An Autonomous Carrier Landing System for Unmannned Aerial Vehicles ∗ Jovan D. Boˇskovi´c† and Joshua Redding‡ Scientific Systems Company, Inc.

One of the important problems related to naval Unmanned Aerial Vehicles (UAV), is the design of an automatic landing system that would enable autonomous landing of a UAV on an aircraft carrier. When landing needs to be accomplished safely in the high sea states and during the carrier turns, the problem becomes highly complex. In this paper we present an innovative autonomous carrier landing system for UAVs, referred to as the Carrier Motion Prediction & Autonomous Landing (CM-PAL) system. The system is based on real-time estimation of magnitudes and frequencies of waves encountered by the carrier, and online prediction of the carrier motion. This prediction generates information regarding the carrier states at touchdown; this information is in turn used to generate corrections in the UAV’s heading and flight path angle commands to achieve minimum dispersion around the desired touchdown point and heading. We also present performance evaluation results of the CM-PAL system on a high-fidelity simulation of typical aircraft carrier dynamics.

I. Introduction To address the automatic landing concept, the U.S. Department of Defense is developing Joint Precision Approach and Landing System (JPALS) program. Under this program, the Navy is responsible for its shipboard component termed Shipboard Relative Global Positioning System (SRGPS).1 The SRGPS will support all Air Traffic Control (ATC) functions, including takeoff, departure, taxi, holding, approach, landing, bolter, missed approach, and long range navigation. In addition to supporting manned aircraft, SRGPS will fully support automatic takeoff, approach, landing and ATC automation required by future unmanned systems such as the Naval Unmanned Combat Aerial Vehicle. Recently, Northrop Grumman Corporation was awarded a six-year, $636 million UCAS-D contract after its X-47B was selected over Boeing’s X-45N. The first of two demonstrators is scheduled to fly in November 2009, and the first carrier landing is planned for 2011. The problem of autonomous landing of Unmanned Aerial Vehicles (UAV) and Unmanned Combat Aerial Vehicles (UCAV) on a ship is highly challenging due to stringent constraints with respect to dispersion around the desired touchdown point, approach speed, approach heading and pitch attitude. When accurate landing under these constraints needs to be achieved under wind gust disturbances, communication dropouts and in the presence of ship motion under high sea states, the problem becomes truly formidable. An additional complexity in the context of UAVs is that of bolter recovery. Bolter is a term for a failed attempt to capture the arresting cable when landing, and is a highly dangerous situation from a safety perspective. This problem needs to be specifically addressed in the case of UAVs. Hence, the control strategy for UAV carrier landing needs to have the following capabilities: ∗ This research was supported by Boeing Phantom Works under a contract to Scientific Systems Company. † Principal Research Engineer & Intelligent & Autonomous Control Systems Group Leader, 500 W. Cummings Park, Suite 3000, Woburn, MA, AIAA Senior Member, [email protected] ‡ Ph.D. Candidate, MIT Aerospace Controls Laboratory, on leave from SSCI, AIAA Member, [email protected]

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• Efficient prediction and compensation of the carrier motion under communication blackouts • Capability to autonomously recover from bolter • Flexibility to readily incorporate changes in the landing parameters due to heave, sway and surge motion of the touchdown point to achieve effective Deck Motion Compensation • Effective rejection of atmospheric disturbances such as wind gust. To address these issues, we developed a Carrier Motion Prediction & Autonomous Landing (CM-PAL) system that consists of a Ship Motion Predictor (SMP), and an algorithm for the determination of optimal UAV heading for ship-relative course line following during landing on a turning aircraft carrier. The main objective was to develop an algorithm for course-line following, and the SMP module to allow for UAV heading and flight path angle corrections at the carrier landing stage based on predicted carrier states ten seconds before touchdown. We show in Section VIII that the SMP system accurately predicts all the states of the ship 10 seconds ahead of touchdown with errors well below the stated specifications. The proposed CM-PAL system consists of the following modules: 1. A signal conditioning module that extracts the actual wave disturbance signal from the measurements 2. A frequency estimation module that employs a modified Fast Fourier Transform (FFT) algorithm and generates an accurate wave frequency estimate. 3. A parameter estimation module that uses Batch Least Squares algorithm to estimate amplitudes and phases of the wave disturbance signal, as well as the signal itself. 4. A prediction module that uses a Kalman Filter to predict the behavior of ship’s states due to wave disturbances. 5. A confidence measure calculation module that calculates a wave-off criterion. The diagram of the SMP system is shown in Figure 1. Since the position and velocity measurements are given in geodetic coordinates, these are first converted to Earth-Centered, Earth-Fixed (ECEF) Cartesian coordinates, and then to North-East-Down (NED) coordinates which are attached to the body of the carrier. The measurements contain the information about both the carrier dynamics and the effect of waves. Based on the known carrier dynamics and these measurements, the dynamics of waves can be extracted. The next step is to run the Fast Fourier Transform (FFT) on the waves data to estimate wave frequencies from noisy signals. Once the wave frequencies have been estimated, a Least-Squares Estimator is run to estimate the magnitudes and phases of the wave signals. After attaining accurate estimates wave frequencies and propagating the effect of the waves, these estimates are integrated with the model of carrier dynamics to generate predicted carrier motion. A confidence measure for the estimates is also calculated such that, if above a threshold, the UAV is waved-off. The specifications under which the algorithms were developed are described in Section II below.

II. Specifications During the design, the following specifications were assumed: • The algorithm should be valid for sea states up to and including level 5. • The algorithm should be valid for turning motion of the carrier of up to 0.5deg/s. • It is assumed that the UAV control system has a wind disturbance rejection capability, and that the effect of the wind of the carrier can be neglected.

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Figure 1. Structure of the Carrier Motion Prediction & Autonomous Landing (CM-PAL) System

• The algorithm shall utilize the broadcast messages from the carrier containing its current attitudes, rates and accelerations in the keel axis. These messages will be available within 10 nautical miles from the ship and received at 20Hz. • The ship motion prediction model shall be robust to momentary dropouts of these periodic messages. • The ship motion prediction algorithm shall output a minimum of four values: predicted roll, pitch and heading angles of the carrier vehicle (CV) keel axis at the specified time, along with a confidence factor of these predicted values. The confidence factor will be used to determine an autonomous wave-off criterion. • The attitude outputs of ship motion prediction for constant carrier turn rates shall have accuracies specified in Table 1. Specified Prediction Time (seconds) 5.0 ≤ T ≤ 10.00 T ≤ 5.0

Error Tolerance at Prediction Time ±0.25 deg ±0.1 deg

Table 1. Attitude Error Tolerances

• Additional outputs shall include the ship reference center of motion position (lat, lon, altitude), velocities (NED), and accelerations (NED). These values will be needed to to complete the approach after loss of data link within 5 seconds from the touchdown.

