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: [email protected]).

Abstract: In this paper control system design for robotic airship is developed. The nonlinear multilinked mathematic model of airship is considered. The results of aerodynamic analysis, parametric and structure disturbances 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 of significant interest nowadays. This interest is attracted by unique capabilities of airships and robotic systems on basis of airships (Pshikhopov, 2004, Elfes et al., 1998, Sang-Jong Lee et al., 2004, Lacroix, 2000): capability to hover without additional power costs; large-scale flight range and carrying capacity; safety in case of control system failure; vertical take-off and landing, etc. All these capabilities make airships an attractive solutions for the civilian and military objectives, connected with environment monitoring, supervision and diagnostics of highrise facilities, patrolling, providing communication, air reconnaissance, map-making, radar supervision, etc. Implementation of such systems as autonomous mobile robots increases its functional capabilities, minimizes human participation to objective description. Obviously, such target is connected with a number of problems, resulted from high dimensional and multilinked airship mathematical model, parameters non-stationarity, external disturbances, and a priori non-formalized environment (Pshikhopov, 2006, Medvedev, 2006). The procedure of constructing control systems (CS) of RABP is presented in this work. This procedure considers development of a valid mathematical model, effective control algorithms, motion planner, and also correct hardware selection. 2. MATHEMATICAL MODEL OF AN AIRSHIP To design control system on base of paper (Pshikhopov, Medvedev, 2006) it is possible to consider model of dynamics and kinematics of an airship as a differential equation system:

x& = M -1 ( Fu - Fd - Fv ) ,

(1)

d& = KU ,

(2)

æ S P (Q, x ) ö ÷÷ , Y& = S(Q, x ) = çç è S Q ( Q, x ) ø

(3)

x – m-vector of projections of terrestrial and angular velocities vectors of airship in a body coordinate system OXYZ, m £ 6 ; M(l) - (m×m)- matrix of mass-inertial parameters, where l – vector of no stationary parameters, elements of this vector are airship mass, moments of inertia, apparent masses; Fu (x, P, d, l) - m-vector of control forces and control moments; Fd (x, P, l) - m-vector of nonlinear dynamic component; Fv - m-vector of measurable and no measurable external disturbances, d - m-vector of controllable components (air mass inside an envelope, deflection angle of aerodynamic control surfaces and operating levers of motor thrust, etc.); K – (m×m)-matrix of control coefficients; U – n-vector of control actions; Y = (Q, P )T - n-vector of position P and orientation Q of body coordinate system relative to base coordinate system; S(Q, x ) - n-vector of kinematical constraints; S P (Q, x ) vector of linear velocities of body coordinate system relative to base system; S Q (Q, x ) - vector of angular velocities of body coordinate system relative to base system. Further we consider m = n lossless in generality. Airship dynamic models (1), (2), (3) are multilinked systems of nonlinear differential equations. Its components are defined by design and parameters of specific airship, as well as by structure and type of external disturbances. Besides, distinctive feature of an airship is non-stationarity of vector l components, dependent on functioning conditions of airship and its design characteristics. Necessity for considering full airship dynamics is defined by strict requirements for airship functioning quality. It is necessary to

perform airship aerodynamic properties analysis for the most correct definition of vector Fv . 3. ANALISYS OF AERODYNAMIC FORCES AND TORQUES

Pressure and temperature distribution over surface, velocities field distribution of incident stream in vicinity of airship under different attack angles and velocities also have been acquired. Figure 2 shows velocities vectors distribution by its values and directions in plane, which is lies on airship symmetry axis.

Dependences of basic aerodynamic coefficients on angles of attack and slide had been got using NUMECA software suit for hydro- and aerodynamic calculations. Figure 1 shows diagrams of dependences of head resistance coefficient and lift force coefficient on attack angle into speed coordinate system with three different airship velocities: v = 30, 50, and 80 m/s. These dependences are well conformed to both theoretical and experimental data of such type of airship (Kirilin, Ivchenko, 2000).

Fig. 2. Incident flow velocities distribution on aerostat vicinity. Use of NUMECA software suit for obtaining required aerodynamic characteristics significantly decreased financial expenditure, which could be necessarily for experimental blowing of researched object. 4. DISTURBANCIES ESTIMATION Fig. 1a. Head resistance coefficient depending on attack angle in speed coordinate system plot.

Controller equations are complemented by dynamic adaptive estimator, based on results presented in paper (Pshikhopov, Medvedev, 2006): dz1i ( t ) dt

dz2i ( t ) dt

(

)

(

)

= -l1i Fi0 + z1i + l1i mV j + z2i + l2i mV j , = -l2i Fi0 + z1i + l1i mV j ,

Fˆi = z1i + l1i mV j , dz1 j ( t ) dt

dz2 j ( t ) dt

(

)

(

)

= -l1 j M 0j + z1 j + l1 j J 0j w j + z2 j + l2 j J 0j w j , = -l2 j M 0j + z1 j + l1 j J 0j w j ,

Mˆ j = z1 j + l1 j J 0j w j .

