�

Abstract—For the nonlinear and open-loop unstable characteristics of the small helicopter, autonomous flight control is a challenging problem. In order to reduce the complexity of the helicopter autonomous control, this paper constructs an indoor autonomous flight control platform for a small coaxial helicopter ESky LAMA4, which is convenient for data collection, data analysis and control law design. Firstly, the Vicon Mx Motion Capture System is installed to obtain the attitudes and positions of the coaxial helicopter. Secondly, a PCTx converter for the radio controller is used to convert the control commands into PPM signals which are sent into the radio controller. Hence the attitude and translational motion can be controlled. Then in the inner attitude loop and outer translational loop, several PID controllers are designed for the autonomous hovering control of the small coaxial helicopter. Finally the flight results demonstrate the feasibility of the proposed approach, which can be adopted into the study of small unmanned helicopters in the future.

I. INTRODUCTION nmanned Aerial Vehicle(UAV), also called unmanned aerial vehicle, has recently reached unprecedented levels of growth

in diverse military and civilian application domains, such as power lines inspection, border patrol, rescue missions, natural gas search, fire prevention, natural disasters and agricultural applications. Among many UAVs, the small unmanned aerial vehicles will play an important role in providing unprecedented situational awareness. VTOL (the Vertical Take-off and Landing UAV) can help us realize most military and civilian applications [1].

Small unmanned helicopters have the characteristics of vertical take-off and landing. So small unmanned helicopters can perform better than other aircrafts in loading. However, a helicopter system is very complex to control for the characteristics of non-linearity, open loop instability and channel coupling. Challenges of the research for the helicopter are received more and more concentration by many researchers. Some researchers prefer to make system identification and then continue the study

This work was supported in part by the Chinese Aviation Science Fund under Grant 2008ZG51092 and National Nature Science Foundation of China (60904066).

The authors are with the National Key Laboratory of Science and Technology on Holistic Control, Department of Automatic Control, Beijing University of Aeronautics and Astronautics, Beijing 100191, R. P. China (Email: jakievo@yahoo.com.cn, zhengz@buaa.edu.cn, kycai@buaa.edu.cn)

of autonomous flight control [2-5]. However, the approach has two limitations: i) it needs high level of remote pilot; ii) experimental data and the selected approach will affect the result of system identification, and then will impact the control performance. Therefore, other researchers directly focus on the design of autonomous flight control for the helicopter avoiding system identification process. This approach has merits of low cost and easy implementation [5-9].

This paper focuses on indoor autonomous hovering using Vicon Mx Motion Capture System and PCTx controller converter. Firstly several markers are installed on the coaxial helicopter. Then the Vicon Mx motion capture system can capture attitude and translational data. Thus the linear attitude control law and translational control law are combined to realize the helicopter hovering. Final flight performance can verify the practicability of the proposed control platform for the helicopter.

The remainder of this paper is organized as follows. Section II elaborates the design of the platform for the coaxial helicopter. Section III describes the control laws of attitude and translation. Experimental results are presented in Section IV. Conclusions and future work then follow.

II. CONTROL PLATFORM FOR THE COAXIAL HELICOPTER This section will describe the design scheme of the remote

flight control platform for the coaxial helicopter. Principles of Vicon Mx, characteristics of the coaxial helicopter ESKY LAMA IV and finally principles of remote flight control are introduced successively.

A. Principles of Vicon Motion Capture System

Vicon MX systems [10] are the most advanced digital optical motion capture system available, delivering greater precision, performance and practicality. The major components of the Vicon MX system used in this paper are six cameras above the helicopter, the controlling hardware modules, the software to analyze and present the data, and a host computer to run the software. Motion capture is based on the idea of tracking key points of a subject. The most common technologies for motion capture are Electro Magnetic (using electro magnetic fields and magnetic sensors) and Optical (using special markers that reflect back infra-red light coming from special cameras as shown in Fig.

Indoor autonomous hovering control for a small unmanned coaxial helicopter

Shanjie Wu, Zheng Zheng, Kai-Yuan Cai

U

2010 8th IEEE International Conference onControl and AutomationXiamen, China, June 9-11, 2010

WeD2.1

978-1-4244-5196-8/10/$26.00 ©2010 IEEE 267

1). Six markers are installed on the helicopter as shown in Fig. 2. Then the attitude and translational data can be obtained through rigid body modeling in the Vicon Mx software interface.