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III. Ship Dynamics Model This section outlines the dynamics model assumed for the ship Center of Motion. We use this model in the design of the desired UAV dynamics to achieve accurate following of the carrier course line. Γ˙ x + Vnom cos (ψt ) − Γ˙ y sin (ψt ) E˙ = Γ˙ x + Vnom sin (ψt ) + Γ˙ y cos (ψt ) D˙ = Γ˙ z ,

N˙ =

(1)

where north-east-down coordinate frame is assumed for the center-of-motion coordinates (Keel Axis), Γ˙ ∗ denote the ship’s body accelerations, Vnom is the nominal ship velocity (e.g. 20 knots), and ψt is the ship’s heading track, which is a lag-filtered heading with time constant τ as a function of Vnom . Ship rotation is assumed to be due to the waves modeled by the sum of sinusoids: φ˙ =

n X

θ˙ =

n X

i=1

ψ˙ =

i=1 n X i=1

aφi sin ωφi t + νφi aθi sin ωθi t + νθi

(2)

aψi sin ωψi t + νψi + ψcmd ,

where a∗ , ω∗ , and ν∗ are amplitude, frequency and phase shift inputs based on ship motion data and ψcmd is an adequately filtered ship turn command. The ship’s body velocities are denoted as Γ x,y,z , and refer to ship surge, sway and heave respectively. Body accelerations are given by: Γ˙ x =

n X i=1

aΓxi sin ωΓxi t + νΓxi

Γ˙ y =

n X

aΓyi sin ωΓyi t + νΓyi

i=1

aΓzi sin ωΓzi t + νΓzi ,

Γ˙ z =

i=1 n X

(3)

and body-axis rotational rates are: p = φ˙ − sin (θ)ψ˙ q = sin (φ) cos (θ)ψ˙ + cos (φ)θ˙ r = cos (φ) cos (θ)ψ˙ − sin (φ)θ˙,

(4)

where p, q and r denote respectively the roll, pitch and yaw rate. A. Cant Axes System The Cant axes system is an important coordinate frame as this is the reference associated with the desired UAV touchdown point and corresponding course line. Figure 2 shows the locations of the Keel and Cant

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Figure 2. Keel to Cant axis coordinate transformation

axes on the ship deck. The relationship between the two is given by: ∆x xca x yca = y + R ∆y , ∆z z zca

where ∆(x,y,z) are defined as the Cant axis offset in the Keel reference frame, as shown in Figure 2, and the rotation R is given by sψcθ cψcφ + sψsθsφ −cψsφ + sψsθcφ (5) R = cψcθ −sψcφ + cψsθsφ sψsφ + cψsθcφ −sθ cθsφ cθcφ where s∗, c∗ denotes sin(∗), cos(∗) respectively. The velocity and acceleration of the Cant axes system are given by: x˙ca x˙ ∆x ˙ ∆y y˙ ca = y˙ + R z˙ca z˙ ∆z

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(6)

∆x x¨ca x¨ ¨ ∆y y¨ ca = y¨ + R ∆z z¨ z¨ca

(7)

In Equation (6) and (7) above, the derivatives are simple since ∆∗ represents fixed distances and hence have a zero derivative. The first and second derivative of the rotation, R, are tedious but straightforward and hence, are not given.

IV. Coordinate transformations In order to implement the landing algorithm, we need to define several coordinate frames and the transformations between them. We have already introduced the ship’s keel, or center of motion, and Cant coordinate systems. Additional frames include the following: 1. Local north, east, down (NED) Ship information is provided to the unmanned aircraft landing system in this coordinate frame. It is formed by a plane tangent to the Earth’s surface fixed to a specific location, hence it is sometimes known as the local tangent, or local geodetic plane. By convention, the east axis is labeled x, the north y and, in our case, down z. 2. Earth-centered Earth-fixed (ECEF) This is the conventional terrestrial coordinate system and rotates with the Earth as its origin is at the Earth’s center. The X axis passes through the equator at the prime meridian, the Z axis passes through the north pole, and the Y axis passes through the equator at 90◦ longitude, following the right-hand rule. 3. Geodetic The geodetic system represents more accurately the fact that the earth is not a perfect sphere. Under this system, the Earth’s surface is approximated by an ellipsoid and locations near the surface are described in terms of latitude, longitude and height. The ellipsoid is completely parameterized by the semi-major axis a, and the flattening f . Sections A to C outline the transformations between these various coordinate frames. A. Local to ECEF Transforming from a local NED coordinate system to a earth-centered earth-fixed system is accomplished by the following: Xecef − sin(lat) cos(lon) − sin(lon) − cos(lat) cos(lon) N Yecef = − sin(lat) sin(lon) cos(lon) − cos(lat) sin(lon) E , Zecef cos(lat) 0 − sin(lat) D

where the rotation matrix is built using geodetic latitude and longitude.

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B. ECEF to Geodetic We use the direct algorithm in Ref. [12] to transform from earth-centered earth-fixed to the geodetic system. This transformation is given by: lon = arctan(Y, X) e = e2 (a/b)2 p p = X2 + Y 2 q p2 + Z 2 r =

bZ (1 + eb/r) u = arctan ap

!

Z + eb sin3 u lat = arctan p − e2 a cos3 u a v = q 1 − e2 sin2 (lat)

!

h = p cos(lat) + Z sin(lat) − a2 /v,

where X, Y, Z are ECEF coordinates, e2 = 6.69437999014e−3 denotes the first eccentricity squared, a = 2.092564632545929e+07 ft is the semi-major axis, and b = 2.085548659528727e+07 ft is the semi-minor axis. C. Geodetic to ECEF Transforming back to earth-centered earth-fixed coordinates from geodetic is given by: X = (Φ + alt) cos(lat) cos(lon)

p where Φ = a/ 1 − e2 sin(lat)2 .

Y = (Φ + alt) cos(lat) sin(lon) Z = Φ(b/a)2 + alt sin(lat),

V. Real-time Ship Motion Prediction We now turn to our Ship Motion Prediction algorithm, as developed and tested on a high-fidelity ship motion model. As described previously,4 there are a large number of approaches that can be used to predict ship motion including: • Time-series prediction techniques such as those using ARMA models and neural networks • Prediction based on detailed modeling techniques such as those arising from the strip theory • Parametric and non-parametric identification techniques. These approaches differ in several aspects including the prior information regarding the environmental disturbances, algorithm dependence on the ship velocity, and the sensor system. We addressed the Ship Motion Prediction problem using a combination of Fast Fourier Transform (FFT), nonlinear on-line parameter estimation, and state estimation and prediction using Kalman Filtering. The main idea is the following: 1. Ship motion is described by a model of ship dynamics whose inputs are waves described by sums of sine and cosine functions with uncertain amplitudes and frequencies. 7 of 17 American Institute of Aeronautics and Astronautics

2. Frequencies are estimated accurately in real time using Fast Fourier Transform (FFT). 3. Since attitude, rate and acceleration measurements are available, uncertain amplitudes are estimated on-line using Batch Least Squares. 4. These estimates are input into the Kalman Filter at every instant to generate the state estimates and associated covariances. 5. At the end of the “learning” interval T , parameter estimates are frozen and their values at t = T are input into the Kalman Filter, when the prediction stage starts. Since during this stage there are no measurement inputs, the covariance of the state estimates will keep increasing. 6. The confidence in the state estimates generated during the prediction interval is calculated based on a combination of covariances of the parameter estimates and covariances of the state estimates. A. Wave Frequency Estimation To arrive at an accurate prediction model for the ship motion, it is crucial to accurately estimate the wave frequencies. Since there is a relatively long time interval between the start of the approach and the touchdown, we used the Fast Fourier Transform (FFT) to estimate wave frequencies. The FFT is an efficient algorithm to compute the Discrete Fourier Transform (DFT). The DFT transforms a function from the time domain into the frequency domain. The DFT requires an input function that is discrete and whose non-zero values have a limited (finite) duration. This is achieved by sampling the timedomain signal. The DFT only evaluates enough frequency components to reconstruct the finite segment that is analyzed. The FFT has been widely used in estimation of multiple frequencies from noisy signals. It is a standard function in Matlab, and we used it to estimate wave frequencies given the ship dynamics and measurements of the ship state variables. After the implementation of FFT, Figure 3 shows a noisy signal (top figure) from which the wave frequencies were obtained (middle figure), and a plot of the frequency estimation errors (bottom figure). It is seen that the FFT results in accurate frequency estimates. B. Estimation of Magnitudes Once the frequencies are known, the wave model becomes linear in parameters, i.e. in magnitudes, and many parameter estimation technique can be used to estimate the magnitudes. We chose a Batch leastSquares algorithm due to its accuracy and ease of implementation. The estimation results are shown in Figure 4.

