当前位置：文档库 › Multirotor aerial vehicles_ Modeling, estimation, and control of quadrotor

Multirotor aerial vehicles_ Modeling, estimation, and control of quadrotor

By Robert Mahony,Vijay Kumar,and Peter Corke

IEEE ROBOTICS &AUTOMATION MAGAZINE

SEPTEMBER 20121070-9932/12/$31.00a2012IEEE

Digital Object Identifier 10.1109/MRA.2012.2206474Date of publication:27August 2012

his article provides a tutorial introduction to modeling,es-timation,and control for multi-rotor aerial vehicles that includes the common four-rotor or quad-Aerial robotics is a fast-growing field of robotics and multirotor air-craft,such as the quadrotor (Fig-ure 1),are rapidly growing in popularity.In fact,quadrotor aerial robotic vehicles have become a standard platform for robotics research worldwide.They already have sufficient payload and flight endurance to support a number of indoor and outdoor applications,and the improvements of battery and other technology is rapidly increasing the scope for commercial opportunities.They are highly ma-neuverable and enable safe and low-cost experimentation in mapping,navigation,and control strategies for robots that move in three-dimensional (3-D)space.This ability to move in 3-D space brings new research challenges com-pared with the wheeled mobile robots that have driven mobile robotics research over the last decade.Small quadrotors have been demon-strated for exploring and mapping 3-D environ-ments;transporting,manipulating,and assembling objects;and acrobatic tricks such as juggling,balancing,and flips.Additional rotors can be added,leading to general-ized N -rotor vehicles,to improve payload and reliability.

Modeling,Estimation,and Control of Quadrotor

?ISTOCK https://www.wendangku.net/doc/3315409547.html,/?ANDREJS ZAVADSKIS

This tutorial describes the fundamentals of the dynamics, estimation,and control for this class of vehicle,with a bias toward electrically powered micro(less than1kg)-scale vehicles.The word helicopter is derived from the Greek words for spiral(screw)and wing.From a linguistic perspec-tive,since the prefix quad is Latin,the term quadrotor is more correct than quadcopter and more common than tet-racopter;hence,we use the term quadrotor throughout. Modeling of Multirotor Vehicles

The most common multirotor aerial platform,the quadro-tor vehicle,is a very simple machine.It consists of four individual rotors attached to a rigid cross airframe,as shown in Figure1.Control of a quadrotor is achieved by differential control of the thrust generated by each rotor. Pitch,roll,and heave(total thrust)control is straightfor-ward to conceptualize.As shown in Figure2,rotor i rotates anticlockwise(positive about the z axis)if i is even and clockwise if i is odd.Yaw control is obtained by adjusting the average speed of the clockwise and anticlockwise rotat-ing rotors.The system is underactuated,and the remaining degrees of freedom(DoF)corresponding to the transla-tional velocity in the x-y plane must be controlled through the system dynamics.

Rigid-Body Dynamics of the Airframe

Let f~x,~y,~z g be the three coordinate axis unit vectors without a frame of reference.Let{A}denote a right-hand inertial frame with unit vectors along the axes denoted by f~a1,~a2,~a3g expressed in{A}.One has algebraically that~a1?~x,~a2?~y,~a3?~z in{A}.The vector r?(x,y,z)2 f A g denotes the position of the center of mass of the vehicle. Let{B}be a(right-hand)body fixed frame for the airframe with unit vectors f~b1,~b2,~b3g,where these vectors are the axes of frame{B}with respect to frame{A}.The orientation of the rigid body is given by a rotation matrix A R B?R??~b1,~b2,~b3 2SO(3)in the special orthogonal group. One has~b1?R~x,~b2?R~y,~b3?R~z by construction.

We will use Z-X-Y Euler angles to model this rotation, as shown in Figure3.To get from{A}to{B},we first rotate about a3by the the yaw angle,w,and we will call this inter-mediary frame{E}with a basis f~e1,~e2,~e3g where~e i is expressed with respect to frame{A}.This is followed by a rotation about the x axis in the rotated frame through the roll angle,/,followed by a third pitch rotation about the new y axis through the pitch angle h that results in the body-fixed triad f~b1,~b2,~b3g

c w c hàs/s w s hàc/s w c w s htc h s/s w

c h s wtc w s/s h c/c w s w s hàc w c h s/

àc/s h s/c/c h

where c and s are shorthand forms for cosine and sine, respectively.

Let v2f A g denote the linear velocity of{B}with respect to{A}expressed in{A}.Let X2f B g denote the angular velocity of{B}with respect to{A};this time expressed in{B}.Let m denote the mass of the rigid object, and I2R333denote the constant inertia matrix(expressed

in the body fixed frame{B}).The rigid body equations of motion of the airframe are[2]and[3]

_n?v,(1a)

m_v?mg~a3tRF,(1b)

_R?R X

,(1c)

I_X?àX3I Xts:(1d) The notation X3denotes the skew-symmetric matrix,such that X3v?X3v for the vector cross product3and any vector v2R3.The vectors F,s2f B g combine the princi-pal nonconservative forces and moments applied to the quadrotor airframe by the aerodynamics of the rotors. Dominant Aerodynamics

The aerodynamics of rotors was extensively studied during the mid1900s with the development of manned helicop-ters,and detailed models of rotor aerodynamics are avail-able in the literature[4],[5].Much of the detail about these aerodynamic models is useful for the design of rotor systems,where the whole range of parameters(rotor

{B}

Front

Φi

Figure2.Notation for quadrotor equations of motion.N?4;U i

is a multiple of p=4(adapted with permission from[1]).

Figure1.A quadrotor made by Ascending Technologies with VICON markers for state estimation.

U SEPTEMBER2012?IEEE ROBOTICS&AUTOMATION MAGAZINE?21

geometry,profile,hinge mechanism,and much more)are

fundamental to the design problem.For a typical robotic quadrotor vehicle,the rotor design is a question for choos-ing one among five or six available rotors from the hobby shop,and most of the complexity of aerodynamic model-ing is best ignored.Nevertheless,a basic level of aerody-namic modeling is required.

The steady-state thrust generated by a hovering rotor (i.e.,a rotor that is not translating horizontally or verti-cally)in free air may be modeled using momentum theory [5,Sec.2.26]as

T i :?C T q A r i r 2i -2i ,

(2)

where,for rotor i,A r i is the rotor disk area,r i is the radius,

-i is the angular velocity,C T is the thrust coefficient that depends on rotor geometry and profile,and q is the density of air.In practice,a simple lumped parameter model

T i ?

c T -2i

(3)

is used,where c T >0is modeled as a constant that can be

easily determined from static thrust tests.Identifying the thrust constant experimentally has the advantage that it will also naturally incorporate the effect of drag on the air-frame induced by the rotor flow.

The reaction torque (due to rotor drag)acting on the airframe generated by a hovering rotor in free air may be modeled as [5,Sec.2.30]

Q i :?c Q -2i ,

(4)

where the coefficient c Q (which also depends on A r i ,r i ,and

q )can be determined by static thrust tests.

As a first approximation,assume that each rotor thrust is oriented in the z axis of the vehicle,although we note that this assumption does not exactly hold once the rotor begins to rotate and translate through the air,an effect that

is discussed in “Rotor Flapping.”For an N -rotor airframe,we label the rotors i 2f 1áááN g in an anticlockwise direc-tion with rotor 1lying on the positive x axis of the vehicle (the front),as shown in Figure 2.Each rotor has associated an angle U i between its airframe support arm and the body-fixed frame x axis,and it is the distance d from the central axis of the vehicle.In addition,r i 2fà1,t1g denotes the direction of rotation of the i th rotor:t1corre-sponding to clockwise and à1to anticlockwise.The sim-plest configuration is for N even and the rotors distributed symmetrically around the vehicle axis with adjacent rotors counter rotating.

The total thrust at hover (T R )applied to the airframe is the sum of the thrusts from each individual rotor

T R ?

X N i ?1

j T i j ?c T

N i ?1

-2i !:

(5)

The hover thrust is the primary component of the exoge-nous force

F ?T R ~

z tD (6)

in (1b),where D comprises secondary aerodynamic forces

that are induced when the assumption that the rotor is in hover is violated.Since F is defined in {B },the direction of application is written ~z ,although in the frame {A }this

direction is ~b 3?R ~z .

The net moment arising from the aerodynamics (the combination of the produced rotor forces and air resistan-ces)applied to the N -rotor vehicle use are s ?(s 1,s 2,s 3).

s 1?c T

X N i ?1

d i sin (U i )-2i ,s 2?àc T X N i ?1

d i cos (U i )-2i ,

s 3?c Q

X N i ?1

r i -2i :

(7)

For a quadrotor,we can write this in matrix form T R

s 1s 2s 3

0B B B B @1

C C C C A ?c T

c T c T c T

0dc T 0àdc T àdc T

dc T

0àc Q c Q àc Q c Q

B B B @1

C C C C A |??????????????????????????{z??????????????????????????}

-21

-22-23-24

B B B B @1

C C A

,(8)and given the desired thrust and moments,we can solve for the required rotor speeds using the inverse of the con-stant matrix C .In order for the vehicle to hover,one must choose suitable -i by inverting C ,such that s ?0and T R ?mg .

x , b 1

y , b 2

e 2e 1

X , a 1

Y , a 2

Z, a 3Z, b 3C

ψψ

{A }

{B }

{E }

Figure 3.The vehicle model.The position and orientation of

the robot in the global frame are denoted by n and R ,respectively.