B. Characteristics of Coaxial Helicopter

This paper chose the coaxial helicopter model ESKY LAMA IV as the control member for the flight control platform. The coaxial helicopter can be controlled remotely through a four-channel radio controller: i) throttling channel determines vertical motion; ii) yaw channel directs the heading direction of the helicopter; iii) pitch channel drives the helicopter fly forward or backward; iv) roll channel controls the sideslip motion of the helicopter. ESKY LAMA IV is designed specifically for indoor flight. First, it uses a stabilizer on the top rotor, which slows the top rotor’s response to rapid changes in cyclic pitch of the bottom rotor by automatically controlling the cyclic pitch of the top rotor. Second, cyclic pitch of the bottom rotor is controlled by a sliding swash plate. Third, there is no collective pitch control in LAMA. However, lift can only be controlled by changing rotational velocity. Finally, the helicopter is integrated with a rate gyro augmentation system which is fitted to counter the rotor torque.

C. Principle of Flight Control Platform

This paper obtains the attitude and translational data by Vicon MX motion capture system. Additionally, another import device is the PCTx controller converter, which connects between the computer and radio controller. It connects into the computer

through USB interface and plugs into the trainer port of the PCTx controller converter. The PCTx converter is used to convert commands from the computer into signals recognized by the radio controller. When the control signals are sent into the helicopter airborne controller through the aerial, the attitude and translational motion of the helicopter can be controlled.

The flight control platform for the coaxial helicopter model is shown in Fig. 3. The computer accesses the attitude and translational data from Vicon MX motion capture system through TCP protocol. Then the attitude controllers and translational controllers are used to compute commands for the helicopter, which is transformed into PPM radio signals to be sent into the helicopter airborne controller. Obviously, the platform is a closed loop which can realize the autonomous flight control for the helicopter model.

PCTx Converter

Lateral PID Controller

Translational Control

Height PID Controller

Vertical PID Controller

Pitch PD Controller

Roll PD Controller

Heading PD Controller

Attitude Control

Vicon Mx

Commands Integration

Fig. 3 Autonomous flight control platform for the coaxial helicopter

III. CONTROL LAW DESIGN The coordinate system of Vicon MX using in this paper

corresponds to geographic east, north and upward side. The body coordinate system as shown in Fig. 4 is adopted to coincide with the coordinate system of Vicon MX. In Fig. 4 the roll angle, the pitch angle and the yaw angle are defined as well.

viconxvicony

viconz

bodyxbodyy

bodyz

�

�

�

Fig. 4 The coordinate system of Vicon MX

Because this paper focuses on hovering control of the coaxial helicopter model, the attitude and translational motion of the

Fig. 1 Vicon Mx special cameras

Fig. 2 Coaxial helicopter installed with six markers

WeD2.1

268

helicopter can be considered as a linear perturbed motion near the equilibrium. In this paper, we transform the MIMO system into several SISO systems. Hovering control is classified into one inner loop attitude control (to realize stability of the helicopter) and one outer loop translational control (to implement hovering control precision). The control inputs for the four channel are

1U , 2U , 3U and 4U , which correspond with roll, yaw, pitch, and throttling channels. 1U controls the roll and translational motion along y axis. 2U determines the pitch and translational motion along x axis. 3U directs the heading direction of the helicopter. While 4U controls the height of the helicopter. The control input parameters of the four channels are shown in Table I. Note that although the control input range is [100,200] , the actual input range is smaller than the range mentioned above to prevent the phenomena of overshoot and concussion during autonomous flight.

A. Attitude Control Law Design

This paper assumes the desired pitch angle is r� , the desired roll angle is r� , the desired yaw angle is r� . The actual pitch angle c� , the actual roll angle c� and the actual yaw angle c� are captured from Vicon MX motion capture system. Three PD controllers for attitudes are used to realize the attitude stability of the helicopter: i) the roll PD controller with r c� �� as input is used to implement the lateral stability; ii) the pitch PD controller with

r c� �� as input is adopted to stabilize the longitudinal motion; iii) the yaw PD controller with r c� �� as input is used to orient the heading direction. The three attitude controllers are implemented using the structure as shown in Fig. 5. In derivative term a low pass filter is adopted to filter high frequency noise in order to improve the robustness of the system.

1I D

Pf

K K sK

s T s� �

�Helicopter

� �

( )R s ( )E s ( )U s ( )Y s( )U s

��

Fig. 5 Principle of the PID controller used in this paper

The outputs of three attitude PD controllers are control input variations of pitch, roll and yaw channel ( )A

iU t ( 1, 2,3i correspond with pitch, roll and yaw channel).

( )AiU t can be obtained as follows:

( ) )( ( ) ( )( )1

iD

iP i i

A Ai

f

A

A AK s

K R s sT s

U Ys � ��

(1)

If the desired attitude angles are not chosen properly, it will cause the helicopter fly toward certain direction. So PK is set small to let derivative term play an important role. Through this approach satisfied attitude stability can be achieved.

