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A Local Control Network Autopilot for an Unmanned Surface Vehicle *SK Sharma, *R Sutton and **GN Roberts

Marine and Industrial Dynamic Analysis Group, Advanced Materials and Engineering Systems School of Marine Science and Engineering, Plymouth University, Plymouth, PL4 8AA, UK (Sanjay.Sharma, R.Sutton) @plymouth.ac.uk **Faculty of Mathematics, Computing and Technology The Open University in the South West, Bristol, BS1 6ND, UK ([email protected] Abstract: Although marine craft are renowned for their nonlinear dynamic behaviour, autopilot system designs are still being developed based on linear control methodologies. Thus to overcome any limitations in the performance capabilities of such systems, it is appropriate to consider designing nonlinear autopilots. This paper reports an investigation into a novel approach to marine control systems design based on local control network (LCN) techniques. The approach is used to design an autopilot for controlling the nonlinear yaw dynamics of an unmanned surface vehicle and is benchmarked against another based on a standard proportional-integral-derivative controller. Simulation results are presented and the performances of the autopilots are compared using standard system performance criteria. From the results it can be observed that the LCN is more efficient compared to the PID controller. Also it out performs its PID counterpart in terms of the selected criteria. Copyright © 2012 IFAC Keywords: Unmanned surface vehicle, autopilot design, proportional-integral-derivative control, local control network, genetic algorithm.

1. INTRODUCTION Unmanned surface vehicle (USV) technology is becoming widespread in the commercial, naval and scientific sectors. Indeed they are now used for mine counter-measures (Yan et al 2010) , surveying (Majohr et al 2000) and environmental data gathering (Caccia 2007), to name but a few. Of particular interest in this paper is their application in environmental monitoring which is a major issue in the modern age. An USV named Springer has been specifically designed, built and continues to be developed at Plymouth University. Springer is intended to be a cost effective and environmentally friendly USV which is designed primarily for undertaking pollutant tracking, and environmental and hydrographical surveys in rivers, reservoirs, inland waterways and coastal waters, particularly where shallow waters prevail. For the vehicle to be capable of undertaking the kinds of mission that are being contemplated, Springer requires robust, reliable, accurate and adaptable navigation, guidance and control (NGC) systems which allow seamless switching between automatic and manual control modes. Such properties in NGC systems being necessary for the changes in the dynamic behaviour of the vehicle that may occur owing to the deployment of different payloads, mission requirements and varying environmental conditions. The dynamic characteristics of marine vessels are invariably nonlinear and the Springer USV is no exception. This being so it would seem appropriate to control the vehicle with nonlinear autopilots. Since a local control network (LCN) can ©2012 IFAC

374

provide nonlinear control to complex nonlinear plant, they were deemed worthy of investigation for application in marine control systems design. Thus the intention of this paper is to report a novel autopilot system based on a LCN design for the Springer vehicle and to benchmark its performance against another with a standard proportionalintegral derivative (PID) controller architecture. Details of the navigation and line-of-sight guidance subsystems for the vehicle can be found in Naeem et al (2008).With regards to the structure and content of the paper, on completion of this introductory material, section 2 reports the Springer vehicle hardware briefly, and gives details of the nonlinear model of its yaw dynamics. Whilst section 3 describes the two autopilot designs, and in section 4 simulation results and a discussion are presented. Finally concluding remarks are given in section 5. 2. THE SPRINGER UNMANNED SURFACE VEHICLE Since full details of the Springer’s hardware can be found in Naeem et al( 2008), only an outline will be presented here. The Springer USV was designed as a medium waterplane twin hull vessel which is versatile in terms of mission profile and payload. It is approximately 4m long and 2.3m wide with a displacement of 0.6 tonnes. Each hull is divided into three watertight compartments. The NGC system is carried in watertight Peli cases and secured in a bay area between the crossbeams. This facilitates the quick substitution of systems on shore or at sea. The batteries which are used to provide the power for the propulsion system and onboard electronics are carried within the hulls, accessed by a watertight hatch. The Springer propulsion system consists of two propellers 10.3182/20120919-3-IT-2046.00064