IEEE ROBOTICS &AUTOMATION MAGAZINE

SEPTEMBER 2012

Blade Flapping and Induced Drag

There are many aerodynamic and gyroscopic effects asso-ciated with any rotor craft that modify the simple force model introduced above.Most of these effects cause only minor perturbations and do not warrant consideration for a robotic system,although they are important for the design of a full-sized rotor craft.Blade flapping and induced drag,however,are fundamental effects that are of significant importance in understanding the natural stabil-ity of quadrotors and how state observers operate.These effects are particularly relevant since they induce forces in the x-y rotor plane of the quadrotor,the underactuated directions in the dynamics,that cannot be easily dominated by high gain control.In this section,we consider a single rotor and we will drop the subscript i used in the“Dominant Aerodynamics”section to refer to particular rotors.

Quadrotor vehicles are typically equipped with light-weight,fixed-pitch plastic rotors.Such rotors are not rigid, and the aerodynamic and inertial forces applied to a rotor during flight are quite significant and can cause the rotor to flex.In fact,allowing the rotor to bend is an important property of the mechanical design of a quadrotor and fit-ting rotors that are too rigid can lead to transmission of these aerodynamic forces directly through to the rotor hub and may result in a mechanical failure of the motor mounting or the airframe itself.Having said this,rotors on small vehicles are significantly more rigid relative to the applied aerodynamic forces than rotors on a full-scale rotor craft.Blade-flapping effects are due to the flexing of rotors,while induced drag is associated primarily with the rigidity of the rotor,and a typical quadrotor will experi-ence both.Luckily,their mathematical expression is equivalent and a single term is sufficient to represent both effects in a lumped parameter dynamic model.

When a rotor translates laterally through the air it dis-plays an effect known as rotor flapping(see“Rotor Flapping”).A detailed derivation of rotor flapping involves a mechanical model of the bending of the rotor subject to aerodynamic and centripetal forces as it is swept through a full rotation[5,Sec.4.5].The resulting equations of motion are a nonlinear second-order dynamical system with a dominant highly damped oscillatory response at the forced frequency corresponding to the angular velocity of the rotor.For a typical rotor,the flapping dynamics converge to steady state with one cycle of the rotor[5,p.137],and for the purposes of modeling,only the steady-state response of the flapping dynamics need be considered.

Assuming that the velocity of the vehicle is directly aligned with the X axis in the inertial frame,v?(v x,0,0), a simplified solution is given by

b:?à

l A1c

1à1

àá,b?:?àl A1s

1t1

àá(9)

for positive constants A1c and A1c,and where l:?j v x j=-r is the advance ratio,i.e.,the ratio of magnitude of the horizontal velocity of the rotor to the linear velocity

of rotor tip.The flapping angle b is the steady-state tilt of the rotor away from the incoming apparent wind and b?is the tilt orthogonal to the incident wind.Here,we use equa-tions(4.46)and(4.47)from[5,p.138],noting that adding the effects of a virtual rotor hinge model[5,Sec.4.7]results

in additional phase lag between the sine and cosine com-ponents of the flapping angles[5,Question4.7,p.157]that are absorbed into the constants A1c and A1s in(9).

Rotor flapping is important because the thrust gener-ated by the rotor is perpendicular to the rotor plane and not to the hub of the rotor.Thus,when the rotor disk tilts the rotor thrust is inclined with respect to the airframe and contains a component in the x and y directions of the body-fixed frame.

In practice the rotors are stiff and oppose the aerody-namic force which is lifting the advancing blade so that its increased thrust due to tip velocity is not fully counteracted by a lower angle of attack and lower lift coefficient—the thrust is increased.Conversely for the retreating blade the thrust is reduced.For any airfoil that generates lift(in our case the rotor blade)there is an associated induced drag

SEPTEMBER2012?IEEE ROBOTICS&AUTOMATION MAGAZINE?23

due to the backward inclination of aerodynamic force with respect to the airfoil motion.The induced drag is proportional to the lift generated by the airfoil.In normal hover conditions for a rotor,this force is equally distrib-uted in all directions around the circumference of the rotor and is responsible for the torque Q(4).However, when there is a thrust imbalance,then the sector of the rotor travel with high thrust(for the advancing rotor)will generate more induced drag than the sector where the rotor generates less thrust(for the retreating blade).The net result will be an induced drag that opposes the direc-tion of apparent wind as seen by the rotor,and that is proportional to the velocity of the apparent wind.This effect is often negligible for full scale rotor craft,however, it may be quite significant for small quadrotor vehicles with relatively rigid blades.The consequence of blade flapping and induced drag taken together ensures that there is always a noticeable horizontal drag experienced by a quadrotor even when maneuvering at relatively slow speeds.

We will now use the insight from the discussion above to develop a lumped parameter model for exogenous force generation(6).We assume that all four rotors are identical and rotate at similar speeds so that,at least to a first approximation,the flapping responses of the rotors and the unbalanced aerodynamic forces are the same.It follows that the reactive torques on the airframe transmitted by the rotor masts due to rotor stiffness cancel.For general motion of the vehicle,the apparent wind results in the advance ratio

??????????????????

v0x2tv0y2

=-r,

where v0?R>v is the linear velocity of the vehicle expressed in the body-fixed frame,with v0x and v0y being the components in the body-fixed x-y plane.Define

A flap?

-R

A1càA1s0

A1s A1c0

000

where-is the set point for the rotor angular velocity. This matrix describes the sensitivities of the flapping angle to the apparent wind in the body-fixed frame,given that l is small and l2is negligible in the denominators of(9). The first row encodes(9)for the velocity along the body-fixed frame x axis.The second row of A flap is a p=2rotation of this response to account for the case where a component of the wind is incoming from the y axis,while the third row projects out velocity in the z axis of the body-fixed frame.

We model the stiffness of the rotor as a simple torsional spring so that the induced drag is directly proportional to this angle and is scaled by the total thrust.The flapping angle is negligible with regard to the orientation of the induced drag,and in the body-fixed frame the induced drag is

D ind:v0%diag(d x,d y,0)v0,

where d x?d y is the induced drag coefficient.

The exogenous force applied to the rotor can now be modeled by

F:?T R~zàT R Dv0,(10) where D?A flaptdiag(d x,d y,0),and T R is the nominal thrust(5).

An important consequence of blade flapping and induced drag is a natural stability of the horizontal dynam-ics of the quadrotor[7].Define

P h:?

100

010

(11)

to be the projection matrix onto the x-y plane.The hori-zontal component of a velocity expressed in{A}is

v h:?P h v?(v x,v y)>2R2:(12)

Recalling(1b)and projecting onto the horizontal compo-nent of velocity,one has

m_v h?àT R P h~ztRDv0

eT:

If the vehicle is flying horizontally,i.e.,v z?0,then v?P>h v h and one can write

m_v h?àT R P h~zàP h RDR>P>h v h,(13)

where the last term introduces damping since,for a typical system,the matrix D is a positive semidefinite.

A detailed dynamic model of the quadrotor,including flapping and induced drag,is included in the robotics tool-box for MATLAB[8].This is provided in the form of Simulink library blocks along with a set of inertial and aerodynamic parameters for a particular quadrotor.The graphical output of the animation block is shown in Fig-ure4.Simulink models,based on these blocks,that illus-trate path following and vision-based stabilization are described in detail in[1].

The discussion provided above does not consider several additional aerodynamic effects that are impor-tant for high-speed and highly dynamic maneuvers for a quadrotor.In particular,we do not consider transla-tional lift and drag that will effect thrust generation at high speed,axial flow modeling and vortex states that may effect thrust during axial motion,and ground effect that will affect a vehicle flying close to the ground.It should be noted that high gain control can dominate all secondary aerodynamic effects,and high

24?IEEE ROBOTICS&AUTOMATION MAGAZINE?SEPTEMBER2012

performance control of quadrotor vehicles has been demonstrated using the simple static thrust model [23],[24].The detailed modeling of the blade flapping and induced drag is provided due to its importance in under-standing the state estimation algorithms introduced later the tutorial.

Size,Weight,and Power (SWAP)Constraints and Scaling Laws

Reducing the scale of the quadrotor has an interesting effect on the inertia,payload,and ultimately the maximum achievable angular and linear acceleration.To gain insight into scaling,it is useful to develop a simple physics model to analyze a quadrotor’s ability to produce linear and angu-lar accelerations from a hover state.

If the characteristic length is d ,the rotor radius r scales linearly with d .The mass scales as d 3and the moments of inertia as d 5.On the other hand,from (3)and (4),it is clear that the lift or thrust,T ,and drag,Q ,from the rotors scale with the square of the rotor speed,-2.In other words,T $-2d 4and Q $-2d 4,the linear acceleration

a ?_v

,which depends on the thrust and mass,and the angular acceleration a ?_X

,which depends on thrust,drag,the moment arm,and the moments of iner-tia,scale as

a $

-2d

?-2d ,a $

-2d

?-2:To explore the scaling of rotor speed with length,it is

useful to adopt the two commonly accepted approaches to study scaling in aerial vehicles [9].Mach scaling is used for compressible flows and essentially assumes that the blade tip speed,v b ,is a constant leading to -$(1=r ).Froude scaling is used for incompressible flows and assumes that,for similar aircraft con-figurations,the Froude number,(v 2

=dg )?(-2r 2=dg ),is constant.Here,g is the acceleration due to gravity.