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

(4)

(5)

Equations (4) are estimation of disturbances on linear velocity circuit; (5) implement disturbances estimation by rotation velocity; i , j = x , y , z , z1i , z2i , z1 j , z2 j – estimator state variables; Fi 0 , M 0j – known or measurable forces and torques, applied to moving object; V j , w j - object linear and

angle velocities; m, J 0j - mass and nominal moments of inertia; l1i , l2i , l1 j , l)2 j - estimators coefficients, providing it operating speed; Fi , Mˆ j - evaluations of indeterminate forces and moments. 5. MOTION PLANNING AND CONTROL ALGORITHMS SYNTHESIS APPROACHES Taking into consideration peculiarities of RABP, following tasks are very actual for its operation: airship stabilization at the certain point in a base coordinates space with desirable values of yaw, pitch and roll angles (for kinematic scheme with convertible thrust vector); path following in base coordinate system, with constant airspeed V and given orientation of body coordinate system; motion to the point in base coordinate system, prescribed path following, without additional requirements to airship airspeed. All these tasks could be represented in a form of vector function Y of base coordinates, orientation angles and its derivations, defined as following: Ytr =

N ( P, t ) Ф ( P, Q, t )

=

P T Ai1 (t ) P + Ai 2 (t ) P + Ai 3 (t ) Ф j ( P , Q, t )

i = 1, v , j = 1, m

= 0,

(6)

N (n ) = x ( P T An 1 (t ) P + An 2 (t ) P + An 3 (t )),

dimYtr = n + m = m, where Aij (t ) – matrices of coefficient corresponding dimension defined by planner; n – dimension of operating space of RABP; m – dimension of vector F defines requirements to orientation of RABP; x = 0 for point stabilization; x = 1 for path following. Jacobi matrix for vector Ψtr is ¶N ¶N 2 PT Ai1 (t ) + Ai 2 (t ) 0 T T J NP J NQ P ¶ ¶ Q Js = = = = ¶F j ¶F j , ¶F ¶F J FP J FQ ¶Y T T ¶P ¶QT ¶PT ¶QT dim J s = (m ´ n ) ¶Ytr

~ Yck = J sY& + J t + V = 0, dimYcr = n + m = m ,

(

(

) ) (t ))P + A&

~ V = 0n -1, x V 2 - V *2 , 0 m Jt =

(P

T

A&i1 (t ) + A&i 2 ¶F tj (P, Q, t )

T

i3

,

,

~ ~ A 0 Y = Ytr + A Yck = 0 , i = 1, v , j = 1, m , A = , 0 AF ~ where A – block diagonal matrix of constant coefficients; ~ dim A = m ´ m , AF – m ´ m matrix determines transients of orientation angles of the RABP; A – n ´n matrix defines transients of linear coordinates. Algorithmic solutions for these tasks for RABP control system are based on work (Pshikhopov, 2009). In result we obtain following control algorithms for airship, defined by math model (1), (3):

(

~~ Fu = -M T AK 0

) (K P& + K -1

1

2

)

~~ (t ) + AV + Ytr + Fd + Fˆn ,

K 0 = ( J1 J SPx + J Q J SQx ) , dim K 0 = (m ´ m), ~~ K1 = T A K11 + K12 , dim K1 = (m ´ n),

K11 = (0m´n J1 J SPQ + J Q J SQQ ) , dim K11 = (m ´ n), ~ ~ ~~ K12 = (T + A) J s + T A Г s , dim K12 = ( m ´ n), T

~ ~ ~~ K 2 = (T + A) J t + T AJ t* , dim K 2 = (m ´ 1),

J1 = ( J P + JV ), J V = (0 (n -1)´n

2x P& T

0 m ´n ) T ,

J Sij =

¶S i , here i = {P, Q}, j = {x, Q} , ¶j

JP =

J NP J , J Q = NQ , J ФP J ФQ

æ ¶ 2 F1 ¶ 2 F 2 ¶ 2 F 3 J t* = çç j t* (1, 1), j t* (1, 2), j t* (1, 3), , , ¶t 2 ¶t 2 ¶t 2 è dim J t* = dim J t = (m ´ 1), && + A && ) P + 2( 2 P T A& + A& ) P& + A && , jt* (1, k ) = ( P T A k1 k2 k1 k2 k3

(

GS =

T

ö ÷ , ÷ ø

)

¶J S ¶Y T

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

,

¶t

where A& ij – matrix of time derivatives of matrix Aij (t ) , F tj – elements of vector F depending from time explicitly; 0n -1 ,0 m – zero vectors; V , V * – real airship motion and it’s desired value. All requirements to steady-state movement operation of RABP can be presented in the next form

where Tg is constant, defining pattern of change of trajectory velocity Vk in transient condition; TF is matrix of constants of suitable dimension, defining on basis of orientation angle of RABP nature of transient conditions; T is diagonal ( v - 1) ´ ( v - 1) matrix, defining robot motion type relevantly to trajectory manifold Y tr .