IFAC MCMC 2012 September 19-21, 2012. Arenzano, Italy

powered by a set of 24V 74lbs Minn Kota Riptide transom mounted saltwater trolling motors. As will be seen in the next subsection, steering of the vessel is based on differential propeller revolution rates.

and 3 hidden nodes were selected for modelling. Figure 2 shows the model performance of the NN model which produced mean-squared errors of 0.0003746 rad 2 . MSE=0.00037466rad2 6

2.1 Vehicle steerage

Desired Actual

5

where n1 and n2 being the two propeller thrusts in revolutions per minute (rpm). Clearly, straight line manoeuvres require both the thrusters running at the same speed whereas the differential thrust is zero in this case.

4 Heading angle (rad)

The vehicle has a differential steering mechanism and thus required two inputs to adjust its course. This was simply modelled as a two input, single output system in the form depicted in Fig. 1.

3 2 1 0 -1 -2

n1 (rpm)

Springer USV Dynamics

100

150 200 Time (sec)

250

300

350

Thereupon this NN model was used to replicate the nonlinear yaw dynamics of the Springer USV and to train a LCN autopilot to follow set point trajectories with its performance being judged against that of the PID autopilot.

Fig. 1. Block diagram representation of a two-input USV By letting nc and nd represent the common mode and differential mode thruster velocities defined then they are defined by

3. AUTOPILOT DESIGNS In this section of the paper, both autopilot designs are now presented. 3.1 Local Control Network Autopilot Design

n1 n2 n n2 ; nd 1 2 2

(1)

In order to maintain the velocity of the vessel, nc must remain constant at all times. The differential mode input, however, oscillates about zero depending on the direction of the manoeuvre. Please note that whilst the actual steerage system operates using rpm, for reasons of convenience and ease of comparisons, results are shown in revolutions per second (rps) where appropriate herein. 2.2 Nonlinear Vehicle Yaw Dynamics The Springer dynamics are highly nonlinear, thus the requirement for a nonlinear model. A multi-layer perception (MLP) type neural network (NN) model was developed here using a dataset gathered during a system identification study. A genetic algorithm (GA) with a population of 20 chromosomes and crossover probability of pc 0.65 and mutation probability of pm 0.03 was used to obtain the best NN architecture with optimised weights and biases (Sharma, McLoone and Irwin, 2002; 2005). The GA was run for 3000 generations and after trial and error, a parallel architecture network with ten inputs:

u( t 1 ), u( t 2 ), ˆy( t 1 ), ˆy( t 2 ), ˆy( t 3 ), ˆy( t ) f NN ˆy( t 4 ), e( t 1 ), e( t 2 ), e( t 3 ), e( t 4 )

where e( t ) y( t ) ˆy( t )

50

Fig. 2. Performance of the neural network model

heading (degrees)

n2 (rpm)

nc

0

(2) 375

As already mentioned a LCN provides a divide-and-conquer approach to the design of a global controller for complex nonlinear systems. It consists of several linear local model controllers (LMCs) spread across the operating regions. The operating space is decomposed into a number of regimes and the required global controller is then formed by interpolating between simpler LMCs that are locally valid (Johansen and Foss 1995). Knowledge of these local operating regimes is therefore a key requirement for building such controllers. It is known that a large class of nonlinear systems can be controlled in this way, including most batch processes and many control system applications (Rippin, 1989). Apart from normal operation, the control system may also have to function correctly during startup and shutdown cycles and to operate during maintenance and fault conditions, all of which constitute different operating regimes. In most applications, the design of a suitable LCN is done on the basis of a priori plant knowledge (Brown et al 1997), (Townsend et al 1998). The interpolation is done such that the local model controller (LMC) which is most valid at an operating point will be given the greatest weight, neighbouring ones will be weighted less, and those for distant operating regimes will not contribute anything to the global control at that point. Each LMC is thus associated with a weighting function that provides smooth interpolation and also indicates the relative validity of it at a given operating point. No work has been undertaken to test the operation of the USV in a nonlinear range. For practical operations, the identification of distinct operating regimes are important, which can only be obtained

