Control System Design for Robotic Airship

Pshikhopov V.Kh., Medvedev M. Y., Sirotenko M.Y., Kostjukov V.A.

Taganrog Technological Institute of South Federal University, Taganrog,Russia ( Tel: (+7)8634 37-16-94; e-mail: pshichop@rambler.ru).

Abstract: In this paper control system design for robotic airship is developed. The nonlinear multilinkedmathematic model of airship is considered. The results of aerodynamic analysis, parametric and structuredisturbances estimation, nonlinear control algorithms, and neural network motion planning are presented.Theoretic results are implemented on experimental robotic mini-airship.Keywords: Nonlinear Control System Design, Estimation, Adaptation, Neural Network Planning.

1. INTRODUCTION

Design of robotic airship-based platform (RABP) is ofsignificant interest nowadays. This interest is attracted byunique capabilities of airships and robotic systems on basis ofairships (Pshikhopov, 2004, Elfes et al., 1998, Sang-Jong Leeet al., 2004, Lacroix, 2000): capability to hover withoutadditional power costs; large-scale flight range and carryingcapacity; safety in case of control system failure; verticaltake-off and landing, etc.

All these capabilities make airships an attractive solutions forthe civilian and military objectives, connected withenvironment monitoring, supervision and diagnostics of high-rise facilities, patrolling, providing communication, airreconnaissance, map-making, radar supervision, etc.

Implementation of such systems as autonomous mobilerobots increases its functional capabilities, minimizes humanparticipation to objective description. Obviously, such targetis connected with a number of problems, resulted from highdimensional and multilinked airship mathematical model,parameters non-stationarity, external disturbances, and apriori non-formalized environment (Pshikhopov, 2006,Medvedev, 2006).

The procedure of constructing control systems (CS) of RABPis presented in this work. This procedure considersdevelopment of a valid mathematical model, effective controlalgorithms, motion planner, and also correct hardwareselection.

2. MATHEMATICAL MODEL OF AN AIRSHIP

To design control system on base of paper (Pshikhopov,Medvedev, 2006) it is possible to consider model ofdynamics and kinematics of an airship as a differentialequation system:

)(1 vdu FFFMx --= -& , (1)KUd =& , (2)

QSQS=QS=

Q ),(),(

),(xx

xY P& , (3)

x m-vector of projections of terrestrial and angularvelocities vectors of airship in a body coordinate systemOXYZ, m 6 ; M(l) - (mm)- matrix of mass-inertialparameters, where l vector of no stationary parameters,elements of this vector are airship mass, moments of inertia,apparent masses; uF (x, P, , l)d - m-vector of control forcesand control moments; dF (x,P, l) - m-vector of nonlineardynamic component; vF - m-vector of measurable and nomeasurable external disturbances, d - m-vector ofcontrollable components (air mass inside an envelope,deflection angle of aerodynamic control surfaces andoperating levers of motor thrust, etc.); K (mm)-matrix ofcontrol coefficients; U n-vector of control actions;

TPY ),(Q= - n-vector of position P and orientation Q ofbody coordinate system relative to base coordinate system;

),( xQS - n-vector of kinematical constraints; ),( xP QS -vector of linear velocities of body coordinate system relativeto base system; ),( xQSQ - vector of angular velocities ofbody coordinate system relative to base system. Further weconsider m n= lossless in generality.

Airship dynamic models (1), (2), (3) are multilinked systemsof nonlinear differential equations. Its components aredefined by design and parameters of specific airship, as wellas by structure and type of external disturbances. Besides,distinctive feature of an airship is non-stationarity of vectorl components, dependent on functioning conditions ofairship and its design characteristics. Necessity forconsidering full airship dynamics is defined by strictrequirements for airship functioning quality. It is necessary to

perform airship aerodynamic properties analysis for the mostcorrect definition of vector vF .

3. ANALISYS OF AERODYNAMIC FORCES ANDTORQUES

Dependences of basic aerodynamic coefficients on angles ofattack and slide had been got using NUMECA software suitfor hydro- and aerodynamic calculations.

Figure 1 shows diagrams of dependences of head resistancecoefficient and lift force coefficient on attack angle intospeed coordinate system with three different airshipvelocities: v = 30, 50, and 80 m/s. These dependences arewell conformed to both theoretical and experimental data ofsuch type of airship (Kirilin, Ivchenko, 2000).

Fig. 1a. Head resistance coefficient depending on attackangle in speed coordinate system plot.

Fig. 1b. Lift force coefficient depending on attack angle inspeed coordinate system plot.

Pressure and temperature distribution over surface, velocitiesfield distribution of incident stream in vicinity of airshipunder different attack angles and velocities also have beenacquired. Figure 2 shows velocities vectors distribution by itsvalues and directions in plane, which is lies on airshipsymmetry axis.

Fig. 2. Incident flow velocities distribution on aerostatvicinity.