Assuming r $d ,we get -$(1=??

r p ).Thus,Mach scaling predicts

a $1d

a $

1d 2

,(14)

while Froude scaling leads to the conclusion

a $1,

a $1d

(15)

Of course,Froude or Mach number similitudes take

neither motor characteristics nor battery properties into account.While motor torque increases with length,the operating speed for the rotors is determined by matching the torque –speed characteristics of the motor to the drag versus speed characteristics of the rotors.Further,the motor torque depends on the ability of the battery to source the required current.All these variables are tightly coupled for smaller designs since there are fewer choices available at smaller length scales.Finally,as discussed in the previous subsection,the assumption that rotor blades are rigid may be wrong.Further,the aerodynamics of the blades may be different for blade designs optimized for smaller helicopters and the quadratic scaling of the lift with speed may not be accurate.

In spite of the simplifications in the above similitude analysis,the key insight from both Froude and Mach num-ber similitudes is that smaller quadrotors can produce faster angular accelerations while the linear acceleration is at worst unaffected by scaling.Thus,smaller quadrotors are more agile,a fact that is easily validated from experi-ments conducted with the Ascending Technologies Pelican quadrotor [10](approximately 2kg gross weight when equipped with sensors,0.75m diameter,and 5,400r/min nominal rotor speed at hover),the Ascending Technolo-gies Hummingbird quadrotor [11](approximately 500g gross weight,0.5m diameter,and 5,000r/min nominal rotor speed at hover),and laboratory experimental proto-types developed at GRASP laboratory at the University of Pennsylvania (approx.75g gross weight,0.21m diameter,and approximately 9,000r/min nominal rotor speed).Estimating the Vehicle State

The key state estimates required for the control of a quad-rotor are its height,attitude,angular velocity,and linear velocity.Of these states,the attitude and angular velocity are the most important as they are the primary variables used in attitude control of the vehicle.The most basic instrumentation carried by any quadrotor is an inertial measurement unit (IMU)often augmented by some form of height measurement,either acoustic,infrared,baromet-ric,or laser based.Many robotics applications require more sophisticated sensor suites such as VICON systems,global positioning system (GPS),camera,Kinect,or scan-ning laser rangefinder.

10.80.60.40.201

0.5

0–0.5

–1–1

–0.5

00.5

y z (H e i g h t A b o v e G r o u n d )

Figure 4.Frame from the Simulink animation of quadrotor dynamics.

SEPTEMBER 2012

IEEE ROBOTICS &AUTOMATION MAGAZINE

Estimating Attitude

A typical IMU includes a three-axis rate gyro,three-axis accelerometer,and three-axis magnetometer.The rate gyro measures the angular velocity of{B}relative to{A} expressed in the body-fixed frame of reference{B}

X IMU?Xtb Xtg2f B g,

where g denotes the additive measurement noise and b X denotes a constant(or slowly time-varying)gyro bias.Gen-erally,the gyroscopes installed on quadrotor vehicles are lightweight microelectromechanical systems(MEMS)devi-ces that are reasonably robust to noise and quite reliable.

The accelerometers(in a strap down IMU configura-tion)measure the instantaneous linear acceleration of{B} due to exogenous force

a IMU?R>(_vàg~z)t

b atg a2f B g,

where b a is a bias term,g a denotes additive measurement noise,and_v is in the inertial frame.Here,we use the nota-tion~z?~a3since we will need to deal with the algebraic expressions of the coordinate axes throughout this section. Accelerometers are highly susceptible to vibration and, mounted on a quadrotor,they require significant low-pass mechanical and/or electrical filtering to be usable.Most quadrotor avionics will incorporate an analogue anti-aliasing filter on a MEMS accelerometer before the signal is sampled.

A commonly used technique to estimate the bias b X and b a is to average the output of these sensors for a few seconds while the quadrotor is on the ground and the motors are not yet active.The bias is then assumed con-stant for the duration of the flight.

The magnetometers provide measurements of the ambient magnetic field

m IMU?R>A mtB mtg b2f B g,

where A m is the Earth’s magnetic field vector(expressed in the inertial frame),B m is a body-fixed frame expression for the local magnetic disturbance,and g b denotes the measurement noise.The noise g b is usually low for magne-tometer readings;however,the local magnetic disturbance B m can be significant,especially if the sensor is placed near the power wires to the motors.

The accelerometers and magnetometers can be used to provide absolute attitude information on the vehicle while the rate gyroscope provides complementary angular veloc-ity measurements.The attitude information in the magne-tometer signal is straightforward to understand;in the absence of noise and bias,m IMU provides a body-fixed frame measurement of R>A m and,consequently,con-strains two DoF in the rotation R.

The case for using the accelerometer signal for attitude estimation is far more https://www.wendangku.net/doc/3315409547.html,ing the simplest model(6)with D 0,a IMU?R>(_vàg~z)?(T R=m)~z%g~z.This shows that the measured acceleration,for this simple model,would always point in the body-fixed frame direc-tion~z and provides no attitude information.In practice,it is the blade-flapping component of the thrust that contrib-utes attitude information to the accelerometer signal[7]. Recalling(10)and ignoring bias and noise terms,the model for a IMU can be written as

a IMU?à

T R

~zà

T R

DR>v:(16)

As we show later in the section,only the low-frequency information from the accelerometer signal will be used in the observer construction.Thus,it is only the low-frequency or approximate steady-state response v of the velocity v that we need to estimate to build a model for the low-frequency component of a IMU.Setting_v?0in(1b),substituting for force(10),and rearranging,we obtain an estimate of the low-frequency component of the velocity signal

DR> v%R>~zà~z:

Substituting DR> v for DR>v in(16),we obtain

a IMU%à

T R

R>~z,(17)

where a IMU denotes the low-frequency component of the accelerometer signal.That is,the low-frequency content of a IMU when the vehicle is near hover is the body-fixed frame expression for the supporting force that is the negative gravitational vector expressed in the body-fixed frame. Most robotics applications involve a quadrotor spending significant periods of time in hover,or slow forward flight, with_v%0,and using the accelerometer reading as an atti-tude reference during this flight regime has been shown to work well in practice.

The attitude kinematics of the quadrotor are given by (1c).Let^R denote an estimate for attitude R of the quadrotor vehicle.The following observer[12]fuses accelerometer, magnetometer,and gyroscope data as well as other direct attitude estimates R E(such as provided by a VICON or other external measurement system)should they be available:

_^R:?^R X

IMU

à^b

àa,

b:?k b a,

a:?

k a

((^R>~z)3 a IMU)t

k m

j A m j2

((^R>A m)3m IMU)

3tk E P so(3)^RR>E

àá

,(18)

where k a,k m,k E,and k b are arbitrary nonnegative observer gains and P so(3)(M)?(MàM>)=2is the Euclidean

26?IEEE ROBOTICS&AUTOMATION MAGAZINE?SEPTEMBER2012

matrix projection onto skew-symmetric matrices.If any one of the measurements in the innovation a are not avail-able or unreliable,then the corresponding gain should be set to zero in the observer.Note that both the attitude^R and the bias corrected angular velocity^X?X IMUà^b are estimated by this observer.The observer(18)has been extensively studied in the literature[12],[13]and shown to converge exponentially(both theoretically and experi-mentally)to the desired attitude estimate of attitude with^b converging to the gyroscope bias b.The filter has a com-plementary nature,using the high-frequency part of the gyroscope signal and the low-frequency parts of the magnetometer,accelerometer,and external attitude measurements[12].The roll-off frequencies associated with each of these signals is given by the gains k a,k m,and k E in rad.sà1,and good performance of the observer depends on how these gains are tuned.In particular,the accelerometer gains must be tuned to a frequency below the normal band-width of the vehicle motion,less than5rad.sà1for a typical quadrotor.The magnetometer gain and external gain can be tuned for a higher roll-off frequency depending on the reliability of the signals.The bias gain k b is typically chosen an order of magnitude slower than the innovation gains k b

A particular advantage of this observer formulation is that the gains can be adjusted in real time as long as care is taken that the bias gain is small.Adjusting the gains in real time allows one to use the accelerometer during a period when the vehicle is in hover and then set the gain k a?0 during acrobatic maneuvers when the low-frequency assumptions on a IMU no longer hold.The nonlinear robustness,guaranteed asymptotic stability,and flexibility in gain tuning make this observer a preferred candidate for quadrotor attitude estimation compared with classical fil-ters such as the extended Kalman filter(EKF),multiplica-tive EKF,or more sophisticated stochastic filters. Estimating Translational Velocity

The blade-flapping response provides a way to build an observer for the horizontal velocity of the vehicle based on the IMU sensors[7],at least while the vehicle is flying in the horizontal plane.Assume that a good estimate of the vehicle attitude^R is available and that the vehicle is flying at constant height.

Recalling the projector(11),the horizontal component of the inertial acceleration can be measured by

A a

:?P h A a?P h Ra%P h^Ra,(19) where the signals a and^R are available.Since we assume that the vehicle is flying at a constant height,one has v z%0,and recalling(12),P>h v h%v.Further,the thrust

T R%mg must compensate the weight of the vehicle. Recalling(16)and taking the horizontal component, one has

A a

%àg P h^R~zàg P h^RDR>P>h v h:(20)

Assuming that the attitude filter estimate is good,i.e., ^R?R,then(19)and(20)can be solved for an estimate

of v h

v h%à

P h^RD^R>P>h

h ià1

A a

tg P h^R~z

àá

:(21)

This estimate of v h will be well defined as long as the232 matrix P h^RD^R>P>h is invertible,a condition that will hold as long as the vehicle pitches or rolls by less than90°dur-ing flight.