IFAC MCMC 2012 September 19-21, 2012. Arenzano, Italy

with a priori plant knowledge. The identification of local operating regimes and simultaneous design of a global LCN is difficult in the absence of a priori knowledge about the unknown plant. This paper finds such operating regimes and constructs a suitable LCN based on GAs for Springer.

The equivalent PID controller in discrete form is

x

1 (φ)

3.1.1 Local Control Networks The general discrete LCN representation is shown in Fig. 3. Here, the same inputs, x , are fed to all the LMCs and the outputs are weighted according to some scheduling variable or variables, ψ . The LCN output ˆy is given by the weighted sum:

2 (φ)

φ

N (φ)

f1 ( x )

f 2 ( x)

∑

yˆ

f N (x)

N

ˆy ρi (ψ)f i (x) where

) local control network N (xa Fig. 3. General architecture fof

(3)

i 1

u( k ) u( k 1 ) k p [ e( k ) e( k 1 )] k d [ e( k ) 2e( k 1 ) e( k 2 )] Ts k I e( k )

ρi (ψ) is the validity or interpolation function

associated with the i th LMC, f i ( x ) and N is the total number of LMCs.

where k is the sample number and Ts is the sampling interval.

The validity functions ρi (ψ) are normalized so that the total contribution from all the LMCs is 100%. The most widely used ρi (ψ) in the literature are normalized Gaussian functions represented as:

i ( ψ )

exp( ψ s i N

exp( ψ s j j 1

2

For (4) and (6) the unknown parameters in each regime are the validity function centres, s i , standard deviations σ i and the PID control parameters k p , k d and k I . Figure 4 shows the design of a LCN involving PID-type LMCs. Here the LCN consists of m PID-type local model controllers. The output of the i th PID-type LMC at sample k is ci ( k ) and the overall LCN output is defined as

2

/ 2σ i ) 2

(4)

2

/ 2σ j )

m

while the f i ( x ) are linear controllers. In this paper, discretetype PID controllers are considered for the LCN construction.

c( k ) ci ( k ) . The control action applied to the Springer i 1

USV at sample k is given by u( k ) c( k ) u( k 1 ) . The same error e( k ) r( k ) y( k ) , is applied to all LMCs in the network. The scheduling variable for the validity function, ρi (ψ) , were chosen as ψ [y(k 1 ), u(k-1 )] , where

A continuous-time PID control law is described by u( t ) k p e( t ) k d e( t ) k I edt

(5)

y( k ) is the heading angle output after filter, u( k ) is the controller effort and r( k ) is the reference setpoint. The GA then simultaneously searches for the optimal number of

where k p , k d and k I are the proportional, differential and the integral gains, u is the control action and e is the error.

z-1

Validity function

PID 1 r(k)

e(k)

+ -

C(k)

C m(k) PID m

z -1

z -1 C 1(k)

(6)

LCN

Fig. 4. General architecture of a local control network 376

u(k)

Springer x(k) USV

Filter

y(k)

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LMCs (from a given maximum number), the parameters of these LMCs and the parameters of the validity functions and filter. Apart from reducing the tracking error and total controller effort, the fitness function of the GA is also incorporated to promote transparency by encouraging all valid LMCs to be mutually orthogonal, such that each local controller acted independently of the rest at its operating point. In this application a steady-state GA with crossover probability of pc 0.65 and mutation probability of

MSE=0.82501rad2 6

Heading angle (rad)

5

pm 0.03 was applied to a population of 20 chromosomes.