Use of NUMECA software suit for obtaining requiredaerodynamic characteristics significantly decreased financialexpenditure, which could be necessarily for experimentalblowing of researched object.

4. DISTURBANCIES ESTIMATION

Controller equations are complemented by dynamic adaptiveestimator, based on results presented in paper (Pshikhopov,Medvedev, 2006):

( ) ( )( ) ( )

1 01 1 1 2 2

2 02 1 1

1 1

,

,

,

ii i i i j i i j

ii i i i j

i i i j

dz tl F z l mV z l mV

dtdz t

l F z l mVdt

F z l mV

= - + + + +

= - + +

= +(4)

( ) ( )( ) ( )

1 0 0 01 1 1 2 2

2 0 02 1 1

01 1

,

,

.

jj j j j j j j j j j

jj j j j j j

j j j j j

dz tl M z l J z l J

dtdz t

l M z l Jdt

M z l J

= - + + w + + w

= - + + w

= + w (5)

Equations (4) are estimation of disturbances on linearvelocity circuit; (5) implement disturbances estimation byrotation velocity; , , ,i j x y z= , 1 2 1 , 2, ,i i j jz z z z estimatorstate variables; 0iF ,

0jM known or measurable forces and

torques, applied to moving object; ,j jV w - object linear and

angle velocities; 0, jm J - mass and nominal moments ofinertia; 1 2 1 , 2, ,i i j jl l l l - estimators coefficients, providing itoperating speed; ,i jF M

)- evaluations of indeterminate forces

and moments.

5. MOTION PLANNING AND CONTROL ALGORITHMSSYNTHESIS APPROACHES

Taking into consideration peculiarities of RABP, followingtasks are very actual for its operation: airship stabilization atthe certain point in a base coordinates space with desirablevalues of yaw, pitch and roll angles (for kinematic schemewith convertible thrust vector); path following in basecoordinate system, with constant airspeed V and givenorientation of body coordinate system; motion to the point inbase coordinate system, prescribed path following, withoutadditional requirements to airship airspeed. All these taskscould be represented in a form of vector function Y of basecoordinates, orientation angles and its derivations, defined asfollowing:

0),,(

)()()(),,(

),( 321 =Q

++=Q=Y tPtAPtAPtAP

tPtPN

j

iiiT

tr ,

vi ,1= , m,1=j (6)

)),()()(()( 321 tAPtAPtAPNT

nnnxn ++=,dim mtr =+=Y mn

where ( )tAij matrices of coefficient correspondingdimension defined by planner; n dimension of operatingspace of RABP; m dimension of vector F definesrequirements to orientation of RABP; 0=x for pointstabilization; 1=x for path following.Jacobi matrix for vector tr is

( ) ( )

( )nmJP

tAtAP

JJJJ

P

NPN

YJ

s

Tj

Tj

iiT

P

NNP

TT

TT

Ttr

s

=QF

F

+==

QF

F

Q

=Y=

FQF

Q

dim

,02 21

mVJYJ crtsck =+=Y=++=Y mndim,0~& ,

( )( )TVVV mn x 0,,0~ 2*21 -= - ,( ) ( )( )

( ) ,,, 321t

tPAPtAtAP

J tjiii

T

t

QF

++=

&&&

where ijA& matrix of time derivatives of matrix ( )tAij , tjF elements of vector F depending from time explicitly;

mn 0,0 1- zero vectors; V , *V real airship motion and itsdesired value.

All requirements to steady-state movement operation of RABPcan be presented in the next form

0~ =Y+Y=Y cktr A , vi ,1= , m,1=j , ,00~

F=

AA

A

where A~ block diagonal matrix of constant coefficients;mmA =~dim , FA mm matrix determines transients

of orientation angles of the RABP; A nn matrix definestransients of linear coordinates.

Algorithmic solutions for these tasks for RABP controlsystem are based on work (Pshikhopov, 2009). In result weobtain following control algorithms for airship, defined bymath model (1), (3):

( ) ( ) nFFVAtKPKKATMF dtru ~~)(~~ 2110 ++Y+++-= - & ,( ) ),(dim, 010 mmKJJJJK xPx =+= SQQS

),(dim,~~ 112111 nmKKKATK =+=

( ) ),(dim,0 11111 nmKJJJJK TPm =+= SQQQQSn),(dim,

~~)~~( 1212 nmKATJATK ss =++=

),1(dim,~~)

~~( 2*

2 =++= mKJATJATK tt

),(1 VP JJJ += ,)020( )1( TnTnV PJ -= mn x &

{ } { },,,,here, Q=Q=S=S xjPij

J iij

,,Q

QQ ==

N

P

NPP J

JJ

JJ

J

),1(dimdim

,,,),3,1(),2,1(),1,1(

*

23

2

22

2

21

2****

==

F

F

F=

mJJ

tttjjjJ

tt

T

tttt

( )32121* )2(2)(),1( kkkTkkTt APAAPPAAPkj &&&&&&&&& ++++= ,

TS

S YJ

=G

where T% , A% , - functional coefficients, their structure is:

, ,

where gT is constant, defining pattern of change of trajectoryvelocity kV in transient condition; TF is matrix of constantsof suitable dimension, defining on basis of orientation angleof RABP nature of transient conditions; T is diagonal( ) ( )1 1v v- - matrix, defining robot motion type relevantlyto trajectory manifold trY .