Equation(21)provides a measurement of the horizon-tal velocity;however,since it directly incorporates the unfiltered accelerometer readings,it is generally too noisy

to be of much use.Its low-frequency content can,however, be used to drive a velocity complementary observer that uses the attitude estimate and the system model(1b)along with the thrust model(10)for its high-frequency compo-nent.Let^v h be an estimate of the horizontal component of the inertial velocity of the vehicle.Recalling(1b),we pro-pose the following observer

_^v

?àg P>h^R~zt^RD^R>P>h^v h

àk w(^v hàv h),(22)

where v h is given by(21).The gain k w>0provides a tun-ing parameter that adjusts the roll-off frequency for the information from^v h that is used in the filter.It also uses an estimated velocity^v h to provide an approximation of the more correct RDR>P>h v h term in the feedforward velocity estimate;however,since the underlying dynamics associ-ated with this term are stable,the observer is stable even with this approximation.

Estimating Position

The final part of state that must be estimated is position, which is typically considered separately as position in the plane and height.Considering the height first,there are in fact two separate heights that are of importance:the first is the absolute height of the vehicle and the second is the rela-tive height over the terrain at a given time.Unfortunately, there is no effective way to use the IMU to estimate abso-lute height;at best,some low-frequency information from the z axis of the accelerometer provides limited informa-tion about vertical motion.Most quadrotors include a barometric sensor that can resolve absolute height to a few centimeters.Absolute height can also be estimated using GPS,VICON,or a full SLAM system.Relative height can be estimated using acoustic,laser-ranging or infrared

SEPTEMBER2012?IEEE ROBOTICS&AUTOMATION MAGAZINE?27

sensors.Once a sufficiently accurate height measurement is available,it is better to use this directly in the control than add additional levels of complexity in designing a height observer,especially since,for a typical system,the only feedforward information available is the noisy accel-erometer readings.

Position in the plane can also be determined in a rela-tive or absolute way.Absolute position can be obtained from a GPS(few-centimeter accuracy at up to10Hz[6]) or an external localization device such as a VICON motion capture system(50l m accuracy at375Hz).How-ever,a GPS does not work indoors and motion-capture systems are expensive,and their sensor array has a limited spatial extent that is impractical to scale up for large indoor environments.

Relative position can be estimated by measuring the dis-tance to objects in the environment from onboard sensors, typically small onboard laser range finders(LRFs)or RGBD camera systems such as the Kinect.Well-known SLAM techniques,borrowing LRF-based techniques similar to those developed for mobile ground robots over the last decade,have been applied to quadrotors[14]. However,LRFs provide only a cross section of the3-D environment and this scan plane tilts as the vehicle maneu-vers,resulting in apparent changes to the distance of walls, and,in extreme cases,the scan plane can intersect the floor or ceiling.LRFs are heavy and power hungry,which pre-vents their application to the next generation of much smaller quadcopters.

Vision has the advantage that the sensor is small,light-weight,and low power,which will become increasingly important as the size of aerial vehicles decreases.Vision can provide essential navigational competencies such as odometry,attitude estimation,mapping,place and object recognition,and collision detection.There is a long history of applying vision to aerial robotic systems[15]–[19]for indoor and outdoor environments,and the well-known Parrot AR.Drone game device makes strong use of vision for attitude and odometry[20].Vision can also be used for object recognition based on color,texture,and shape,as well as collision avoidance.

Vision is not without its challenges.First,vision is com-putationally intense and can result in a low sample rate. Since onboard computational power is limited(by SWAP consumption),most reported systems transmit the images wirelessly to a ground station,which increases system complexity,control latency,and the susceptibility to inter-ference and dropouts.However,processor speed continues to improve,and we can also utilize the vision and control techniques used by flying insects that perform complex tasks with very limited sensing and neural capability[21]. Second,there is an ambiguity between certain rotational and translational motions,particularly,when a narrow field of view perspective camera is used.Third,the under-actuated quadrotor uses the roll and pitch DoF to point the thrust vector in the direction of the desired translational motion.For a camera that is rigidly attached to the quadro-tor,this attitude control motion induces a large apparent motion in the image.It is therefore necessary to estimate vehicle attitude at the instant the image was captured by the sensor to eliminate this effect.Biological systems face similar problems,and interestingly,mammals and insects have developed similar solutions:gyroscopic sensors (the vestibular sensors of the inner ear and the halteres, respectively)[22].Finally,there exists a problem with recovering motion scale when using a single camera.Stereo is possible,but the baseline is constrained,particularly as vehicles get smaller.

Control

The control problem,to track smooth trajectories R?(t),n?(t)

eT2SE(3),is challenging for several reasons. First,the system is underactuated:there are four inputs u?(T R,s>)>,while SE(3)is six dimensional.Second,the aerodynamic model described above is only approximate. Finally,the inputs are themselves idealized.In practice,the motor controllers must overcome the drag moments to generate the required speeds and realize the input thrust (T R)and moments(s).The dynamics of the motors and their interactions with the drag forces on the propellers can be difficult to model,although first-order linear mod-els are a useful approximation.

A hierarchical control approach is common for quadro-tors.The lowest level,the highest bandwidth,is in control of the rotor rotational speed.The next level is in control of vehicle attitude,and the top level is in control of position along a trajectory.These levels form nested feedback loops, as shown in Figure5.

Controlling the Motors

Rotor speed drives the dynamic model of the vehicle according to(8),so high-quality control of the motor

speed is fundamentally important

for overall control of the vehicle;

high bandwidth control of the

thrust T R,denoted by u1,and the

torques(s x,s y,s z),denoted by u2,

lead to high performance attitude

and position control.Most quadro-

tor vehicles are equipped with

brushless dc motors that use back

electromotive force(EMF)sensing

Figure5.The innermost motor control loop,the intermediate attitude control loop,and the outer position control loop.

28?IEEE ROBOTICS&AUTOMATION MAGAZINE?SEPTEMBER2012

for rotor commutation and high-frequency pulsewidth modulation(PWM)to control motor voltage.The simplest systems generally use a direct voltage control of the motors since steady-state motor speed is propor-tional to voltage;however;the dynamic response is second-order due to the mechanical and electrical dynamics.Improved performance is obtained by in-corporating single-input single-output control at the motor/rotor level

V i?k(-?ià-i)tV ff(-?i),(23) where V i is the applied motor voltage,-?i is the desired speed,and the actual motor speed-i can be measured from the electronic commutation in the embedded speed controller.This can help to overcome a common problem where the rotor speed for a given PWM com-mand setting will decrease as the battery voltage reduces during flight.The significant load torque due to aerodynamic drag will lead to a tracking error that can be minimized by high proportional gain(k)and/or a feedforward term.A positive benefit of the drag torque is that the system is heavily damped,which precludes the need for derivative control.The feed-forward term V ff(-?i)compensates for the steady-state PWM associated with a given velocity set point by incorporating the best available thrust model deter-mined using static thrust tests and possibly including battery voltage.

The performance of the motor controllers is ultimately limited by the current that can be supplied from the bat-teries.This may be a significant limiting factor for smaller vehicles.Overly aggressive tuning and extreme maneuvers may cause the voltage bus to drop excessively,reducing the thrust from other rotors and,in extreme cases,causing the onboard electronics to brownout.For this reason,it is common to introduce a saturation,although this destroys the linearity of the motor/rotor response during aggressive maneuvers.

Attitude Control

We first consider the design of an exponentially converg-ing controller in SO(3).Given a desired airframe attitude R?,we want to first develop a measure of the error in rota-tions.We choose the measure

e R

(R?)T RàR T R?

àá

,(24)

which yields a skew-symmetric matrix representing the axis of rotation required to go from R to R?and whose magnitude is equal to the sine of the angle of rotation.

To derive linear controllers,we linearize the dynamics about the nominal hover position at which the roll(/)and pitch(h)are close to zero and the angular velocities are close to zero.If we write R?A R B as a product of the yaw rotation A R E(w)and E R B(/,h),which is a composition of the roll and pitch,we can linearize the rotation about (w,/,h)?(w0,0,0)

A R

?A R E(w0tD w)E R B(D/,D h)

cos wàsin w D h cos wtD/sin w

sin w cos w D h sin wàD/cos w

àD h D/1

B B

C C

C A,

where w?w0tD w.If R??A R B(w0tD w,D/,D h)and

R?A R B(w0,0,0),(24)gives

e R

0D wàD h

àD w0D/

D hàD/0

B B

C C

A,(25) which,as we expect,corresponds to the error vector

e R?(D/,D h,D w)>,

with components in the body-fixed frame.If the desired angular velocity vector is zero,we can compute the proportional and derivative error to obtain the PD con-trol law

u2?àk R e Ràk X e X,(26) where k R and k X are positive definite gain matrices.This controller guarantees stability for small deviations from the hover position.

To obtain convergence for larger deviations from the hover position,it is necessary to revert back to(24) without linearization.This allows us to directly compute the error on SO(3).By compensating for the nonlinear inertial terms and by including the correct error term, we obtain

u2?J(àk R e Ràk X e X)tX3J XàJ(X3R T R?X?àR T R?_X?):

(27) This controller is guaranteed to be exponentially stable for almost any rotation[23].From a practical standpoint,it is possible to neglect the last three terms

in the controller and achieve satisfactory performance, but the correct calculation of the error term is impor-tant[24].