VI. An Algorithm for Determination of Optimal Ship-Relative Course Line Commands The main objective here was to develop an algorithm that uses the information from the Ship Motion Prediction module and modify the desired landing parameters in response to the deck motion. Specifically, it modifies the lineup, glide slope, and pitch angle to achieve landing within the touchdown point dispersion limits. The objective is to determine an optimal course line command for carrier approach. The course line is defined as a straight-line ship-relative trajectory that intersects the targeted touchdown point. The assumptions made during the design include: • The aerial vehicle is designed to precisely follow the commanded ship-relative course line while flying an approach to the aircraft carrier.

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Magnitude

Signal

Time

Magnitude

Estimated Frequencies in Signal

Frequency −3

Normalized Error

1

x 10

Estimation Error

0.8 0.6 0.4 0.2 0 Frequency

Figure 3. Ship motion in a single axis, estimated frequencies in the signal, and estimation error

• Commanded rotation of the course line is constrained such that an aerial vehicle with a first-order bank response with one second time constant will not exceed a bank angle of 20 degrees while tracking the commanded course line. • The commanded course line shall be optimized to be as steady as possible during the last 10 seconds of an approach. For cases where ship is turning during the approach, a steady course line is defined as a course line that is rotating along with the ship’s average rotation rate. • The course line shall be optimized in order to minimize cross-track error relative to the centerline of the angle deck, ∆x feet beyond the ideal touchdown location, assuming a constant course line following touchdown. This ∆x shall be adjustable between 0 and 1100 ft. For a ∆x of 0 ft, the course line should ideally line up with the centerline of the angle deck. • It shall be assumed that average ship turn rate will be steady during the last 20 seconds of each approach. Realistic ship turn dynamics for ship turn rate changes made prior to the last 20 seconds of the are assumed. • The algorithm shall be valid for the same ship motion and sea states specified in the previous section.

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Magnitude

Signal

Time

a cosν, a sinν

Estimated Magnitudes in Signal

Magnitude Estimation Error Normalized Error

0.4 0.3 0.2 0.1 0 Magnitude

Figure 4. Estimated wave magnitudes, and estimation error

• The algorithm shall be robust enough to allow for the aircraft to continue approach and bolter after loss of ship data link five seconds prior to touchdown. Figure 5 shows the modifications in the glide slope and lineup in response to deck sway, surge and heave. (Please note that the sizes in the figure are slightly exaggerated to illustrate the command modification concept). In the case of bolter, the command generator will generate the desired speed (full throttle) and lineup to achieve safe take-off. We next describe the design of an optimal trajectory for the course-line following, along with the outerloop control law designed to follow accurately the optimal trajectory.

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Original glide slope

Original touchdown point

Modified glide slope Original touchdown point

Predicted touchdown point

Original lineup

Modified lineup Figure 5. Modification of commands in response to the deck motion

A. UAV Equations of Motion In the case of carrier landing, a reasonable assumption is that the UAV dynamics is of the form of a constrained point-mass model. The assumed equations are of the form: x˙v = V · cos(ψ) · cos(γ) y˙ v = V · sin(ψ) · cos(γ) z˙v = V · sin(γ) V˙ = −λV · (V − Vc ), V˙ ≤ V¯ ψ˙ = −λψ · (ψ − ψc ), ψ˙ ≤ ψ¯ γ˙ = −λγ · (γ − γc ) γ˙ ≤ γ¯ where ψ is the heading angle, γ is the flight-path angle, V is the total velocity of the helicopter, xv , yv , and zv are the positions of the UAV in the inertial frame, λV , λψ , and λγ are the positive constants, and ψc , Vc , and γc are the control inputs. Let p = [xv yv zv ]T . We now write the UAV equations of motion as:

where

and

Vc x¨ y¨ = p¨ = f (V, ψ, γ) + g(V, ψ, γ) · ψc , γc z¨

(8)

−λV · V · cos(ψ) · cos(γ) + λψ · ψ · V · sin(ψ) · cos(γ) + λγ · γ · V · cos(ψ) · sin(γ) f (V, ψ, γ) = −λV · V · sin(ψ) · cos(γ) − λψ · ψ · V · cos(ψ) · cos(γ) + λγ · γ · V · sin(ψ) · sin(γ) −λV · V · sin(γ) − λγ · γ · V · cos(γ) λV · cos(ψ) · cos(γ) −λψ · V · sin(ψ) · cos(γ) −λγ · V · cos(ψ) · sin(γ) g(V, ψ, γ) = λV · sin(ψ) · cos(γ) λψ · V · cos(ψ) · cos(γ) −λγ · V · sin(ψ) · sin(γ) λV · sin(γ) 0 λγ · V · cos(γ) 11 of 17 American Institute of Aeronautics and Astronautics

.

, the expression (8) simplifies to:

Vc V + Vcc It is seen that by choosing ψc = ψ + ψcc γ + γcc γc

Vcc p¨ = g(V, ψ, γ) · ψcc γcc

.

(9)

Let p∗ (t) be a twice differentiable function describing the desired trajectory that the vehicles is to follow. One possible control law that assures tracking of the desired trajectory p∗ (t) is that based on nonlinear inverse dynamics and is of the form: Vcc h i ψcc = g−1 (V, ψ, γ) −k1 (p − p∗ ) − k2 ( p˙ − p˙ ∗ ) + p¨ ∗ , (10) γcc

where k1 , k2 > 0. The resulting closed-loop control system consists of three decoupled second-order error equations of the form: e¨ + k2 e˙ + k1 e = 0,

where e = p − p∗ , so that limt→∞ e(t) = limt→∞ e˙(t) = 0. B. Desired UAV Location, Velocity, Acceleration Desired UAV Location: The remaining task is to define the vector p∗ . Let p∗ = [x∗v y∗v z∗v ]T . The desired UAV location is defined with respect to the cant axis under an assumption that the UAV approaches the carrier with constant ship-relative velocity V ∗ . The resulting UAV position is defined as: x∗v = xca − (d − V ∗ (t − to )) cos(ψo + ψ) cos(γ∗ )

(11)

y∗v z∗v

(12)

∗

∗

= yca − (d − V (t − to )) sin(ψo + ψ) cos(γ ) ∗

= d sin(γ ),

(13)

where d is the initial UAV distance from the ship, and V ∗ is the desired relative velocity of UAV with respect to the ship. Desired UAV Velocity: Upon differentiation of the above equations one obtains: x˙∗v = x˙ca + (d − V ∗ (t − to )) sin(ψo + ψ) cos(γ∗ )ψ˙ + V ∗ cos(ψo + ψ) cos(γ∗ ) y˙ ∗v = y˙ ca − (d − V ∗ (t − to )) cos(ψo + ψ) cos(γ∗ )ψ˙ + V ∗ sin(ψo + ψ) cos(γ∗ )

(14)

z˙∗v

(16)

∗

∗

= V sin(γ )