B. Translational Control Law Design

Without considering the height during hovering, the hovering state of the helicopter is defined as ( , , )x y � , where x , y denote the locations in the coordinate system for Vicon MX respectively, � signifies the heading direction of the helicopter.

In order to achieve autonomous hovering control, the location variation in the Vicon MX coordinate system is needed to convert into the variation in the body coordinate system. As shown in Fig. 6, we assume the desired hovering state is ( , , )h h hx y � , the current state is ( , , )c c cx y � . Then the location variation relative to the hovering position in the body coordinate system can be got through a simple transform between the body coordinate ( , , )body body bodyx y z and the Vicon MX coordinate

system ( , , )vicon vicon viconx y z :

�( , )h hx y viconx

vicony

( , )c cx y

cx

cy

bodyxbodyy

Fig. 6 Relative translation in the body coordinate system

TABLE I PARAMETERS FOR FOUR CHANNELS

[100,200] [100,200] [100,200] [100,200]

[122,162] [125,165] [130,170] [100,200]

142 145 150 100

� � � � � � z �

WeD2.1

269

( ) cos ( )sin

.( )sin ( ) cos

body h c c h c c

body h c c h c c

x x y yx

y x x y y

� �

� �

� � � �� � � �

�� (2)

The translational control law in this paper is used to reduce variation during hovering flight: i) longitudinal translation PID controller is adopted to control the longitudinal movement; ii) lateral translation PID controller is used to control the lateral movement; iii) vertical velocity proportional controller controls the vertical velocity. Three controllers adopt the PID controller structure. Equation (2) gives the two inputs for the longitudinal translation PID controller and lateral translation PID controller.

To eliminate the static location error during hovering flight, this paper adopt the PID controller using integral term separation and anti integral term saturation, where the control algorithm of integral term separation can be denoted as:

0

( ) ( 1)( (( ) ) ) ,P Ij s

k

s D

e k e ke k e j Tk Ku K K

T�

� �� � � (3)

where e is the longitudinal or lateral translation error in the body coordinate system ( bodyx or bodyy ), sT is the sampling time interval, � is the switching factor for the integral term. The hovering error is controlled in the range of ( , )� �� , then:

1 | ( ) |0 | ( ) |

error k

error k

��

��

� �� (4)

It means equivalence with PD controller if | ( ) |error k �� , which can prevent generating too large overshoot during flight and assure fast response. If | ( ) |error k �� it means equivalence with PID controller, which improve the control precision during hovering flight.

Anti integral saturation algorithm is adopted into the integral term to prevent system overshoot problem. Here we assume the accumulated error in the integral term has the superior limitation iMax and the lower limitation iMin . Then the error accumulation in the integral term is allowed when the accumulated error locates in the range of ( , )iMin iMax .

The derivative terms in translational controllers are combined with low pass filters to eliminate high frequency perturbation.

Additionally, we change the throttling value in the flight control platform interface to control the hovering height. To avoid the drastic movement in the vertical direction caused by the instability of the electrical motor, a proportional controller is used to control the vertical speed which can improve the stability in the vertical direction.

In summary, the control inputs for the lateral PID controller, longitudinal PID controller and vertical speed PID controller can be obtained as follows:

( ) ( )( ( ) ( )),1

iI iD

iP i i

T T

T T TTi

f

K K sK R

sU s Y s

T ss � � �

� (5)

where 1,2,3i .

C. Commands Integration

The reference inputs for the roll, pitch, yaw and throttling channels are 1

rU , 2rU , 3

rU , 4rU (refer the inertial inputs for every

channel in Table I, 4rU is the reference input given in the flight

control platform). Actual control inputs for four channels can be got by combining Equation (1) and Equation (5):

1 1 1

2 2 3

3 3

1

3

4 4 4

2

( ) ( )( )

( )( )

( )( )

,( )

) ( )(

r A T

r A T

r A

r T

U t

U

U U t U t

U U t U t

U U U t

U

t

t

t U U t

� �

� � � ��

� �� � �

(6)

where 1, 2,3, 4i correspond with roll, pitch, yaw and throttling channel.

IV. EXPERIMENT RESULT AND ANALYSIS In the hovering flight experiments, parameters for all the PID

controllers are shown in Table II.