Fig 3. Neural network planning system Works (Pshikhopov, 2004) and (Pshikhopov, Medvedev, 2006) explains the necessity of taking into account multilinked math models. Synthesis procedure for internal coordinates and external disturbances estimator, and modeling results, confirming correctness of a theoretical statements are also presented. RABP application areas define its functioning into indeterminate and non-stationary environments, which raises requirements for a motion planning system. Specifically, intelligent motion planning system is essential for providing airship low level control system with feasible motion trajectories by analyzing computer vision data. A neural network planner is proposed (Pshikhopov, Sirotenko, 2004) to form a motion trajectory to be performed by a controller. A planner consists of two parts: global path planning module and local planner. Global path planning

Fig 4. Airship onboard flight control system

module calculates robot trajectory according to the current flight task and map using well-known A* algorithm. Local planner uses pretrained convolutional neural network (LeCun, Bengio 1995) to extract information about environment from visual data and make a corrections to current trajectory on a base of visual data. Corrections may be different depending on task: object following, obstacle avoidance, lengthy objects tracking. Structure of this planner is shown on fig. 3. A main distinctive feature of the proposed planner from similar (Hadsell et al, 2009) is the way motion trajectories are planned. The output of planner is coefficients of quadric and linear form equation, defining the trajectory in base coordinate space. Such representation of robot motion trajectories together with proposed planning and control algorithms refining the quality of performing path-following tasks. 6. STRUCTURE OF ROBOTIC AIRSHIP ONBOARD CONTROL SYSTEM Obtained theoretical and simulation results enables to suggest the structure of RABP control system, shown on the figure 4. Airship on-board flight control system (OFCS) can be separated into few functional blocks: onboard control system, onboard equipment control system, actuators, embedded modules of on-board equipment, and power-supply system. Board carrier control system includes actuators state sensors, GLONASS/GPS navigation system, inertial navigation system, and computer. Actuators state sensors are various

type encoders. It provides actuators position data to control system. Satellite navigation system GLONASS/GPS is necessary for obtaining airship global coordinates. Inertial navigation unit consists of inertial measurement devices such as gyroscopes, accelerometers etc, which are essential for orientation and coordinates calculation. Computer forms motion trajectory, and calculate control signals according to synthesized control law, current objective and data from listed systems. Next these signals are input to actuators, which are drives of propellers, traction vector angle changer or aerodynamic rudders. Embedded modules of on-board equipment could be transceiver 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, and radar systems could be used for both fight tasks and environment data receiving to provide a valid trajectory planning. Presence or absence any of modules is determined by given task, defined for RABP. Power-supply system controls distribution of electric power into a system, and implement energy-efficient algorithms. 7. HARDWARE IMPLEMENTATION OF CONTROL SYSTEM Results of research are implemented in prototype of airshipbased autonomous mobile robot “Sterkh”, shown on figure 5. These results also can be used to design perspective RABP.

build on nonlinear and multilinked motion model with consideration of dynamic, kinematic and actuators equations. Comparing with traditional (separated by linear and lateral motion) approaches, this method allows to expand system’s functional capabilities by taking into account non-linear operation modes and multilinked math model of control object. Identification of aerodynamic properties of airship performed by airflow simulation software, which is significantly speeding up and reduces price of parametric support for math model. Unmeasured disturbances are evaluated by non-linear estimators, distinguished by generality, which enables to obtain estimations of disturbances, caused by parametric uncertainties, external influence and object structure changes, such as elastic strains. Automatic control system makes possible to plan airship motion trajectory in global coordinate system, which allows performing motions along all trajectories that could be described by quadric and linear forms. Achieved theoretical results have been implemented in several projects. Onboard flight control system structure, shown on fig. 3, allows to perform fully autonomous flight, semiautomatic flight by a given target points and parameters and airship remote control mode. 9. ACKNOWLEDGMENTS The work was supported by Russian Fund of Basic Research. Grant N 07-08-00373-a. REFERENCES

Fig. 5. Autonomous mobile robot “Sterkh” based on miniairship 8. CONCLUSION This paper presented algorithms and structure of airship based robotic complex control system. Control system is

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