Desired UAV Acceleration: Similarly, upon differentiation of the above equations one obtains: x¨∗v = x¨ca + (d − V ∗ (t − to )) cos(ψo + ψ) cos(γ∗ )ψ˙ 2 −2V ∗ sin(ψo + ψ) cos(γ∗ )ψ˙ + (d − V ∗ (t − to )) sin(ψo + ψ) cos(γ∗ )ψ¨ y¨ ∗v = y¨ ca + (d − V ∗ (t − to )) sin(ψo + ψ) cos(γ∗ )ψ˙ 2 ¨ +2V ∗ cos(ψo + ψ) cos(γ∗ )ψ˙ − (d − V ∗ (t − to )) cos(ψo + ψ) cos(γ∗ )ψ, z¨∗v = 0. The above equations define p∗ , p˙ ∗ and p¨ ∗ needed to implement the outer-loop control law (10). 12 of 17 American Institute of Aeronautics and Astronautics

(15)

VII. Angle corrections to compensate for carrier motion We now address UAV control system compensation for carrier motion in altitude and heading. A. Carrier Motion Compensation in z Due to the ship heave, pitch and roll, the actual location of the touchdown point may be different from the nominal one. The ship motion predictor will generate the actual touchdown point xca , yca , zca . The problem of compensating for this difference can be divided into problems of correction of the flight path angle, and the problem of modification of the UAV heading angle in the final landing stage. The correction is implemented 10 seconds before touchdown. The equations in the z axis are of the form: z∗ (t) = z∗t=tF −10 − V ∗ sin(γ∗ )(t − tF + 10), where tF is the nominal touchdown time. The nominal touchdown value for z is zN = z∗t=tF −10 − 10V ∗ sin(γ∗ ). Let the composite perturbation in the z-coordinate of the touchdown point due to ship heave, roll and pitch be denoted by ∆zN .

Figure 6. Variables of interest in the γ compensation analysis

Then the dN from Figure 6 is calculated as dN = 10V ∗ . Based on this we have: z′ = dN sin(γ∗ ) z′′ = z′ − ∆zN = dN sin(γ∗ ) − ∆zN d′N cos(γ∗ − ∆γ) = dN cos(γ∗ ) q d2N + ∆z2N − 2dN ∆zN cos(γ∗ ) d′N =

from where it follows that the correction in γ is:

∆γ = γ∗ −

dN arccos γ∗ . d′N

The above equations neglect the difference between the actual and nominal touchdown times. If the difference between the nominal and actual touchdown time is large, an iterative procedure can be implemented to calculate the actual touchdown point at the touchdown time tF . B. Heading Angle Compensation In this case the heading angle correction is applied at t = tF − 10. The correction takes into account not only the heading of the cant axis, but also the heading of a point where the UAV would be after a prespecified time on deck. This assures that the UAV will be aligned with the cant axis when on deck even when landing on a turning ship. 13 of 17 American Institute of Aeronautics and Astronautics

VIII. Simulation Results A typical simulation result is shown in Figure 7. The simulation consist of the high-fidelity aircraft carrier dynamics, and wave dynamics described by a sum of sines with eight distinct frequencies. The wave dynamics affects surge, heave and sway and their rates, and roll, pitch and yaw, and their rates. The SMP

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Figure 7. Simulation result generated using the SMP module – Solid blue line: actual variables; Dashed red line: estimated variables; and Dashed black line: predicted variables

module is seen to accurately estimate all the variables. To verify its prediction capabilities, the figures are zoomed in last ten seconds before touchdown, and shown in Figure 8. It is seen that the SMP module accurately predicts all the states 10 seconds into the future while assuring that the errors are well within specifications. In fact, while the specifications were given for prediction over the horizon of 10 seconds (±1 f t in (x, y, z), and ±0.25◦ for angles), we tested the SMP module over larger time horizons and found that the prediction errors are within specifications most of the time even when the prediction horizon is extended to 30 seconds. Figure 9 shows the error between actual and estimated parameters during the 10 second prediction 14 of 17 American Institute of Aeronautics and Astronautics

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Figure 8. Prediction result generated using the SMP module – Solid blue line: actual variables; Dashed red line: estimated variables; and Dashed black line: predicted variables

horizon under communication blackout. Table 2 shows the 10 second prediction error to be well within the specified bounds. Variable Lat (ft) Lon (ft) Alt (ft) φ (deg) θ (deg) ψ (deg)

Error at Touchdown 0.09 0.33 0.16 0.02 0.01 0.23

Specification 1.0 1.0 1.0 0.25 0.25 0.25

Table 2. Table of prediction errors at touchdown

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0.35 0 0.25

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0.3

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0 210

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−0.15 −0.2 210

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0.04 0

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214 216 Time (s)

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210

Figure 9. Estimation errors over the 10 second prediction horizon

IX. Conclusions One of the important problems related to naval Unmanned Aerial Vehicles (UAV), is that of the design of an automatic landing system that enables autonomous landing of a UAV on an aircraft carrier. When landing needs to be accomplished safely in the high sea states and during the carrier turns, the problem becomes highly complex. In this paper we present an innovative autonomous carrier landing system for UAVs, referred to as the Carrier Motion Prediction & Autonomous Landing (CM-PAL) system. The system is based on real-time estimation of magnitudes and frequencies of waves encountered by the carrier, and on-line prediction of the carrier motion. This prediction generates information regarding the carrier states at touchdown; this information is in turn used to generate corrections in the UAV’s heading and flight path angle commands to achieve minimum dispersion around the desired touchdown point. In the paper we present performance evaluation results of the CM-PAL system on a high-fidelity simulation of a typical aircraft carrier dynamics and show that the desired performance specifications are met.

