-200
X: α
Full envelope side force coefficient CY
Coordinate frames and aerodynamic nomenclatures
B. Aerodynamics The aerodynamic analysis of a tail-sitter UAV is similar to that of a conventional airplane [19], [21]. To begin with, one can define the airspeed u, which is the vehicle speed relative to the surrounding air mass, as follows: u = RT (v − w),
(5)
where v refers to the linear velocity of the UAV in Eq. (1) and w denotes the wind speed expressed in the earth frame. The wind speed can be measured by sensors such as a pitot tube, or estimated by an algorithm similar to [22] . The airspeed magnitude U, angle of attack α and sideslip angle β are defined as q U = u2x + u2y + u2z (6) uz α = tan−1 (7) ux u y β = sin−1 . (8) U The aerodynamic force faero and moment Maero are expressed in the body frame. The components of faero = [X,Y, Z]T are the axial force X, side force Y and normal force Z, while the components of Maero = [l, m, n]T are the rolling moment l, pitching moment m and yawing moment n, respectively. The aerodynamic forces are commonly defined and measured in the stability axes frame [20] where the
aerodynamic force consists of the lift L, drag D and the same side force Y . As shown in Fig. 2, the lift is perpendicular to the airspeed while the drag is in line with and opposes to the airspeed. The directions of drag, side force and lift form a right-handed frame. It follows from these definitions that X − cos α 0 sin α D Y = Y , 0 1 0 (9) Z − sin α 0 − cos α L the aerodynamic lift, drag, side force, and moments are: L = CL QS; D = CD QS; Y = CY QS l = Cl QSc; ¯ m = Cm QSc; ¯ n = Cn QSc. ¯ Where Q = 12 ρU 2 is the dynamic pressure, S is the reference area, c¯ is the mean aerodynamic chord (MAC), CL , CD and CY are the lift, drag and side force coefficients, respectively, and Cl , Cm and Cn are the rolling, pitching and yawing moment coefficients, respectively. For a specific airplane operating far off the speed of sound, these coefficients do not depend on speed, but are functions of angle of attack α and sideslip angle β , and can be characterized by a wind tunnel experiment. Fig. 3 – 5 shows the regression surface of lift, drag and side force coefficients. Detailed explanations of the modeling process and wind tunnel experiments are shown in [27]. With the knowledge of flight dynamics and aerodynamics, we proceed to the controller design shown in the next section.
III. C ONTROL A RCHITECTURE Since the actuation mechanism of the tail-sitter UAV is similar to a quadrotor [20], the same dual-loop control structure is used to control the vehicle. As shown in Fig. 6, the controller consists of an inner loop attitude controller, which tracks the commanded attitude, and an outer loop position controller that computes the desired attitude from the position tracking error. As the tail-sitter aircraft experiences large attitude variation during transition, a singularity-free and global stable attitude controller is highly favorable.
Position Controller
Rd
Attitude Controller
Fig. 6.
VTOL Dynamics
Control structure
Recall that the attitude equation is described as b = Rω
(10)
= −ω × (Iω) + τ + Maero
(11)
In order to resolve the nonlinearities in the attitude kinematics, an outer-loop proportional controller is employed to track the desired attitude Rd . ωd = −Kξe ,
(12)
where ωd is the desired angular rate, K is the gain, and ξe is the axis-angle representation of the error attitude ξe = log(RTd R)∨ . As shown in [23], this simple controller achieves local asymptotic tracking performance given K 0. Only local stability can be implied because the logarithmic function is singular at the rotation angle of π. However, this can be overcome by using a quaternion representation of the error attitude. Let qe = [η, ε] be the quaternion representation of Re [25] where η and ε are respectively the scalar and vector part of the quaternion, the axis-angle error ξe can then be computed as θ ξe
ωe dt + Kd
B. Position control loop Recall the translational motion is described as = v
p˙
= 2 cos−1 |η| θ = sgn(η) ε. sin θ2
(16) (17)
Given a desired trajectory pd (t), the position error is computed as e p = pd (t) − p. Then, a PID controller can compute the desired acceleration with a feedforward acceleration term Z de p ad = p¨d (t) + K p e p + Ki e p dt + Kd . (18) dt Eq. (17) implies that achieving the desired acceleration ad requires the attitude R and the total thrust T to satisfy the following equation:
A. Attitude control loop
R˙ I ω˙
dωe + ω × (It ω), (15) dt where ωe = ωd − ω is the angular rate tracking error. Z
τ = K p ωe + Ki
mv˙ = mge3 + R (Te1 + faero ) .