Additionally, other parameters are set as follows: The derivative separation limitation � for translational PID controllers in x and y axes is set equal to 50mm; iMax =200mm; iMin =-200mm; the sampling time sT interval during hovering flight control is set equal to 15ms; the low pass filters adopted in PID controllers have the time constant 3f sT T ; the range for the

throttling proportional controller is ( 3,3)� . The hovering flight state for the helicopter is (0,0,0) which

also means we hope the helicopter hovers near the location (0 ,0 )mm mm with 0rad heading direction. Fig. 7 demonstrates the hovering flight of the coaxial helicopter in our experiment. Fig. 8 shows the translational change in the

TABLE II PARAMETERS FOR EVERY PID CONTROLLERS

PID controllers PK IK DK

� 100 0 100

� 100 0 100 � 200 0 50 x 0.06 0.03 0.06 y 0.06 0.03 0.06

zv 0.02 0 0

In this paper the translational unit is mm according to the Vicon MX motion capture system. The unit of attitude angle is rad.

WeD2.1

270

horizontal plane within 60s’ hovering flight. The location errors in the longitudinal and lateral direction are in the range of ( 60 ,60 )mm mm� , which means good control precision is achieved during hovering flight.

Fig. 9 shows variations of pitch angle, roll angle and yaw angle during 60s’ hovering flight. Pitch angle and roll angle locate in the range of ( 3 ,3 )� � � while yaw angle is in the range of ( 2 , 2 )� � � . Fig. 10 also reveals that roll angular velocity and pitch angular velocity are both in the range of ( 3 / ,3 / )s s� � � . The yaw angular

velocity is controlled in the range of ( 2 / , 2 / )s s� � � . Fig. 11 displays the three translational speeds and Fig. 11 shows inputs of roll, pitch, and yaw channels during hovering flight. Consequently, from Fig. 10, Fig. 11 and Fig. 12 we conclude that the helicopter can respond quickly according to its movements.

V. CONCLUSIONS AND FUTURE WORK This paper focuses on the design of autonomous hovering

flight control for the coaxial helicopter ESKY LAMA IV using the Vicon MX Motion Capture System. The inner loop attitude

PD controllers and outer loop translational PID controller are adopted to achieve the hovering flight control of coaxial helicopter. Experiment results show that the translational error is within the range of ( 60 ,60 )mm mm� and attitude angles locate in

the range of ( 3 ,3 )� � � . Future work will focus on trajectory track and path planning for the coaxial helicopter.

REFERENCES [1] K. P. Valavanis. Advances in unmanned aerial vehicles: State of the art and

the road to autonomy. Netherlands: Springer-Verlag, 2007. [2] P. Castillo, R. Lozano, and A. Dzul. Modeling and control of mini-flying

machines. London: Springer-Verlag, 2005. [3] B. Kim, Y. Chang, and M. H. Lee. “System identification and 6-DOF

hovering controller design of unmanned model helicopter”. JSME International Journal. 2006, pp. 1048-1057.

[4] J. D. Wu, P. Li, and B. Han. “A modeling method of miniature unmanned helicopter based on parameter identification”. ACTA Aeronautica ET Astronautica Sinica. Vol. 28, No. 4, 2007, pp. 845-850.

[5] K. Tanaka, T. Komatsu, H. Ohtake, and H. O. Wang. “Micro helicopter control: LMI approach vs SOS approach”. IEEE World Congress on Computational Intelligence. 2008, pp. 347-353.

[6] J. M. Roberts, P. I. Corke, and G. Buskey. “Low-cost flight control system for a small autonomous helicopter”. Australasian Conference on Robotics and Automation. 2003, pp. 546-551.

[7] W. B. Chen, M. Liu, and J. J. Ge. “System designing for a small-scale autonomous helicopter”. International Journal of Information Acquisition. 2006, Vol. 3, No. 4, pp. 359-367.

[8] C. Bermes, K. Sartori, D. Schafroth, S. Bouabdallah, and R. Siegwart. “Control of a coaxial helicopter with center of gravity steering”. Workshop Proceeding of SIMPAR. Venice, 2008, pp. 492-500.

[9] A. Y. Ng, H. J. Kim, M. I. Jordan, and S. Sastry. “Autonomous helicopter flight via reinforcement Learning”. In International Symposium on Experimental Robotics. 2004.

[10] L. Chen and P. McKerrow. “Modeling the Lama coaxial helicopter. Australasian Conference on Robotics and Automation”. Brisbane, 2007, pp. 1-9.

Fig. 9 Attitude angles during hovering flight

Fig. 8 Translational variation in the horizontal plane

Fig. 7 Hovering flight control experiment

WeD2.1

271

Fig. 10 Attitude rates during hovering flight

Fig. 12 Inputs of roll, pitch and yaw channels

Fig. 11 Translational velocities during hovering flight

WeD2.1

272