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References 1

P. Sousa, L. Wellons, G. Colby, J. Waters and J. Weir, ”Test Results of an F/A-18 Automatic Carrier Landing using Shipboard Relative Global Positioning System”, Report No. NAWCADPAX/RTR-2003/122, Naval Air Warfare Center Aircraft Division, Patuxent River, MD, Sept. 2003. 2 J. F. Sweger, ”Design Specifications Development for Unmanned Aircraft Carrier Landings: A Simulation Approach”, U.S.N.A. Trident Scholar Project Report No. 316, May 2003. 3 R. Heffley, ”Outer-Loop Control Factors For Carrier Aircraft”, Report number: RHE- NAV-90-TR-1, Naval Air Systems Command, Dec. 1990. 4 Baha M. Suleiman, ”Identification of Finite-Degree-of-Freedom Models for Ship Motions”, PhD Thesis Virginia Polytechnic Institute and State University, Dec 2000. 5 G. C. Goodwin and K. S. Sin, Adaptive Filtering Prediction and Control, Prentice Hall, Englewood Cliffs, NJ, 1984. 6 T. I. Fossen, ”Guidance and Control of Ocean Vehicles”, John Wiley & Sons Ltd. ISBN 0-471-94113-1 7 K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, Prentice Hall Inc., Englewood Cliffs, New Jersey, 1988. 8 J. D. Boˇskovi´c, R. Prasanth and R. K. Mehra, ”Retrofit Reconfigurable Flight Control under Control Effector Damage”, to appear in AIAA Journal of Guidance, Control & Dynamics, March 2007. 9 J. D. Boˇskovi´c and R. K. Mehra, ”Robust Integrated Flight Control Design Under Failures, Damage and State-Dependent Disturbances”, AIAA Journal of Guidance, Control & Dynamics, Vol. 28, No. 5, pp. 902-917, September-October 2005. 10 J. D. Boˇskovi´c, R. Prasanth and R. K. Mehra, ”A Multi-Layer Autonomous Intelligent Control Architecture for Unmanned Aerial Vehicles”, AIAA Journal of Aerospace Computing, Information, and Communication (JACIC), Special Issue on Intelligent Systems, Vol. 1, pp. 605-628, Dec. 2004. 11 R. Prasanth and J. D. Boˇskovi´c, “Design of stabilizing optimal one step ahead controllers”, AIAA-2005-6078, AIAA Guidance, Navigation and Control Conference, San Francisco, CA, 15-18 August, 2005. 12 B.R. Bowring, “The accuracy of geodetic latitude and height equations”, Survey Review, vol28 #218, October 1985, pp.202-206. 13 J. D. Boˇskovi´c and R. K. Mehra, ”An Adaptive Reconfigurable Formation Flight Control Design”, in Proceedings of the 2003 American Control Conference, Denver, CO, June 4-6, 2003. 14 J. D. Boˇskovi´c, S.-M. Li and R. K. Mehra, ”Semi-Globally Stable Formation Flight Control in Three Dimensions”, in Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, December 2001. 15 S.-M. Li, J. D. Boˇskovi´c and R. K. Mehra, ”A Globally Stable Formation Flight Controller in Two Dimensions”, AIAA2001-4046, in Proceedings of the 2001 AIAA Guidance, Navigation and Control (GNC) Conference, Montreal, Canada, August 2001. 16 J. D. Boˇskovi´c, S. E. Bergstrom, R. K. Mehra, J. M. Urnes and M. Hood, ”Performance Evaluation of an Integrated Retrofit Failure Detection, Identification and Reconfiguration (FDIR) System using High-Fidelity and Piloted Simulations”, Proc. SAE World Aviation Congress, Reno, NV, Nov. 2004. 17 J. D. Boˇskovi´c, ”Adaptive Control of a Class of Nonlinearly-Parametrized Plants”, IEEE Transaction on Automatic Control, Vol. 43, No. 7, pp. 930-934, July 1998. 18 G. Prado, ”Optimal estimation of ship’s attitudes and attitude rates”, in IEEE Journal of Oceanic Engineering, Vol 4, Issue 2, April 1979. 19 X. Zhao, R. Xu and C. Kwan, ”Ship-motion prediction: algorithms and simulation results”, in IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP ’04), Vol 5, May 2004. 20 A. Khan, C. Bil and K. E. Marion, ”Ship motion prediction for launch and recovery of air vehicles”, in Proceedings of MTS/IEEE OCEANS, 2005, Vol 3, pg 2795-2801. 21 M. Ben Ghalia and A. T. Alouani, ”Robust control design of an autolanding system”, in Proceedings of the Twenty-Fifth Southeastern Symposium on System Theory (SSST ’93), Mar 1993. 22 Li Yan, N. Sundararajan, P. Saratchandran and W. Zhifeng, ”Robust neuro-H∞ controller design for aircraft auto-landing”, in IEEE Transactions on Aerospace and Electronic Systems, Vol 40, Jan 2004.

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One of the important problems related to naval Unmanned Aerial Vehicles (UAV), is the design of an automatic landing system that would enable autonomous landing of a UAV on an aircraft carrier. When landing needs to be accomplished safely in the high sea states and during the carrier turns, the problem becomes highly complex. In this paper we present an innovative autonomous carrier landing system for UAVs, referred to as the Carrier Motion Prediction & Autonomous Landing (CM-PAL) system. The system is based on real-time estimation of magnitudes and frequencies of waves encountered by the carrier, and online prediction of the carrier motion. This prediction generates information regarding the carrier states at touchdown; this information is in turn used to generate corrections in the UAV’s heading and flight path angle commands to achieve minimum dispersion around the desired touchdown point and heading. We also present performance evaluation results of the CM-PAL system on a high-fidelity simulation of typical aircraft carrier dynamics.

I. Introduction To address the automatic landing concept, the U.S. Department of Defense is developing Joint Precision Approach and Landing System (JPALS) program. Under this program, the Navy is responsible for its shipboard component termed Shipboard Relative Global Positioning System (SRGPS).1 The SRGPS will support all Air Traffic Control (ATC) functions, including takeoff, departure, taxi, holding, approach, landing, bolter, missed approach, and long range navigation. In addition to supporting manned aircraft, SRGPS will fully support automatic takeoff, approach, landing and ATC automation required by future unmanned systems such as the Naval Unmanned Combat Aerial Vehicle. Recently, Northrop Grumman Corporation was awarded a six-year, $636 million UCAS-D contract after its X-47B was selected over Boeing’s X-45N. The first of two demonstrators is scheduled to fly in November 2009, and the first carrier landing is planned for 2011. The problem of autonomous landing of Unmanned Aerial Vehicles (UAV) and Unmanned Combat Aerial Vehicles (UCAV) on a ship is highly challenging due to stringent constraints with respect to dispersion around the desired touchdown point, approach speed, approach heading and pitch attitude. When accurate landing under these constraints needs to be achieved under wind gust disturbances, communication dropouts and in the presence of ship motion under high sea states, the problem becomes truly formidable. An additional complexity in the context of UAVs is that of bolter recovery. Bolter is a term for a failed attempt to capture the arresting cable when landing, and is a highly dangerous situation from a safety perspective. This problem needs to be specifically addressed in the case of UAVs. Hence, the control strategy for UAV carrier landing needs to have the following capabilities: ∗ This research was supported by Boeing Phantom Works under a contract to Scientific Systems Company. † Principal Research Engineer & Intelligent & Autonomous Control Systems Group Leader, 500 W. Cummings Park, Suite 3000, Woburn, MA, AIAA Senior Member, [email protected] ‡ Ph.D. Candidate, MIT Aerospace Controls Laboratory, on leave from SSCI, AIAA Member, [email protected]

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• Efficient prediction and compensation of the carrier motion under communication blackouts • Capability to autonomously recover from bolter • Flexibility to readily incorporate changes in the landing parameters due to heave, sway and surge motion of the touchdown point to achieve effective Deck Motion Compensation • Effective rejection of atmospheric disturbances such as wind gust. To address these issues, we developed a Carrier Motion Prediction & Autonomous Landing (CM-PAL) system that consists of a Ship Motion Predictor (SMP), and an algorithm for the determination of optimal UAV heading for ship-relative course line following during landing on a turning aircraft carrier. The main objective was to develop an algorithm for course-line following, and the SMP module to allow for UAV heading and flight path angle corrections at the carrier landing stage based on predicted carrier states ten seconds before touchdown. We show in Section VIII that the SMP system accurately predicts all the states of the ship 10 seconds ahead of touchdown with errors well below the stated specifications. The proposed CM-PAL system consists of the following modules: 1. A signal conditioning module that extracts the actual wave disturbance signal from the measurements 2. A frequency estimation module that employs a modified Fast Fourier Transform (FFT) algorithm and generates an accurate wave frequency estimate. 3. A parameter estimation module that uses Batch Least Squares algorithm to estimate amplitudes and phases of the wave disturbance signal, as well as the signal itself. 4. A prediction module that uses a Kalman Filter to predict the behavior of ship’s states due to wave disturbances. 5. A confidence measure calculation module that calculates a wave-off criterion. The diagram of the SMP system is shown in Figure 1. Since the position and velocity measurements are given in geodetic coordinates, these are first converted to Earth-Centered, Earth-Fixed (ECEF) Cartesian coordinates, and then to North-East-Down (NED) coordinates which are attached to the body of the carrier. The measurements contain the information about both the carrier dynamics and the effect of waves. Based on the known carrier dynamics and these measurements, the dynamics of waves can be extracted. The next step is to run the Fast Fourier Transform (FFT) on the waves data to estimate wave frequencies from noisy signals. Once the wave frequencies have been estimated, a Least-Squares Estimator is run to estimate the magnitudes and phases of the wave signals. After attaining accurate estimates wave frequencies and propagating the effect of the waves, these estimates are integrated with the model of carrier dynamics to generate predicted carrier motion. A confidence measure for the estimates is also calculated such that, if above a threshold, the UAV is waved-off. The specifications under which the algorithms were developed are described in Section II below.