Trajectory Control

We now turn our attention to the control of the trajec-tory along a specified trajectory n?(t).As before,we first consider linear controllers by linearizing the dy-namics about n?n?(t),h?/?0,w?w?(t),_n?0,and

SEPTEMBER2012?IEEE ROBOTICS&AUTOMATION MAGAZINE?29

?_h ?_w ?0,with the nominal input given by u 1?mg ,u 2?0.Linearizing (1a),we get

€n

1?g (D h cos w ?tD /sin w ?),€n

2?g (D h sin w ?àD /cos w ?),€n

3?1m

u 1àg :(28)

To exponentially drive all three components of error,we

want to command the acceleration vector €n

com to satisfy (€n

?(t )à€n com )tK d (_n ?(t )à_n )tK p (n ?(t )àn )?0:From (28),we can immediately write

u 1?m g t€n ?3tk d ,z (_n ?3à_n 3)tk p ,z (n ?3àn 3)

(29)

to guarantee (n 3(t )àn ?3(t ))!0.Similarly,for the other

two components,we choose to command the appropriate h ?and /?to guarantee exponential convergence

/??1g

(€n com

1sin w ?(t )à€n com 2

cos w ?(t )),(30a)h ??1g

(€n com

1cos w ?(t )t€n com 2

sin w ?(t )),(30b)

where the above equations are obtained by replacing D h by h ?and D /by /?in (28).Finally,(w ?,/?,h ?)are provided as set points to the attitude controller discussed in the previous section.Thus,as shown in Figure 5,the control problem is addressed by decoupling the position control and attitude control subproblems,and the position control loop provides the attitude set points for the attitude controller.

The position controller can also be obtained without linearization.This is done by projecting the position error (and its derivatives)along b 3and applying the input u 1that cancels the gravitational force and provides the appro-priate proportional plus derivative feedback

u 1?m ~b T 3€n ?tK d (_n ?à_n )tK p (n ?àn )tg ~a 3 :(31)Note that the projection operation is a nonlinear function

of the roll and pitch angles,and,thus,this is a nonlinear controller.In [23],it is shown that the two nonlinear con-trollers (27)and (31)result in exponential stability and allow the robot to track trajectories in SE(3).

Trajectory Planning

The quadrotor is underactuated,and this makes it difficult to plan trajectories in 12-dimensional state space (6DoF position and velocity).However,the problem is considerably simplified if we use the fact that the quadrotor dynamics are differentially flat [25].To see this,we consider the output position n and the yaw angle w .We show that we can write all state variables and

inputs as functions of the outputs (n ,w )and their derivatives.Derivatives of n yield the velocity v and the acceleration,

?1m

u 1~

b 3tg ~a 3:From Figure 3we see that

~e 1?cos w ,sin w ,0? T ,

and the unit vectors for the body-fixed frame can be writ-ten in terms of the variables w and _v

as ~b 3?_v àg ~a 3_v àg ~a 3k k ,~b 2?~b 33~e 1~b 33~e 1 ,~b 1?~b 23~b 3

provided ~b 33~e 1?0.This defines the rotation matrix A R B as

a function of _v

(the second derivative of n )and w .In this way,we write the angular velocity and the four inputs as functions of position,velocity,acceleration,jerk (c ),and snap,or the derivative of jerk (r ).From these equations,it is possible to ver-ify that there is a diffeomorphism between the 1831vector

n T ,v T ,a T ,c T ,r T ,w T ,_w T ,€w T

and

R 3n T

,_n

,X T

,u 1,_u 1,€u 1,u T 2

This property of differential flatness makes it easy to design

trajectories that respect the dynamics of the underactuated system.Any four-times-differentiable trajectory in the space of flat outputs,(n >(t ),w (t ))>,corresponds to a feasible trajec-tory —one that satisfies the equations of motion.All inequality constraints of states and inputs can be expressed as functions of the flat outputs and their derivatives.This mapping to the space of flat outputs can be used to generate trajectories that minimize a cost functional formed by a weighted combination of the different flat outputs and their derivatives:

min

n (t ),w (t )

0L (n ,_n ,€n ,n ááá,n áááá

w ,_w ,€w )dt ,g (n (t ),w (t )) 0:

(32)

In [24],minimum snap trajectories were generated by

minimizing a cost functional derived from the snap and the angular yaw acceleration with

L (n ,_n ,€n ,n ááá,n áááá

w ,_w ,€w )?(1àc )(n áááá

)4tc (€w )2:By suitable parameterizing trajectories with basis functions in

the flat space and by considering linear inequalities in the flat

IEEE ROBOTICS &AUTOMATION MAGAZINE

SEPTEMBER 2012

space to model constraints on states and inputs (e.g .,u 1!0),it is possible to turn this optimization into a quadratic pro-gram that can be solved in real time for planning.

Finally,as shown in [11],it is possible to combine this controller with attitude-only controllers to fly through vertical windows or land on inclined perches with close to zero normal velocity.A trajectory controller is used by the robot to build up momentum,while the attitude con-troller enables reorientation while coasting with the gener-ated momentum.

Vision-Based Perception and Control

There are two approaches to the question of controlling an aerial vehicle based on visual information.The first is to use classical robotic SLAM techniques,although with the caveat that the environment and state estimation are inher-ently 3-D.There are many researchers currently working on this problem,and we will not attempt to discuss this approach further,except to say that should a good-quality environmental estimation and localization algorithm be developed,the control techniques discussed above can be applied.The second approach is direct sensor-based con-trol [26],the most commonly referred to case,being that of image-based visual servo control [27]–[29].

The motion of a point in an image is a function of its coordinate (u,v )and the camera motion

?J (u ,v ,Z )m ,(33)

where Z is the point depth,m ?(v x ,v y ,v z ,x x ,x y ,x z )>is the spatial velocity of the camera (and vehicle),and J (á)is the visual Jacobian or interaction matrix.J can be formu-lated for a perspective camera [30],where (u,v )are pixel coordinates;or a spherical camera [31]where (u,v )are lat-itude and longitude angles.

The pitch and roll motion of the vehicle are controlled by the attitude subsystem to maintain a position or to fol-low a path in space,and this causes image motion.We par-tition the equations as

?J 1(u ,v )(v x ,v y ,v z ,x z )>tJ 2(u ,v )x x x y ,(34)

where the right-most term describes the image motion due to the exogenous roll and pitch motion.Rearranging we can write

_u 0_v 0

?_u

_v >àJ 2(u ,v )

x x x y

(35)?J 1(u ,v )(v x ,v y ,v z ,x z )>,

(36)

where (u 0,v 0)represent image points for which the roll and

pitch motion has been removed based on the knowledge of x x and x y ,which can be obtained from gyroscopes.

Now consider a point in the image (u 0i ,v 0i )and its

desired location in the image (u ?i ,v ?

i ).This desired position might come from a snapshot of the scene taken when the vehicle was at the desired pose that we wish to return

to.The desired image motion is therefore (_u ?i ,_v

?i )?k (u ?i éu 0i ,v ?i év 0

i ),where the operator érepresents the difference on image plane or sphere.For N points,we can write k _u ?1

_v ?1..._u ?N _v

?N 0

B B B B B B B B B @1

C C C C C C C C C A àJ 1(u 1,v 1)...J 1(u N ,v N )0B

B B @

1C C C A x x x y !0B B B B B B B B B @1

C C C

C C C C C

C A

?J 2(u 1,v 1)

...J 2(u N ,v N )

B B @

C C C A |???????????{z???????????}B

v x

v y v z x z

B B B B B @1

C C C C C A

:(37)If N >2and the matrix B is nonsingular,we can solve for

the required translational and yaw velocity to move the vehicle to a pose where the feature points have the desired

image coordinates (u ?i ,v ?

i ).The desired velocity is input to a control system as discussed earlier.This is an example of image-based visual servoing for an underactuated vehicle,and the technique can be applied to a wider variety of problems,such as holding station,path following,obstacle avoidance,and landing.

Conclusions

In this article,we have provided a tutorial introduction to modeling,estimation,and control for multirotor aerial vehicles,with a particular focus on the most common form —the quadrotor.The dynamic model includes the rigid body motion of the vehicle in SE(3),the simple aero-dynamics associated with hover,and the extension to the case of forward motion where blade flapping becomes important.State estimation based on accelerometers,gyro-scopes,and magnetometers was discussed for attitude and translational velocity,and GPS,motion-capture systems,and cameras for position estimation.A hierarchy of con-trol techniques was discussed,from the individual rotors through attitude control,aggressive trajectory following,and image-based visual control.The future possibilities of highly agile small-scale vehicles were laid with a discussion on dimensional scaling for which vision will be an impor-tant sensing modality.

Acknowledgment

This research was partly supported by the Australian Research Council through Future Fellowship FT0991771,

SEPTEMBER 2012

IEEE ROBOTICS &AUTOMATION MAGAZINE

Foundations of Vision Based Control of Robotic Vehicles, the U.S.Army Research Laboratory Grant W911NF-08-2-0004,and the U.S.Office of Naval Research Grants N00014-07-1-0829,N00014-09-1-1051,and N00014-08-1-0696.

References

[1]P.I.Corke,Robotics,Vision&Control:Fundamental Algorithms in MATLAB.Berlin:Springer-Verlag,2011.

[2]T.Hamel,R.Mahony,R.Lozano,and J.Ostrowski,“Dynamic model-ling and configuration stabilization for an X4-flyer,”in Proc.Int.Federa-tion of Automatic Control Symp.(IFAC),2002,p.6.

[3]S.Bouabdallah,P.Murrieri,and R.Siegwart,“Design and control of an indoor micro quadrotor,”in Proc.IEEE Int.Conf.Robotics and Auto-mation(ICRA),Apr.26–May1,2004,vol.5,pp.4393–4398.

[4]R.W.Prouty,Helicopter Performance,Stability and Control.Mel-bourne,FL:Krieger,1995(reprint with additions,original edition1986).