T pd
design methodologies such as loop-shaping, and H∞ synthesis. In this work, a simple PID controller is employed.
(13) (14)
Mayhew et al. [24] pointed out that even though the controller in Eq. (12) achieves global asymptotic stability when using quaternion representation, it is not robust to measurement noise. This claim was proven by constructing a piecewise constant measurement noise that constantly maintains the error attitude in a small neighborhood of π. However, actual measurement noise is unlikely to be piecewise constant and the controller given in Eq. (12) achieves global stability in practice. The attitude dynamics Eq. (11) are expressed in Euclidean space, enabling the use of well-established linear controller
1 R (Te1 + faero ) = ad . (19) m In the conventional quadrotor controller development, the aerodynamic force faero is usually ignored. The attitude and thrust in Eq. (19) can hence be solved analytically [20]. While this is a reasonable assumption for quadrotors due to their simple airframes, the primary design goal of a tail-sitter UAV is to use the wing aerodynamic force as the lift during level flight. As a result, the aerodynamic forces have to be considered in determining the attitude and thrust explicitly. As discussed in Section II, the aerodynamic force can be expressed as a general nonlinear function of the attitude R, vehicle speed v and wind speed w: ge3 +
faero = f (RT (v − w)).
(20)
This nonlinear dependence on attitude will significantly complicate Eq. (19) and obstruct the derivation of an analytical solution. Therefore, numerical methods are employed in this work to solve for the attitude and thrust. Since the three equality constraints put forward by Eq. (19) are inadequate to determine the attitude and thrust uniquely, an objective function is added to form an optimization problem. The objective function attempts to align the vehicle’s heading with its velocity v, which is consistent with aerodynamic requirements and the actual flight experience. As a result, the optimization problem can be formulized as Eq. (21), where e1 = [1, 0, 0]T , e2 = [0, 1, 0]T and e3 = [0, 0, 1]T . In this optimization problem, we parameterize the attitude R by two successive rotations: one is a rotation along an axis ν12 in the body XY plane, and the second rotation is along the body Z axis by angle ξ3 , which therefore represents the heading of the vehicle and needs to be aligned with the desired heading ψd as formulated in the objective function in Eq. (21). For v = 0, where the aircraft is hovering, the heading ψd is
defined by user command as the aerodynamic effects can be neglected in this case; otherwise, ψd is the direction current of the vehicle velocity, i.e., ψd = tan−1 vvxy . The desired thrust T should be bounded by its limits Tmin and Tmax , which depend on the current velocity, and are respectively the total thrust of the 4 motors running at minimum PWM and maximum PWM. Tmin can be a negative value because of the high advanced ratio when the forward speed is high. When T is equal to Tmin or Tmax , the integrator of the PID controller will be turned off (i.e., anti-windup). min
[ξ ,T ]∈R4
symmetrically mounted on the aircraft, and the decrement of each motor thrust caused by v is the same, so the differential motor thrust (i.e., τ) will not be affected by v.
|eT3 ξ − ψd | 1 R Te1 + faero RT (v − w) − ad = 0 m R = exp(νb12 ) exp(νb3 ) (21)
s.t. ge3 +
ν12 = [ξ1 , ξ2 , 0]T ν3 = [0, 0, ξ3 ]T Tmin ≤ T ≤ Tmax , The optimization problem in Eq. (21) is non-convex, and is solved by a sequential convex programming (SCP) algorithm shown in [30]. We implemented it using CVX, a MATLAB package designated for convex optimization problems, and tuned the optimization parameters appropriately. As the position control loop is running in real time, it requires the solver to converge within the update period (i.e., 0.02 s) of the position loop. The current MATLAB based implementation, although converges to the expected attitudes and thrust stably, is too slow for real-time implementation. Fortunately, it is possible to improve the algorithm’s execution time, as we have learned from past experience and reference [31] that algorithms that run on a dedicated computer using C++ can be over 500 times faster than MATLAB code. As the sampling time of the position loop is 0.02 s, we need the computation time of this solver in MATLAB to be less than 10 s. Indeed, the current computation time of the SCP solver in MATLAB is 1 s on average, satisfying this requirement. The attitude and thrust solved from Eq. (21) will yield the desired acceleration ad by the position controller. Therefore, the vehicle remains fully controlled in all flight modes: hovering, transition and level flight. Actually, the controller does not distinguish these flight modes at all.
Fig. 7.