II. Specifications During the design, the following specifications were assumed: • The algorithm should be valid for sea states up to and including level 5. • The algorithm should be valid for turning motion of the carrier of up to 0.5deg/s. • It is assumed that the UAV control system has a wind disturbance rejection capability, and that the effect of the wind of the carrier can be neglected.

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Figure 1. Structure of the Carrier Motion Prediction & Autonomous Landing (CM-PAL) System

• The algorithm shall utilize the broadcast messages from the carrier containing its current attitudes, rates and accelerations in the keel axis. These messages will be available within 10 nautical miles from the ship and received at 20Hz. • The ship motion prediction model shall be robust to momentary dropouts of these periodic messages. • The ship motion prediction algorithm shall output a minimum of four values: predicted roll, pitch and heading angles of the carrier vehicle (CV) keel axis at the specified time, along with a confidence factor of these predicted values. The confidence factor will be used to determine an autonomous wave-off criterion. • The attitude outputs of ship motion prediction for constant carrier turn rates shall have accuracies specified in Table 1. Specified Prediction Time (seconds) 5.0 ≤ T ≤ 10.00 T ≤ 5.0

Error Tolerance at Prediction Time ±0.25 deg ±0.1 deg

Table 1. Attitude Error Tolerances

• Additional outputs shall include the ship reference center of motion position (lat, lon, altitude), velocities (NED), and accelerations (NED). These values will be needed to to complete the approach after loss of data link within 5 seconds from the touchdown.

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III. Ship Dynamics Model This section outlines the dynamics model assumed for the ship Center of Motion. We use this model in the design of the desired UAV dynamics to achieve accurate following of the carrier course line. Γ˙ x + Vnom cos (ψt ) − Γ˙ y sin (ψt ) E˙ = Γ˙ x + Vnom sin (ψt ) + Γ˙ y cos (ψt ) D˙ = Γ˙ z ,

N˙ =

(1)

where north-east-down coordinate frame is assumed for the center-of-motion coordinates (Keel Axis), Γ˙ ∗ denote the ship’s body accelerations, Vnom is the nominal ship velocity (e.g. 20 knots), and ψt is the ship’s heading track, which is a lag-filtered heading with time constant τ as a function of Vnom . Ship rotation is assumed to be due to the waves modeled by the sum of sinusoids: φ˙ =

n X

θ˙ =

n X

i=1

ψ˙ =

i=1 n X i=1

aφi sin ωφi t + νφi aθi sin ωθi t + νθi

(2)

aψi sin ωψi t + νψi + ψcmd ,

where a∗ , ω∗ , and ν∗ are amplitude, frequency and phase shift inputs based on ship motion data and ψcmd is an adequately filtered ship turn command. The ship’s body velocities are denoted as Γ x,y,z , and refer to ship surge, sway and heave respectively. Body accelerations are given by: Γ˙ x =

n X i=1

aΓxi sin ωΓxi t + νΓxi

Γ˙ y =

n X

aΓyi sin ωΓyi t + νΓyi

i=1

aΓzi sin ωΓzi t + νΓzi ,

Γ˙ z =

i=1 n X

(3)

and body-axis rotational rates are: p = φ˙ − sin (θ)ψ˙ q = sin (φ) cos (θ)ψ˙ + cos (φ)θ˙ r = cos (φ) cos (θ)ψ˙ − sin (φ)θ˙,

(4)

where p, q and r denote respectively the roll, pitch and yaw rate. A. Cant Axes System The Cant axes system is an important coordinate frame as this is the reference associated with the desired UAV touchdown point and corresponding course line. Figure 2 shows the locations of the Keel and Cant

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Figure 2. Keel to Cant axis coordinate transformation

axes on the ship deck. The relationship between the two is given by: ∆x xca x yca = y + R ∆y , ∆z z zca

where ∆(x,y,z) are defined as the Cant axis offset in the Keel reference frame, as shown in Figure 2, and the rotation R is given by sψcθ cψcφ + sψsθsφ −cψsφ + sψsθcφ (5) R = cψcθ −sψcφ + cψsθsφ sψsφ + cψsθcφ −sθ cθsφ cθcφ where s∗, c∗ denotes sin(∗), cos(∗) respectively. The velocity and acceleration of the Cant axes system are given by: x˙ca x˙ ∆x ˙ ∆y y˙ ca = y˙ + R z˙ca z˙ ∆z

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(6)

∆x x¨ca x¨ ¨ ∆y y¨ ca = y¨ + R ∆z z¨ z¨ca

(7)

In Equation (6) and (7) above, the derivatives are simple since ∆∗ represents fixed distances and hence have a zero derivative. The first and second derivative of the rotation, R, are tedious but straightforward and hence, are not given.

IV. Coordinate transformations In order to implement the landing algorithm, we need to define several coordinate frames and the transformations between them. We have already introduced the ship’s keel, or center of motion, and Cant coordinate systems. Additional frames include the following: 1. Local north, east, down (NED) Ship information is provided to the unmanned aircraft landing system in this coordinate frame. It is formed by a plane tangent to the Earth’s surface fixed to a specific location, hence it is sometimes known as the local tangent, or local geodetic plane. By convention, the east axis is labeled x, the north y and, in our case, down z. 2. Earth-centered Earth-fixed (ECEF) This is the conventional terrestrial coordinate system and rotates with the Earth as its origin is at the Earth’s center. The X axis passes through the equator at the prime meridian, the Z axis passes through the north pole, and the Y axis passes through the equator at 90◦ longitude, following the right-hand rule. 3. Geodetic The geodetic system represents more accurately the fact that the earth is not a perfect sphere. Under this system, the Earth’s surface is approximated by an ellipsoid and locations near the surface are described in terms of latitude, longitude and height. The ellipsoid is completely parameterized by the semi-major axis a, and the flattening f . Sections A to C outline the transformations between these various coordinate frames. A. Local to ECEF Transforming from a local NED coordinate system to a earth-centered earth-fixed system is accomplished by the following: Xecef − sin(lat) cos(lon) − sin(lon) − cos(lat) cos(lon) N Yecef = − sin(lat) sin(lon) cos(lon) − cos(lat) sin(lon) E , Zecef cos(lat) 0 − sin(lat) D

where the rotation matrix is built using geodetic latitude and longitude.

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B. ECEF to Geodetic We use the direct algorithm in Ref. [12] to transform from earth-centered earth-fixed to the geodetic system. This transformation is given by: lon = arctan(Y, X) e = e2 (a/b)2 p p = X2 + Y 2 q p2 + Z 2 r =

bZ (1 + eb/r) u = arctan ap

!

Z + eb sin3 u lat = arctan p − e2 a cos3 u a v = q 1 − e2 sin2 (lat)

!

h = p cos(lat) + Z sin(lat) − a2 /v,

where X, Y, Z are ECEF coordinates, e2 = 6.69437999014e−3 denotes the first eccentricity squared, a = 2.092564632545929e+07 ft is the semi-major axis, and b = 2.085548659528727e+07 ft is the semi-minor axis. C. Geodetic to ECEF Transforming back to earth-centered earth-fixed coordinates from geodetic is given by: X = (Φ + alt) cos(lat) cos(lon)

p where Φ = a/ 1 − e2 sin(lat)2 .