[5]J.Leishman.(2000).Principles of Helicopter Aerodynamics(Cambridge Aerospace Series).Cambridge,MA:Cambridge Univ.Press.[Online]. Available:https://www.wendangku.net/doc/3315409547.html,.au/books?id=nMV-TkaX-9cC

[6]H.Huang,G.Hoffmann,S.Waslander,and C.Tomlin,“Aerodynamics and control of autonomous quadrotor helicopters in aggressive maneuvering,”in Proc.IEEE Int.Conf.Robotics and Automa-tion(ICRA),May2009,pp.3277–3282.

[7]P.Martin and E.Salaun,“The true role of accelerometer feedback in quadrotor control,”in Proc.IEEE Int.Conf.Robotics and Automation, Anchorage,AK,May2010,pp.1623–1629.

[8]P.Corke.Robotics toolbox for MATLAB.(2012).[Online].Available: https://www.wendangku.net/doc/3315409547.html,/robot.

[9]C.H.Wolowicz,J.S.Bowman,and W.P.Gilbert,“Similitude require-ments and scaling relationships as applied to model testing,”NASA, Tech.Rep.1435,Aug.1979.

[10]S.Shen,N.Michael,and V.Kumar,“3D estimation and control for autonomous flight with constrained computation,”in Proc.IEEE Int. Conf.Robotics and Automation,Shanghai,China,May2011,p.6. [11]D.Mellinger,N.Michael,and V.Kumar,“Trajectory generation and control for precise aggressive maneuvers with quadrotors,”Int.J.Robot. Res.,vol.31,no.5,pp.664–674,Apr.2012.

[12]R.Mahony,T.Hamel,and J.-M.Pflimlin,“Non-linear complemen-tary filters on the special orthogonal group,”IEEE Trans.Automat. Contr.,vol.53,no.5,pp.1203–1218,June2008.

[13]S.Bonnabel,P.Martin,and P.Rouchon,“Non-linear symmetry-pre-serving observers on lie groups,”IEEE Trans.Automat.Contr.,vol.54, no.7,pp.1709–1713,2009.

[14]A.Bachrach,S.Prentice,R.He,and N.Roy,“Range-robust autono-mous navigation in GPS-denied environments,”J.Field Robot.,vol.28, no.5,pp.644–666,2011.

[15]O.Amidi,T.Kanade,and https://www.wendangku.net/doc/3315409547.html,ler,“Vision-based autonomous heli-copter research at Carnegie Mellon Robotics Institute,”in Proc.Heli Japan,1998,vol.98,p.6.

[16]P.Corke,“An inertial and visual sensing system for a small autonomous helicopter,”J.Robot.Syst.,vol.21,no.2,pp.43–51,Feb.2004.

[17]L.Meier,P.Tanskanen,F.Fraundorfer,and M.Pollefeys,“Pixhawk:

A system for autonomous flight using onboard computer,”in Proc.ICRA, 2011,p.6.[18]C.Kemp,“Visual control of a miniature quad rotor helicopter,”Ph.D.dissertation,Univ.Cambridge,Cambridge,U.K.,2006.

[19]M.Achtelik,A.Bachrach,R.He,S.Prentice,and N.Roy,“Stereo vision and laser odometry for autonomous helicopters in GPS-denied indoor environments,”in Proc.SPIE Unmanned Systems Technology XI. Orlando,FL,SPIE,2009,vol.7332,p.10.

[20]P.Bristeau,F.Callou,D.Vissi e re,and N.Petit,“The navigation and control technology inside the AR.drone micro UAV,”in Proc.World Congress,2011,vol.18,no.1,pp.1477–1484.

[21]V.Srinivasan and S.Venkatesh,From Living Eyes to Seeing Machines.London,U.K.:Oxford Univ.Press,1997.

[22]P.Corke,J.Lobo,and J.Dias,“An introduction to inertial and visual sensing,”Int.J.Robot.Res.,vol.26,no.6,pp.519–536,June 2007.

[23]T.Lee,M.Leok,and N.McClamroch,“Geometric tracking control of a quadrotor UAV on SE(3),”in Proc.IEEE Conf.Decision and Control, 2010,p.6.

[24]D.Mellinger and V.Kumar,“Minimum snap trajectory generation and control for quadrotors,”in Proc.Int.Conf.Robotics and Automation (ICRA),Shanghai,China,May2011,p.6.

[25]M.J.V.Nieuwstadt and R.M.Murray,“Real-time trajectory genera-tion for differentially flat systems,”Int.J.Robust and Nonlinear Control, vol.8,no.11,pp.995–1020,1998.

[26]C.Samson,M.Le Borgne,and B.Espiau,Robot Control:The Task Function Approach(The Oxford Engineering Science Series).Oxford, U.K.:Oxford Univ.Press,1991.

[27]T.Hamel and R.Mahony,“Visual servoing of an under-actuated dynamic rigid-body system:An image based approach,”IEEE Trans. Robot.Automat.,vol.18,no.2,pp.187–198,Apr.2002.

[28]N.Guenard,T.Hamel,and R.Mahony,“A practical visual servo control for a unmanned aerial vehicle,”IEEE Trans.Robot.,vol.24,no.2, pp.331–341,Apr.2008.

[29]R.Mahony,P.Corke,and T.Hamel,“Dynamic image-based visual servo control using centroid and optic flow features,”J.Dynamic.Syst., Meas.Contr.,vol.130,no.1,p.12,Jan.2008.

[30]S.Hutchinson,G.Hager,and P.Corke,“A tutorial on visual servo control,”IEEE Trans.Robot.Autom.,vol.12,no.5,pp.651–670,Oct. 1996.

[31]P.I.Corke,“Spherical image-based visual servo and structure estimation,”in Proc.IEEE Int.Conf.Robotics and Automation,Anchor-age,AK,May2010,pp.5550–5555.

Robert Mahony,Research School of Engineering,Austra-lian National University,Canberra0200,Australia.E-mail: Robert.Mahony@https://www.wendangku.net/doc/3315409547.html,.au.

Vijay Kumar,Department of Mechanical Engineering and Applied Mechanics,GRASP Laboratory,University of Pennsylvania,Philadelphia,USA.E-mail:vijay.kumar@ https://www.wendangku.net/doc/3315409547.html,.

Peter Corke,School of Electrical Engineering and Computer Science,Queensland University of Technology, Australia.E-mail:Peter.Corke@https://www.wendangku.net/doc/3315409547.html,.au.

32?IEEE ROBOTICS&AUTOMATION MAGAZINE?SEPTEMBER2012

电影电视名词解释(中英文对照)

电影电视名词解释（中英文对照） ABERRATION 像差摄影镜头因制作不精密，或人为的损害，不能将一点所发出的所有光线聚焦于底片感光膜上的同一位置，使影像变形，或失焦模糊不清。 ABSOLUTE FILM 绝对电影一种用抽象图形来诠释音乐的影片。由德国羊肠小道前卫电影导演奥斯卡费辛格于1925-1930年首创。 ABSTRACT FILM 抽象电影一种通过影片的剪辑、视觉技巧、声音性质、色彩形状以及韵律设计等，来表达意念，给人一种自由自在、不拘形式感觉的电影。电影术语以及解释 ACADEMIC EDITING 学院式剪接一种仔细依循电影剧情发展过程的剪接方式。其目的是在于重建一个事件的全部过程，维持电影剧情发展的流畅性。因这种剪接方式不会引起观众对剪接本身的注意，有时也被称为"无痕迹剪接" ，是好莱坞最常用的剪接方式之一。 ACADEMY APERTURE 影艺学院片门由美国影艺学院推行的一种电影片门规格，主要是用于35毫米电影摄影机和放映机。此种规格宽高比例为1.33：1。亦称ACADEMY FRAME。

ACADEMY AWARDS 奥斯卡金像奖美国影艺学院于1972年设立的奖项，每年颁给表现杰出的电影工作者。每一个奖项最多有五个提名。个人项目奖，可以提高演员或电影工作者的身价。 ACADEMY LEADER 影艺学院导片依据影艺学院所设定的标准，连接在放映拷贝首尾的一段胶片。导片中含有一系列倒数的数字、放映记录和其他信息，便于放映师装片和换片。导片不仅有保护影片的功能，同时可使放映机从起动到第一格画面到达放映机片门之前，达到正常的放映速度。 ACADEMY MASK 影艺学院遮片由影艺学院规画出来的一种遮掩摄影机部分片门的装置。 ACADEMY OF MOTION PICTURE ARTS ＆SCIENCE 美国影艺学院（台）美国电影艺术和科学学院（大陆）成立于1927年，宗旨是"提升电影媒体的艺术品质，提供电影工业不同部门及技术的普遍交流，促进动技术研究与文化发展的代表作，追求其既定的多元化目标"。该学院最知名的是一年一度的奥斯卡金像奖。 ACADEMY STANDARDS 影艺学院标准指美国影艺学院所订立的技术规格，以在电影工业界推行标准化的作业方式。包括：影艺学院画面（ACADEMY FRAME），影艺学院导片（ACADEMY LEADER），影艺学院遮片（ACADEMY MASK） ACCELERATED MONTAGE 加速蒙太奇一种剪接的技巧，目的在于增强动作在影片中的加速度效果。在电影剪接中，常