Works (Pshikhopov, 2004) and (Pshikhopov, Medvedev,2006) explains the necessity of taking into accountmultilinked math models. Synthesis procedure for internalcoordinates and external disturbances estimator, andmodeling results, confirming correctness of a theoreticalstatements are also presented.

RABP application areas define its functioning intoindeterminate and non-stationary environments, which raisesrequirements for a motion planning system. Specifically,intelligent motion planning system is essential for providingairship low level control system with feasible motiontrajectories by analyzing computer vision data.

A neural network planner is proposed (Pshikhopov,Sirotenko, 2004) to form a motion trajectory to be performedby a controller. A planner consists of two parts: global pathplanning module and local planner. Global path planning

module calculates robot trajectory according to the currentflight task and map using well-known A* algorithm. Localplanner uses pretrained convolutional neural network(LeCun, Bengio 1995) to extract information aboutenvironment from visual data and make a corrections tocurrent trajectory on a base of visual data. Corrections maybe different depending on task: object following, obstacleavoidance, lengthy objects tracking. Structure of this planneris shown on fig. 3. A main distinctive feature of the proposedplanner from similar (Hadsell et al, 2009) is the way motiontrajectories are planned. The output of planner is coefficientsof quadric and linear form equation, defining the trajectory inbase coordinate space.

Such representation of robot motion trajectories together withproposed planning and control algorithms refining the qualityof performing path-following tasks.

6. STRUCTURE OF ROBOTIC AIRSHIP ONBOARDCONTROL SYSTEM

Obtained theoretical and simulation results enables to suggestthe structure of RABP control system, shown on the figure 4.

Airship on-board flight control system (OFCS) can beseparated into few functional blocks: onboard control system,onboard equipment control system, actuators, embeddedmodules of on-board equipment, and power-supply system.

Board carrier control system includes actuators state sensors,GLONASS/GPS navigation system, inertial navigationsystem, and computer. Actuators state sensors are various

Fig 3. Neural network planning system

Fig 4. Airship onboard flight control system

type encoders. It provides actuators position data to controlsystem. Satellite navigation system GLONASS/GPS isnecessary for obtaining airship global coordinates. Inertialnavigation unit consists of inertial measurement devices suchas gyroscopes, accelerometers etc, which are essential fororientation and coordinates calculation.

Computer forms motion trajectory, and calculate controlsignals according to synthesized control law, currentobjective and data from listed systems. Next these signals areinput to actuators, which are drives of propellers, tractionvector angle changer or aerodynamic rudders.

Embedded modules of on-board equipment could betransceiver equipment, camera based computer vision system,laser scanners, radar systems, complementary modules.Transceiver equipment is essential for receiving flight task,transmit video, remote control, and other data exchange tasks.Camera based computer vision system, laser scanners, andradar systems could be used for both fight tasks andenvironment data receiving to provide a valid trajectoryplanning. Presence or absence any of modules is determinedby given task, defined for RABP.

Power-supply system controls distribution of electric powerinto a system, and implement energy-efficient algorithms.

7. HARDWARE IMPLEMENTATION OF CONTROLSYSTEM

Results of research are implemented in prototype of airship-based autonomous mobile robot Sterkh, shown on figure 5.These results also can be used to design perspective RABP.

Fig. 5. Autonomous mobile robot Sterkh based on mini-airship

8. CONCLUSION

This paper presented algorithms and structure of airshipbased robotic complex control system. Control system is

build on nonlinear and multilinked motion model withconsideration of dynamic, kinematic and actuators equations.Comparing with traditional (separated by linear and lateralmotion) approaches, this method allows to expand systemsfunctional capabilities by taking into account non-linearoperation modes and multilinked math model of controlobject.

Identification of aerodynamic properties of airship performedby airflow simulation software, which is significantlyspeeding up and reduces price of parametric support for mathmodel.

Unmeasured disturbances are evaluated by non-linearestimators, distinguished by generality, which enables toobtain estimations of disturbances, caused by parametricuncertainties, external influence and object structure changes,such as elastic strains.

Automatic control system makes possible to plan airshipmotion trajectory in global coordinate system, which allowsperforming motions along all trajectories that could bedescribed by quadric and linear forms.

Achieved theoretical results have been implemented inseveral projects. Onboard flight control system structure,shown on fig. 3, allows to perform fully autonomous flight,semiautomatic flight by a given target points and parametersand airship remote control mode.

9. ACKNOWLEDGMENTS

The work was supported by Russian Fund of Basic Research.Grant N 07-08-00373-a.

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