Secondly, we analyze the impact of rotational dynamics on translational dynamics. When designing the position controllers, it is assumed that the planned attitude is instantaneously achieved. However, due to the inertia of the aircraft and the limited bandwidth of the attitude controller, the actual attitude cannot track the desired attitude ideally, creating a transient response. Such a transient response can usually be modeled as first order dynamics. Fig. 7 is the bode plot of the vehicle’s longitudinal direction, where C represents the position controller, P represents the vehicle attitude dynamics, which is modeled as first order dynamics with a 100 ms time constant and a second order integrator indicating that pitch angle causes an acceleration, and L represents the system loop transfer function defined as L = PC. In order to mitigate the effect of the transient response of the attitude loop on the position controller, the bandwidth of L is set to 3.32 rad/s, lower than the bandwidth (i.e., 10 rad/s) of the plant delay, so the transient response of the attitude loop can be reasonably ignored. Stability of the position controller can be implied by Fig. 7 as well, where the phase margin is 69.2 deg, the lower gain margin is -44.7 dB and the upper gain margin is +∞. plant
pd
C. Coupling analysis In previous analysis, we have ignored the coupling between the attitude and position loop, assuming that the commanded attitude can be instantaneously achieved. However, actual vehicles have coupled translation and rotation behaviors. Firstly, we analyze the impact of translational dynamics on rotational dynamics. We have seen that the moment τ is generated by the differential motor thrust, which depends on the vehicle’s linear velocity v. For each motor, when the velocity v increases, the motor thrust decreases as a result of the higher advanced ratio. Fortunately, the four motors are
Control structure
PID
ad
SCP Solver
Rd , T
1 e
T
z e
T
R,T hR,T a
T z 1
2
p
Fig. 8.
Simulation Model
IV. S IMULATION R ESULTS This section presents simulation results. Fig. 8 is the model used for simulation, where h (R, T ) is a function defined to calculate the acceleration for given Rd and T . Several example trajectories have been tested: (1) transition from/to level flight; (2) level flight at different speeds;
(3) circling; and (4) wind effect. In all these cases, a minimum snap trajectory generation method [26] is used to smooth the trajectory and the associated acceleration. Simulation results of the first three cases are respectively shown in Fig. 9, Fig. 10 and Fig. 11 where the desired trajectory (depicted by solid lines) and the actual flight pose are shown. All the cases including wind effect are also shown in the video submitted with this paper. Fig. 9 shows an entire simulated takeoff, transition, level flight and landing process. The vehicle first takes off and hovers at an altitude of 64 m for 2 seconds, then it transits to level flight at a speed of 12 m/s. 16 seconds later, the vehicle transits back to hover mode and subsequently lands vertically, thus completing the entire flight. It can be seen that the whole transition flight is achieved smoothly without dropping significant altitude. In Pucci et.al [17], the author has shown that ideal hover to level transition is not tractable due to equilibrium bifurcation, which is caused by the existence of multiple equilibrium pitch angle for the same speed and by the pitch angle jump at the stall region. In our simulation, the pitch angle variation is less than 9 degrees and no significant altitude drop is observed. This might be because the non-zero desired acceleration in Eq. (18), which is changed by outer position controller in real time, alters the equilibrium bifurcation observed in [17]. It is also interesting to see that during the landing process, the vehicle is slightly tilted. This is because the zero lifting line of the vehicle is not exactly in the direction of -180 degrees in the body frame. In Fig. 10, several level flight cases are shown to demonstrate the controller’s capacity. The vehicle can successfully fly at different pitch angles, which correspond to different forward speeds. As the forward speed increases, the wing can provide more lift, thus reducing the required motor thrust. The maximal lift/drag ratio is achieved at a pitch angle of around 12 degrees. It can be seen that the flight speed extends from zero to the optimal cruise speed, which is around 12 m/s for this designed aircraft. Also note that the entire flight process is fully controlled by a feedback PID controller. Fig. 11 illustrates a full three-dimensional flight trajectory. In this flight, the vehicle first transits to forward flight and then circles at a radius of 40 m. For this entire flight, the same single PID controller is used with the nonlinear optimization solver. It is concluded from these figures that the designed controller can successfully achieve all the flight modes including takeoff, hovering, transitioning and level flying using a single unified control framework. V. E XPERIMENTAL RESULTS This section presents the experimental results to verify the attitude controller. As mentioned previously, the position control loop is still under optimization for real-time implementation, therefore the demonstration on attitude control is presented at this time. Fig. 12 shows the logged data for the attitude control, where Yawsp , Pitchsp , and Rollsp represented in red lines are the commands (i.e. set points) for yaw, pitch and roll, and the blue lines are the the actual values. It can be seen that the attitude can converge to
Fig. 9. A full flight trajectory. The vehicle first takes off and hovers at an altitude of 64 m for 2 seconds, then it transits to level flight with a cruise speed of 12 m/s. Next, the vehicle transits back to hover and completes the flight by landing.