Y = (Φ + alt) cos(lat) sin(lon) Z = Φ(b/a)2 + alt sin(lat),

V. Real-time Ship Motion Prediction We now turn to our Ship Motion Prediction algorithm, as developed and tested on a high-fidelity ship motion model. As described previously,4 there are a large number of approaches that can be used to predict ship motion including: • Time-series prediction techniques such as those using ARMA models and neural networks • Prediction based on detailed modeling techniques such as those arising from the strip theory • Parametric and non-parametric identification techniques. These approaches differ in several aspects including the prior information regarding the environmental disturbances, algorithm dependence on the ship velocity, and the sensor system. We addressed the Ship Motion Prediction problem using a combination of Fast Fourier Transform (FFT), nonlinear on-line parameter estimation, and state estimation and prediction using Kalman Filtering. The main idea is the following: 1. Ship motion is described by a model of ship dynamics whose inputs are waves described by sums of sine and cosine functions with uncertain amplitudes and frequencies. 7 of 17 American Institute of Aeronautics and Astronautics

2. Frequencies are estimated accurately in real time using Fast Fourier Transform (FFT). 3. Since attitude, rate and acceleration measurements are available, uncertain amplitudes are estimated on-line using Batch Least Squares. 4. These estimates are input into the Kalman Filter at every instant to generate the state estimates and associated covariances. 5. At the end of the “learning” interval T , parameter estimates are frozen and their values at t = T are input into the Kalman Filter, when the prediction stage starts. Since during this stage there are no measurement inputs, the covariance of the state estimates will keep increasing. 6. The confidence in the state estimates generated during the prediction interval is calculated based on a combination of covariances of the parameter estimates and covariances of the state estimates. A. Wave Frequency Estimation To arrive at an accurate prediction model for the ship motion, it is crucial to accurately estimate the wave frequencies. Since there is a relatively long time interval between the start of the approach and the touchdown, we used the Fast Fourier Transform (FFT) to estimate wave frequencies. The FFT is an efficient algorithm to compute the Discrete Fourier Transform (DFT). The DFT transforms a function from the time domain into the frequency domain. The DFT requires an input function that is discrete and whose non-zero values have a limited (finite) duration. This is achieved by sampling the timedomain signal. The DFT only evaluates enough frequency components to reconstruct the finite segment that is analyzed. The FFT has been widely used in estimation of multiple frequencies from noisy signals. It is a standard function in Matlab, and we used it to estimate wave frequencies given the ship dynamics and measurements of the ship state variables. After the implementation of FFT, Figure 3 shows a noisy signal (top figure) from which the wave frequencies were obtained (middle figure), and a plot of the frequency estimation errors (bottom figure). It is seen that the FFT results in accurate frequency estimates. B. Estimation of Magnitudes Once the frequencies are known, the wave model becomes linear in parameters, i.e. in magnitudes, and many parameter estimation technique can be used to estimate the magnitudes. We chose a Batch leastSquares algorithm due to its accuracy and ease of implementation. The estimation results are shown in Figure 4.

VI. An Algorithm for Determination of Optimal Ship-Relative Course Line Commands The main objective here was to develop an algorithm that uses the information from the Ship Motion Prediction module and modify the desired landing parameters in response to the deck motion. Specifically, it modifies the lineup, glide slope, and pitch angle to achieve landing within the touchdown point dispersion limits. The objective is to determine an optimal course line command for carrier approach. The course line is defined as a straight-line ship-relative trajectory that intersects the targeted touchdown point. The assumptions made during the design include: • The aerial vehicle is designed to precisely follow the commanded ship-relative course line while flying an approach to the aircraft carrier.

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Magnitude

Signal

Time

Magnitude

Estimated Frequencies in Signal

Frequency −3

Normalized Error

1

x 10

Estimation Error

0.8 0.6 0.4 0.2 0 Frequency

Figure 3. Ship motion in a single axis, estimated frequencies in the signal, and estimation error

• Commanded rotation of the course line is constrained such that an aerial vehicle with a first-order bank response with one second time constant will not exceed a bank angle of 20 degrees while tracking the commanded course line. • The commanded course line shall be optimized to be as steady as possible during the last 10 seconds of an approach. For cases where ship is turning during the approach, a steady course line is defined as a course line that is rotating along with the ship’s average rotation rate. • The course line shall be optimized in order to minimize cross-track error relative to the centerline of the angle deck, ∆x feet beyond the ideal touchdown location, assuming a constant course line following touchdown. This ∆x shall be adjustable between 0 and 1100 ft. For a ∆x of 0 ft, the course line should ideally line up with the centerline of the angle deck. • It shall be assumed that average ship turn rate will be steady during the last 20 seconds of each approach. Realistic ship turn dynamics for ship turn rate changes made prior to the last 20 seconds of the are assumed. • The algorithm shall be valid for the same ship motion and sea states specified in the previous section.

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Magnitude

Signal

Time

a cosν, a sinν

Estimated Magnitudes in Signal

Magnitude Estimation Error Normalized Error

0.4 0.3 0.2 0.1 0 Magnitude

Figure 4. Estimated wave magnitudes, and estimation error

• The algorithm shall be robust enough to allow for the aircraft to continue approach and bolter after loss of ship data link five seconds prior to touchdown. Figure 5 shows the modifications in the glide slope and lineup in response to deck sway, surge and heave. (Please note that the sizes in the figure are slightly exaggerated to illustrate the command modification concept). In the case of bolter, the command generator will generate the desired speed (full throttle) and lineup to achieve safe take-off. We next describe the design of an optimal trajectory for the course-line following, along with the outerloop control law designed to follow accurately the optimal trajectory.

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Original glide slope

Original touchdown point

Modified glide slope Original touchdown point

Predicted touchdown point

Original lineup

Modified lineup Figure 5. Modification of commands in response to the deck motion

A. UAV Equations of Motion In the case of carrier landing, a reasonable assumption is that the UAV dynamics is of the form of a constrained point-mass model. The assumed equations are of the form: x˙v = V · cos(ψ) · cos(γ) y˙ v = V · sin(ψ) · cos(γ) z˙v = V · sin(γ) V˙ = −λV · (V − Vc ), V˙ ≤ V¯ ψ˙ = −λψ · (ψ − ψc ), ψ˙ ≤ ψ¯ γ˙ = −λγ · (γ − γc ) γ˙ ≤ γ¯ where ψ is the heading angle, γ is the flight-path angle, V is the total velocity of the helicopter, xv , yv , and zv are the positions of the UAV in the inertial frame, λV , λψ , and λγ are the positive constants, and ψc , Vc , and γc are the control inputs. Let p = [xv yv zv ]T . We now write the UAV equations of motion as:

where

and

Vc x¨ y¨ = p¨ = f (V, ψ, γ) + g(V, ψ, γ) · ψc , γc z¨

(8)

−λV · V · cos(ψ) · cos(γ) + λψ · ψ · V · sin(ψ) · cos(γ) + λγ · γ · V · cos(ψ) · sin(γ) f (V, ψ, γ) = −λV · V · sin(ψ) · cos(γ) − λψ · ψ · V · cos(ψ) · cos(γ) + λγ · γ · V · sin(ψ) · sin(γ) −λV · V · sin(γ) − λγ · γ · V · cos(γ) λV · cos(ψ) · cos(γ) −λψ · V · sin(ψ) · cos(γ) −λγ · V · cos(ψ) · sin(γ) g(V, ψ, γ) = λV · sin(ψ) · cos(γ) λψ · V · cos(ψ) · cos(γ) −λγ · V · sin(ψ) · sin(γ) λV · sin(γ) 0 λγ · V · cos(γ) 11 of 17 American Institute of Aeronautics and Astronautics

.