UAV英文原站发表

Unmanned Aerial Vehicles (UAVs) Unmanned Aerial Vehicles (UAVs) are remotely piloted or self-piloted aircraft that can carry cameras, sensors, communications equipment or other payloads. They have been used in a reconnaissance and intelligence-gathering role since the 1950s, and more challenging roles are envisioned, including combat missions. Since 1964 the Defense Department has developed 11 different UAVs, though due to acquisition and development problems only 3 entered production. The US Navy has studyied the feasibility of operating VTOL UAVs since the early 1960s, the QH-50 Gyrodyne torpedo-delivery drone being an early example. However, high cost and technological immaturity have precluded acquiring and fielding operational VTOL UAV systems. By the early 1990s DOD sought UAVs to satisfy surveillance requirements in Close Range, Short Range or Endurance categories. Close Range was defined to be within 50 kilometers, Short Range was defined as within 200 kilometers and Endurance as anything beyond. By the late 1990s, the Close and Short Range categories were combined, and a separate Shipboard category emerged. The current classes of these vehicles are the Tactical UAV and the Endurance category. Pioneer: Procured beginning in 1985 as an interim UAV capability to provide imagery intelligence for tactical commanders on land and see at ranges out to 185 kilometers. No longer in the Army inventory (returned to the US Navy in 1995). Tactical UAV : Designed to support tactical commanders with near-real-time imagery intelligence at ranges up to 200 kilometers. Outrider Advanced Concept Technology Demonstration (ACTD) program terminated. Material solution for TUAV requirements is being pursued through a competive acquisition process with goal of contract award in DEC 99. Joint Tactical UAV (Hunter): Developed to provide ground and maritime forces with near-real-time imagery intelligence at ranges up to 200 kilometers; extensible to 300+ kilometers by using another Hunter UAV as an airborne relay. Training base located at Fort Huachuca, with additional baseline at Fort Polk to support JRTC rotations. Operational assets based at Fort Hood (currently supporting the KFOR in Kosovo). Medium Altitude Endurance UAV (Predator): Advanced Concept Technology Demonstration now transitioned to Low-Rate Initial Production (LRIP). Provides imagery intelligence to satisfy Joint Task Force and Theater

SPECIFICATIONS FOR SURVEYING, AERIAL PHOTOGRAPHY AND MAPPING

SPECIFICATIONS FOR SURVEYING, AERIAL PHOTOGRAPHY AND MAPPING OF A PROPOSED TRANSMISSION LINE CORRIDOR 1.0 Introduction These specifications are for plan & profile surveys required by the Engineer to develop computer models for the design of overhead line facilities and modeling for analysis of existing lines. The Engineer uses PLS-CADD computer software for design and analysis of transmission line projects. The survey requirements for development of PLS-CADD profile and plan detail follow. Terrain and obstruction data shall be described by coordinate position and feature characteristic collected by the surveyor. The surveyor shall measure the position of any features of objects described in the attached list of features as necessary to define the project. The method of acquisition shall be proposed by the surveyor and may include ground survey with total station and data recorder, aerial photogrammetric surveys, or remote sensing (i.e. lidar) surveys that produce horizontal and vertical positions with codes to describe different features. 2.0 Area To Be Flown The proposed route of the transmission line is as follows: {Description of Line Route}. The approximate length of this line is {length of route}. The width of coverage shall be a minimum of {300 Note: for existing lines one may wish to consider a much smaller width} meters left and right from the route centerline 3.0 Approximate Route Alignment Drawing {Drawing Number(s)}dated {mm/dd/yy}, represents the current proposed location of the transmission line. The drawing is also attached as an electronic drawing in {AutoCAD, Microstation, other} format for use only with this project. The projection used in the file is {UTM, State Plane, etc. – full description}. 4.0 Deliverables 1. Contact Prints 2. Digital Orthophotography Image files on CD-ROM or DVD-ROM 3. CAD Drawing file on CD-ROM or DVD-ROM 4. DTM (Digital Terrain Model) file on CD-ROM or DVD-ROM 5. Optional: A PLS-CADD backup (“.bak”) file containing all of the above. This is the simplest possible format for the engineer to use as it may be directly opened inside PLS-CADD. The backup file is created using the File/Backup command in PLS-CADD. Specifications for these deliverables are given in the following paragraphs.

基于轨迹优化和运动学补偿的飞行操作臂视觉抓取

哈尔滨工业大学工学硕士学位论文 Abstract With the rapid development of aerial robotics, unmanned aerial vehicle (UAV) has been successfully applied in more and more fields. Nowadays, UAVs are already very mature in observation-based applications such as aerial photography. However, there are still many challenges in other fields. Based on the existing mature algorithms and extensions, more and more researchers have tried and explored the further application of UAVs, including the most representative air transport, air operations and interaction. As a new hot research topic of UAV applications, the study of aerial manipulator system includs flight adaptive robotic arm design, complex system modeling and controller, aerial SLAM, intelligent planning and other related expansion technologies. The research of aerial manipulator system usually focuses on the operation of object grasping. In general, accurate and highly-maneuvering control of aerial manipulator system requires accurate dynamic modeling; however, it is challenging to obtain complete modeling. At present, most of the related researches are based on simulation or in simple environments without obstacles. The existing methods like visual servoing cannot accomplish the collision avoidance task in slightly complicated environments. To solve these problems, a light-weight robotic arm is presented to reduce the dynamic coupling of the system, and furthermore a kinematic aerial grasping method is proposed. The proposed grasping method does not rely on the system dynamics model and thus avoids the difficulty of dynamic parameters’ calib ration. Because the existing visual servoing solutions are easy to lose tracking the target and cannot work in the complicated environments with obstacles, the dissertation presents a novel visual system to track the target in real time and obtain the target pose by using a monocular vision camera. At the same time, by transforming the trajectory planning problem into an optimization problem with multiple objectives and constraints, NSGA-II multi-objective optimization is used to solve the trajectory planning problem. Another innovative point compared with the existing research is that this dissertation considers the problem of pose variations caused by dynamic and external factors, a trajectory correction scheme and a trajectory tracker based on filtering and time-partitioned interpolation control are proposed to achieve high grasping performance. In this dissertation, the visual grasping methods of aerial manipulator are verified by several experiments. By using the proposed approach, autonomous visual grasping operation with our aerial manipulators system under complicated

无人机 unmanned aerial vehicle

无人机unmanned aerial vehicle Chinese authorities are soliciting opinions from the public on the country's new official regulations on unmanned aerial vehicles (UAVs), commonly known as drones, reports https://www.wendangku.net/doc/3315409547.html,. 据澎湃新闻报道，我国有关部门正就无人驾驶航空器（即“无人机”）管理新规向公众征求意见。《征求意见稿》围绕无人驾驶航空器（unmanned aerial vehicles）、驾驶员（human operator）、环境等关键环节，共7章59条明确制度规定，管理对象全面覆盖各类无人机，范围由250克以下至150公斤以上，包含民用、警用、军用等不同类别；囊括全生命周期，涵盖设计制造（design and manufacture），产品适航（airworthiness），运行规范（aviation control），人员管理（ownership registration）、事后查处（accident investigation）等一系列环节。《征求意见稿》详细列出了无人机的分类：无人机分为国家无人机（national UAVs）和民用无人机（civilian UAVs）。民用无人机，指用于民用航空活动的无人机；国家无人机，指用于民用航空活动之外的无人机，包括用于执行军事、海关、警察等飞行任务的无人机（drones used for military, customs and public security purposes）。根据运行风险大小，民用无人机分为微型、轻型、小型、中型、大型。其中：微型无人机（micro-UAVs），是指空机重量（empty weight）小于0.25千克，设计性能同时满足飞行真高不超过50米、最大飞行速度不超过40千米/小时、无线电发射设备符合微功率短距离无线电发射设备技术要求的遥控驾驶航空器。轻型无人机（light UAVs），是指同时满足空机重量不超过4千克，最大起飞重量不超过7千克，最大飞行速度不超过100千米/小时，具备符合空域管理要求的空域保持能力和可靠被监视能力的遥控驾驶航空器，但不包括微型无人机。小型无人机（mini-UAVs），是指空机重量不超过15千克或者最大起飞重量不超过25千克的无人机，但不包括微型、轻型无人机。

无人机的中英文对照

Unmanned Aerial Vehicle (UAV) 无人驾驶飞机 An unmanned aerial vehicle (UAV), commonly known as a drone, is an aircraft without a human pilot onboard. Its flight is either controlled autonomously by computers in the vehicle, or under the remote control of a navigator, or pilot (in military UAVs called a Combat Systems Officer on UCAVs) on the ground or in another vehicle. 无人驾驶飞机,俗称无人机,即无需驾驶员在机内驾驶的飞机。其飞行时接受的并不是机内电脑的自动控制，也不是导航员的远程控制，更不是来自地面或另一飞机上无人作战机指挥官的控制. There are a wide variety of drone shapes, sizes, configurations, and characteristics. Historically, UAVs were simple remotely piloted aircraft, but autonomous control is increasingly being employed. 无人机种类繁多,在外形、大小、结构和性能上各有千秋。过去无人驾驶飞机只是简单的远程人工驾驶飞机，而现在越来越多的的无人机都采用了自动控制驾驶。 Their largest use is within military applications. UAVs are also used in a small but growing number of civil applications, such as firefighting or nonmilitary security work, such as surveillance of pipelines. UAVs are often preferred for missions that are too "dull, dirty, or dangerous" for manned aircraft. 无人机最广泛地运用于军事领域，在民用领域，如消防事业或管道监控这样的非军事保障工作中也占有小额比重，并有所增长。对载人飞机来说，那些“无聊、肮脏或危险的”任务，就可以利用无人机来执行。 History The earliest attempt at a powered unmanned aerial vehicle was A. M. Low's "Aerial Target" of 1916. Nikola Tesla described a fleet of unmanned aerial combat vehicles in 1915. A number of remote-controlled airplane advances followed, including the Hewitt-Sperry Automatic Airplane, during and after World War I, including the first scale RPV (Remote Piloted Vehicle), developed by the film star and model airplane enthusiast Reginald Denny in 1935. More were made in the technology rush during World War II; these were used both to train antiaircraft gunners and to fly attack missions. Jet engines were applied after World War II, in such types as the Teledyne Ryan Firebee I of 1951, while companies like Beechcraft also got in the game with their Model 1001 for the United States Navy in 1955. Nevertheless, they were little more than remote-controlled airplanes until the Vietnam Era.