Fig. 10. Level flight at different speeds (Top: 4 m/s; Middle: 8 m/s and Bottom: 12 m/s). The minimal thrust is achieved at 12 m/s level flight.
Fig. 11. A three-dimensional flight trajectory demonstrates the controller’s capacity for hovering, transition, forward flight, and loitering like an airplane.
the desired values very well in all (pitch, roll and yaw) directions. One thing to notice is the pitch control. It can be seen that the transition from hover to level flight (at 19 s) is quite smooth, while the backward transition (at 24 s) has a longer transient response. The reason is the aerodynamics moment Maero becomes large after the vehicle accumulates enough airspeed. The same phenomenon occurs for the reverse transition. The results are also shown in the video submitted with this paper (high resolution video is available at https://youtu.be/D-59cWGwP1o).
Yaw [deg]
100
Yaw Yawsp
50
0
Pitch [deg]
-50 190
Pitch Pitchsp
140 90 40 -10 400
Roll Roll sp
Roll [deg]
200 0
-200 -400 0
5
10
15
20
Fig. 12.
25
30
35
40
45
50
Attitude Response
VI. C ONCLUSION A dual-loop controller was presented for controlling a quadrotor tail-sitter UAV. The controller consists of an attitude controller and an optimization-based position controller. The attitude controller is global asymptotically stable and its capacity is demonstrated via experimental results. The position controller is capable of uniformly treating all the flight modes including hovering, transition and level flight. It also significantly enlarges the flight envelope such that the aircraft can fly at different pitch angles and at different forward speeds. Numerical results were shown to demonstrate the position controller’s capacity. R EFERENCES [1] A. Frank, J. McGrew, M. Valenti, D. Levine, and J. How, “Hover, transition, and level flight control design for a single-propeller indoor airplane,” in AIAA Guidance, Navigation and Control Conference and Exhibit, Hilton Head, South Carolina, Aug. 2007. [2] B. W. McCormick, “Aerodynamics of V/STOL flight.” New York: Dover Publications, 1967. [3] R. H. Stone, and G. Clarke, “The T-wing: a VTOL UAV for defense and civilian applications,” in UAV Australia Conference, Melbourne, Feb. 2001. [4] D. Chu, J. Sprinkle, R. Randall, and S. Shkarayev, “Automatic control of VTOL micro air vehicle during transition maneuver,” in AIAA Guidance, Navigation and Control Conference, Chicago, Iilinois, Aug. 2009. [5] A. Oosedo, S. Abiko, A. Konno, T. Koizumi, T. Furui, and M. Uchiyama, “Development of a quad rotor tail-sitter VTOL UAV without control surfaces and experimental verification,” in 2013 IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, May, 2013. [6] Y. Wang, X. Lyu, H. Gu, S. Shen, Z. Li and F. Zhang, “Design, implementation and verification of a quadrotor tail-sitter VTOL UAV,” in 2017 International Conference on Unmanned Aircraft Systems (ICUAS), Florida, USA, June, 2017 (to appear). [7] R. H. Stone, “Control architecture for a tail-sitter unmanned air vehicle,” in Proceedings of the 5th Asian Control Conference, Melbourne, Jul. 2004, vol. 2, pp. 736-744. [8] R. H. Stone, and G. Clarke, “Optimization of transition maneuvers for a tail-sitter unmanned air vehicle (UAV),” in Australian international aerospace congress, Canberra, Australia, Mar. 2001. [9] N. Knoebel, S. Osborne, D. Snyder, T. Mclain, R. Beard and A. Eldredge, “Preliminary modeling, control, and trajectory design for miniature autonomous tailsitters,” in AIAA Guidance, Navigation, and Control Conference and Exhibit, Keystone, Colorado, Aug. 2006. [10] K. Kita, A. Konno, and M. Uchiyama, “Transition between level flight and hovering of a tail-sitter vertical takeoff and landing aerial robot,” Advanced Robotics, vol. 24, no. 5-6, pp. 763-781, 2010.
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