4

Desired Actual

3

2

1

0

The filter used in Fig. 4 is of second order with the input/output relation described in the (7) below: a1 y( k ) b1 x( k ) b2 x( k 1 ) b3 x( k 2 ) a 2 y( k 1 ) a3 y( k 2 )

Rise Time = 22 sec Settling Time = 37 Sec % Overshoot = 0.39

0

50

100

150

200

250

Time (sec)

(a) LCN response MSE=1.3043rad2

(7)

6

5

Heading angle (rad)

3.2 Proportional-Integral-Derivative Based Autopilot In this case, the LCN in Fig. 4 was replaced with a PID controller defined in (7) and a GA was then used in a similar manner to optimize the parameters k p , k d and k I .

Desired Actual

Rise Time = 22 sec Settling Time = 46 sec % Overshoot = 0.4

4

3

2

1

4. SIMULATION RESULTS AND DISCUSSION 0

0

50

100

150

200

250

Time (sec)

The GA was run for 2000 generations and to allow for the stochastic nature of genetic learning the training process was repeated for five times. The number of LMCs from the best chromosome was selected as the optimum one along with the centres and covariances of the associated validity function and parameters for the filter. Figure 5a shows the closed-loop response from the local controller network in response to a step change demand in the vehicle heading and Fig 5(b) is the corresponding response from PID controller. Results reveal that a good tracking performances are achieved from both controllers with slightly better settling time in LCN case. Here the rise time is taken as the time required for the system response to rise from 10% to 90% of its final value and settling time is the time required for the system to arrive within 2% of the final value. The two PID-type LMCs defining the LCN were: C1 ( k ) 1.9366 [ e( k ) e( k 1 )] 0.7826 [ e( k ) 2e( k 1 ) e( k 2 )] 0.1201e( k ) C 2 ( k ) 1.6429[ e( k ) e( k 1 )] 0.2200 [ e( k ) 2e( k 1 ) e( k 2 )] 0.0429e( k )

(8)

where e( k ) r( k ) y( k ) is again the error between the reference and controller trajectory. The centres and covariances for the Gaussian interpolation functions were ρ1 : ( -14.0660, 2.0260) and ( 14.8186, 0.6666) and

ρ2 : ( 82.8059,1.9678) and ( 20.1629, 0.4573) .

377

(b) PID response Fig. 5. Heading Step Response The coefficients for the filter were: a1 1.0 , a2 -0.9845 , a3 0.0576 , b1 0.0500 , b2 -0.0063 and b3 0.0318 . The PID controller obtained was: C( k ) 0.0029 [ e( k ) e( k 1 )] 0.0039 [ e( k ) 2e( k 1 ) e( k 2 )] 0.001e( k )

(9)

The robustness of the controller was next tested. Results in Brown et al (1997), Townsend et al (1998) and Sharma et al (2002) indicate that whilst the stability of a local controller acting on a local plant model is easily proved, the global stability of the overall closed-loop system is more problematic. One way to overcome this and to test the robustness of the controller is to demonstrate that it is stable throughout the operating space of a vehicle manoeuvre. To this end, a random sequence of course-changing manoeuvres were employed which covered the entire operating region. Figure 6 and 7 reveal that both LCN and(13) PID generated a stable closed-loop response and smoothly followed the reference trajectory. Additionally, as a measure of accuracy and autopilot control MSE( ) ) activity, the mean-square error of the yaw error ( ACE( Eu ) and the average equivalent controller energy ( ) were used. These may be considered in their discrete forms as:

IFAC MCMC 2012 September 19-21, 2012. Arenzano, Italy

MSE( )

1 N

[ y( k ) ˆy( k )]

1 N

[ u( k ) / 60 ]

N

2

(10)

k 1

and

ACE( Eu )