四旋翼无人机术语

术语：无人机UAV (Unmanned Aerial Vehicle), drone UAS (Unmanned Aerial Systems) 地面控制站Ground Control Station, GCS 固定翼fixed-wing 旋翼rotary-wing Rover 陆路，水路多旋翼multirotors, multicopters 四旋翼4-rotor helicopters, quadcopter 加速计accelerometer 陀螺仪gyroscope 磁力计magnetometer 压力计barometer 射频控制R/C 遥测telemetry altitude GPS WAAS: Wide Area Augmentation System Thermopile: infrared detector, tilt, pitch, earth, sky, pan & tilt 侧视，俯视 roll pitch yaw autopilot 自主导航 takeoff & landing 起飞/着陆 MAV

MAVLink APM AI 意念控制Mind Control BCI 涡流，湍流Turbulence Navier-Stokes equations 定点waypoints DCM (Direction Cosine Matrix) COA (Certificate of Authorization) 2.4 Ghz, 72 Mhz, Kalman Filter: INS: Inertial Navigation System Inner loop / Outer loop FPV (First-Person View) 第一视角 FHSS (Frequency-Hopping Spread Spectrum) DSSS (Direct-Sequence Spread Spectrum) ROI POI PID WAAS ILS LAAS (Next-Gen GPS algorithm standard) PIC (Pilot In Command) LOS (Line of Sight) RTL (Return to Launch) 返航, Return to Home

自由式滑雪空中技巧代码和难度系数

Aerial Jump Code and Degree of Difficulty Chart 1. Jump Code with Degree of Difficulty Jump Description Jump Code DD Back Lay bL 2.050 Back Full bF 2.300 Back Lay–Tuck bLT 2.600 Back Lay-Lay bLL 2.650 Back Full-Tuck bFT 2.850 Back Lay-Full bLF 2.900 Back Full-Full bFF 3.150 Back Lay-Tuck-Tuck bLTT 3.200 Back Double Full-Tuck bdFT 3.225 Back Lay-Double Full bLdF 3.275 Back Lay-Full-Tuck bLFT 3.500 Back Lay-Pike-Full bLPF 3.500 Back Lay-Tuck-Full bLTF 3.500 Back Double Full-Full bdFF 3.525 Back Full-Double Full bFdF 3.525 Back Lay-Full-Full bLFF 3.800 Back Double Full-Double Full bdFdF 3.900 Back Full-Full-Full bFFF 4.050 Back Lay-Double Full-Full bLdFF 4.175 Back Full-Double Full-Full bFdFF 4.425 Back Double Full-Full-Full bdFFF 4.525 Back Full-Full-Double Full bFFdF 4.525 Back Full-Triple Full-Full bFtFF 4.900 Back Double Full-Full-Double Full bdFFdF 5.000

abc cable aerial bundle cable

ZHENGZHOU HONGDA CABLE CO.,LTD Add:Maiduogou Village,Houzhai Xiang,Erqi Dist.,Zhengzhou,Henan,China (Mainland) Company information Zhengzhou Hongda Cable Co.,Ltd.was established in March of1999.Our company owns registered capital of RMB6,000,000.Our company covers an area of46,000square meters,including20,000square meters of building area,and has more than120staff members and professional workers accounting for above one quarter. We mainly aim at managing cross-linking XLPE insulated power cables,PVC insulated power cables,plastic insulated control cables,insulated overhead cables,and stranded aluminum and ACSR.At present,the cables'biggest cross area is500square meters with a maximum electric power of10KV,and the annual producing capacity is20,000 kilometers. The cables are produced conforming to GB standard and approved by ISO9001in2000. Recent years,our company has received a good reputation for our high quality products. Our company insists on the principle of"Taking high and new technology as guide and being based on modern management".Our products sell well all over the world and the main reason is that we attach great importance to business honesty.We sincerely hope to be your partner. Basic Information Company Name:Zhengzhou Hongda Cable Co.,Ltd. Year Established:2004 Business Type:Manufacturer Main Products:Cross-linking XLPE insulated power cables,PVC insulated power cables,plastic insulated control cables,Overhead insulated cables,stranded aluminum and ACSR

美国FDA指南中文版

《美国FDA认证与申办指南》权威资讯系列《合成原料药DMF起草大纲》

使用说明： 1、本大纲是为了帮助我公司客户把握DMF的整体内容而准备的，由于DMF内容繁多，从整体上了解内容框架和组成部分，对于理解FDA对DMF的要求和意图非常有必要； 2、根据FDA的要求，凡是本大纲提到的内容，原料药制造商均应该提供。因此，客户务必依照规定提供尽可能详细的内容。 3、本大纲的内容和相关要求能够确保客户目前的运作达到FDA的cGMP标准，因此，准备DMF的过程，也使客户按照FDA的要求进行整改和提高的过程，这些都为FDA未来的现场检查打下良好基础；4、凡是本大纲中提到的非技术性具体内容要求，请参照本公司专有的与此大纲配套的相关DFM指导性文件，包括《FDA药物主文件指南》、《关于在药品递交中递交的有关原料药生产的支持文件的指南》、《药物申办中质量管理方面通用技术文件格式与内容要求》； 5、凡是本大纲中提到的技术性具体内容要求，如杂质、稳定性、验证等具体技术要求，请参照本公司专有的FDA相关技术标准文件，包括《原料药认证指南》、《制剂认证指南》、《化学药物稳定性指南》、《化学药物杂质指南》、《化学药物化验与合格参数指南》、《化学药物验证指南》等；

《合成原料药DMF起草大纲》一、公司和生产场地的基本描述 1、第一类的DMF文件建议由位于美国之外的人提供，以帮助FDA对他们的生产设施进行现场检查。DMF文件应描述生产场地、设备能力、生产流程图等。A Type I DMF is recommended for a person outside of the United States to assist FDA in conducting on site inspections of their manufacturing facilities. The DMF should describe the manufacturing site, equipment capabilities, and operational layout. 2、第一类的DMF文件对美国国内设施通常不需要，除非该设施没有登记并定期接受检查。A Type I DMF is normally not needed to describe domestic facilities, except in special cases, such as when a person is not registered and not routinely inspected. 3、场地的描述应包括面积、实际地址以及表明该场地与最近的城市的距离的地图。提供该场地的鸟瞰图和平面图。The description of the site should include acreage, actual site address, and a map showing its location with respect to the nearest city. An aerial photograph and a diagram of the site may be helpful. 4、主要生产和加工区域的平面图对于理解整个生产布局会有帮助。应当描述主要设备的生产能力、用途和位置。通常不用描述设备的制造商和型号，除非特别新或独特的设备。A diagram of major production and processing areas is helpful for understanding the operational layout. Major equipment should be described in terms of capabilities, application, and location. Make and model would not normally be needed unless the equipment is new or unique. 5、公司主要的组成部门结构图，包括总公司和生产场地的关键生产、质量控制、质量保证岗位，A diagram of major corporate organizational elements, with key manufacturing, quality control, and quality assurance positions highlighted, at both the manufacturing site and corporate headquarters, is also helpful. 二、原料药的物理和化学特征 1、特性Properties 相关法规要求对原料药的物理和化学特征做出详细描述。该要求可以通过提供下

美国FDA指南-中文版

《美国FDA认证与申办指南》权威资讯系列《合成原料药DMF起草大纲》

使用说明： 1、本大纲是为了帮助我公司客户把握DMF的整体内容而准备的，由于DMF内容繁多，从整体上了解内容框架和组成部分，对于理解FDA对DMF的要求和意图非常有必要； 2、根据FDA的要求，凡是本大纲提到的内容，原料药制造商均应该提供。因此，客户务必依照规定提供尽可能详细的内容。3、本大纲的内容和相关要求能够确保客户目前的运作达到FDA 的cGMP标准，因此，准备DMF的过程，也使客户按照FDA的要求进行整改和提高的过程，这些都为FDA未来的现场检查打下良好基础； 4、凡是本大纲中提到的非技术性具体内容要求，请参照本公司专有的与此大纲配套的相关DFM指导性文件，包括《FDA药物主文件指南》、《关于在药品递交中递交的有关原料药生产的支持文件的指南》、《药物申办中质量管理方面通用技术文件格式与内容要求》； 5、凡是本大纲中提到的技术性具体内容要求，如杂质、稳定性、验证等具体技术要求，请参照本公司专有的FDA相关技术标准文件，包括《原料药认证指南》、《制剂认证指南》、《化学药物稳定性指南》、《化学药物杂质指南》、《化学药物化验与合格参数指南》、《化学药物验证指南》等；

Multirotor aerial vehicles_ Modeling, estimation, and control of quadrotor

电影电视名词解释(中英文对照)

UAV英文原站发表

SPECIFICATIONS FOR SURVEYING, AERIAL PHOTOGRAPHY AND MAPPING

基于轨迹优化和运动学补偿的飞行操作臂视觉抓取

无人机 unmanned aerial vehicle

无人机的中英文对照

四旋翼无人机术语

自由式滑雪空中技巧代码和难度系数

abc cable aerial bundle cable

美国FDA指南 中文版

美国FDA指南-中文版

美国FDA指南中文版