, the expression (8) simplifies to:

Vc V + Vcc It is seen that by choosing ψc = ψ + ψcc γ + γcc γc

Vcc p¨ = g(V, ψ, γ) · ψcc γcc

.

(9)

Let p∗ (t) be a twice differentiable function describing the desired trajectory that the vehicles is to follow. One possible control law that assures tracking of the desired trajectory p∗ (t) is that based on nonlinear inverse dynamics and is of the form: Vcc h i ψcc = g−1 (V, ψ, γ) −k1 (p − p∗ ) − k2 ( p˙ − p˙ ∗ ) + p¨ ∗ , (10) γcc

where k1 , k2 > 0. The resulting closed-loop control system consists of three decoupled second-order error equations of the form: e¨ + k2 e˙ + k1 e = 0,

where e = p − p∗ , so that limt→∞ e(t) = limt→∞ e˙(t) = 0. B. Desired UAV Location, Velocity, Acceleration Desired UAV Location: The remaining task is to define the vector p∗ . Let p∗ = [x∗v y∗v z∗v ]T . The desired UAV location is defined with respect to the cant axis under an assumption that the UAV approaches the carrier with constant ship-relative velocity V ∗ . The resulting UAV position is defined as: x∗v = xca − (d − V ∗ (t − to )) cos(ψo + ψ) cos(γ∗ )

(11)

y∗v z∗v

(12)

∗

∗

= yca − (d − V (t − to )) sin(ψo + ψ) cos(γ ) ∗

= d sin(γ ),

(13)

where d is the initial UAV distance from the ship, and V ∗ is the desired relative velocity of UAV with respect to the ship. Desired UAV Velocity: Upon differentiation of the above equations one obtains: x˙∗v = x˙ca + (d − V ∗ (t − to )) sin(ψo + ψ) cos(γ∗ )ψ˙ + V ∗ cos(ψo + ψ) cos(γ∗ ) y˙ ∗v = y˙ ca − (d − V ∗ (t − to )) cos(ψo + ψ) cos(γ∗ )ψ˙ + V ∗ sin(ψo + ψ) cos(γ∗ )

(14)

z˙∗v

(16)

∗

∗

= V sin(γ )

Desired UAV Acceleration: Similarly, upon differentiation of the above equations one obtains: x¨∗v = x¨ca + (d − V ∗ (t − to )) cos(ψo + ψ) cos(γ∗ )ψ˙ 2 −2V ∗ sin(ψo + ψ) cos(γ∗ )ψ˙ + (d − V ∗ (t − to )) sin(ψo + ψ) cos(γ∗ )ψ¨ y¨ ∗v = y¨ ca + (d − V ∗ (t − to )) sin(ψo + ψ) cos(γ∗ )ψ˙ 2 ¨ +2V ∗ cos(ψo + ψ) cos(γ∗ )ψ˙ − (d − V ∗ (t − to )) cos(ψo + ψ) cos(γ∗ )ψ, z¨∗v = 0. The above equations define p∗ , p˙ ∗ and p¨ ∗ needed to implement the outer-loop control law (10). 12 of 17 American Institute of Aeronautics and Astronautics

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VII. Angle corrections to compensate for carrier motion We now address UAV control system compensation for carrier motion in altitude and heading. A. Carrier Motion Compensation in z Due to the ship heave, pitch and roll, the actual location of the touchdown point may be different from the nominal one. The ship motion predictor will generate the actual touchdown point xca , yca , zca . The problem of compensating for this difference can be divided into problems of correction of the flight path angle, and the problem of modification of the UAV heading angle in the final landing stage. The correction is implemented 10 seconds before touchdown. The equations in the z axis are of the form: z∗ (t) = z∗t=tF −10 − V ∗ sin(γ∗ )(t − tF + 10), where tF is the nominal touchdown time. The nominal touchdown value for z is zN = z∗t=tF −10 − 10V ∗ sin(γ∗ ). Let the composite perturbation in the z-coordinate of the touchdown point due to ship heave, roll and pitch be denoted by ∆zN .

Figure 6. Variables of interest in the γ compensation analysis

Then the dN from Figure 6 is calculated as dN = 10V ∗ . Based on this we have: z′ = dN sin(γ∗ ) z′′ = z′ − ∆zN = dN sin(γ∗ ) − ∆zN d′N cos(γ∗ − ∆γ) = dN cos(γ∗ ) q d2N + ∆z2N − 2dN ∆zN cos(γ∗ ) d′N =

from where it follows that the correction in γ is:

∆γ = γ∗ −

dN arccos γ∗ . d′N

The above equations neglect the difference between the actual and nominal touchdown times. If the difference between the nominal and actual touchdown time is large, an iterative procedure can be implemented to calculate the actual touchdown point at the touchdown time tF . B. Heading Angle Compensation In this case the heading angle correction is applied at t = tF − 10. The correction takes into account not only the heading of the cant axis, but also the heading of a point where the UAV would be after a prespecified time on deck. This assures that the UAV will be aligned with the cant axis when on deck even when landing on a turning ship. 13 of 17 American Institute of Aeronautics and Astronautics

VIII. Simulation Results A typical simulation result is shown in Figure 7. The simulation consist of the high-fidelity aircraft carrier dynamics, and wave dynamics described by a sum of sines with eight distinct frequencies. The wave dynamics affects surge, heave and sway and their rates, and roll, pitch and yaw, and their rates. The SMP

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module is seen to accurately estimate all the variables. To verify its prediction capabilities, the figures are zoomed in last ten seconds before touchdown, and shown in Figure 8. It is seen that the SMP module accurately predicts all the states 10 seconds into the future while assuring that the errors are well within specifications. In fact, while the specifications were given for prediction over the horizon of 10 seconds (±1 f t in (x, y, z), and ±0.25◦ for angles), we tested the SMP module over larger time horizons and found that the prediction errors are within specifications most of the time even when the prediction horizon is extended to 30 seconds. Figure 9 shows the error between actual and estimated parameters during the 10 second prediction 14 of 17 American Institute of Aeronautics and Astronautics

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Figure 8. Prediction result generated using the SMP module – Solid blue line: actual variables; Dashed red line: estimated variables; and Dashed black line: predicted variables

horizon under communication blackout. Table 2 shows the 10 second prediction error to be well within the specified bounds. Variable Lat (ft) Lon (ft) Alt (ft) φ (deg) θ (deg) ψ (deg)

Error at Touchdown 0.09 0.33 0.16 0.02 0.01 0.23

Specification 1.0 1.0 1.0 0.25 0.25 0.25

Table 2. Table of prediction errors at touchdown

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IX. Conclusions One of the important problems related to naval Unmanned Aerial Vehicles (UAV), is that of the design of an automatic landing system that enables autonomous landing of a UAV on an aircraft carrier. When landing needs to be accomplished safely in the high sea states and during the carrier turns, the problem becomes highly complex. In this paper we present an innovative autonomous carrier landing system for UAVs, referred to as the Carrier Motion Prediction & Autonomous Landing (CM-PAL) system. The system is based on real-time estimation of magnitudes and frequencies of waves encountered by the carrier, and on-line prediction of the carrier motion. This prediction generates information regarding the carrier states at touchdown; this information is in turn used to generate corrections in the UAV’s heading and flight path angle commands to achieve minimum dispersion around the desired touchdown point. In the paper we present performance evaluation results of the CM-PAL system on a high-fidelity simulation of a typical aircraft carrier dynamics and show that the desired performance specifications are met.

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References 1

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