N

2

(11)

k 1

Where y( k ) Desired output at k th instant in rad ˆy( k ) Actual output at k th instant in rad u( k ) Controller effort at k th instant in rpm N Total number of samples Table 1 compares between the LCN and PID autopilots for different trajectories with respect to mean square energy and average equivalent controller energy. Table 1: Comparison between the LCN and PID autopilots for different trajectories Methods Trajectory MSE( ) ACE( Eu ) used 2 ( rps ) 2 rad LCN

PID

Step

0.8250

0.00563

Random

0.2752

0.1824

Step

1.3043

0.4897

Random

0.6748

0.4892

Results in table 1 indicate that LCN consumed less controller energy and thus more efficient to achieve the same desired response compare to PID in all cases and also produced better MSE. This will be important for implementing an efficient linear controller for operating this vehicle in a real scenario. 5. CONCLUDING REMARKS A genetic learning approach to the construction of LMCs for the Springer USV has been proposed. The approach optimizes an overall LMC structure and the local PID controller parameters. Also it easily facilitates the inclusion of transparency and generalization of constraints. Further, instead of requiring a priori knowledge of the Springer for designing a LMC, a much easier NN modelling approach from experimental data was utilized. Simulation results show the excellent setpoint tracking accuracy of the LCN design. Future work will include the testing of this controller in full scale trials. REFERENCES Brown MD, Lightbody G and Irwin GW(1997). Non-linear Internal Model Control using Local Model Networks. IEE Proceedings on Control Theory and Applications, Vol. 144, No 6, 505-514. Caccia M, Bibuli M, Bono R, Bruzzone Ga, Bruzzone Gi and Spirandelli E (2007). Unmanned Surface Vehicle for Coastal and Protected Waters Applications: The Charlie Project. Marine Technology Society Journal, Vol 41, No 2, 62-71.

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Johansen TA and Foss BA (1995). Semi-empirical Modeling of Nonlinear Dynamic Systems Through Identification of Operating Regimes and Local Models. Neural Network Engineering in Dynamic Systems, 105-126. Majohr J, Buch T and Korte C (2000). Navigation and Automatic Control of the Measuring Dolphin (MessinTM). Proceedings of 5th IFAC Conference on Manoeuvring and Control of Marine Craft, Aalborg, Denmark, August, 405-410. Naeem W, Xu T, Sutton R and Tiano A ( 2008). The Design of a Navigation, Guidance, and Control System for an Unmanned Surface Vehicle for Environmental Monitoring. Proc Instn Mech Engrs Part M: Journal of Engineering for the Maritime Environment, Vol 222, No M2, ,67-80. Rippin DWT (1989). Control of Batch Processes. Proceedings of the 3rd IFAC DYCORD + '89 Symposium , Maastrict, Netherlands, 115-125. Sharma SK, McLoone S. and Irwin GW (2005). Genetic Algorithms for Local Controller Network Construction. IEE Proc. Control Theory & Application, Vol 152, No 5, pp. 587-597. Sharma SK, McLoone S and Irwin GW(2002). Genetic Algorithms for Local Model and Local Controller Network Design. Proceedings of the American Control Conference, Anchorage, USA, May, 1693-98. Townsend S, Lightbody G, Brown MD and Irwin, GW(1998). Nonlinear Dynamic Matrix Control using Local Model Networks. Trans Inst MC, Vol 20, No 1, 47-56. Yan R-J, Pang S, Sun H-B and Pang Y-J (2010). Development and Missions of Unmanned Surface Vehicle. Journal of Marine Science and Application, Vol 9, No 4, 451-457.

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MSE=0.27524 rad2 6 Desired Actual 5

Heading angle (rad)

4

3

2

1

0

-1

-2

0

500

1000

1500 Time (sec)

2000

2500

3000

Fig. 6. Vehicle response to a random sequence of course-changing demands in heading using the LCN.

MSE=0.67479rad2 6 Desired Actual

5

Heading angle (rad)

4 3 2 1 0 -1 -2

0

500

1000

1500 Time (sec)

2000

2500

Fig. 7. Vehicle response to a random sequence of course-changing demands in heading using the PID.

379

3000