Construction and signal filtering in Quadrotor

Transcription

1 Construction and signal filtering in Quadrotor Arkadiusz KUBACKI, Piotr OWCZAREK, Adam OWCZARKOWSKI*, Arkadiusz JAKUBOWSKI Institute of Mechanical Technology, *Institute of Control and Information Engineering, Poznan University of Technology, ul. Piotrowo 3, Poznań, Poland {arkadiusz.j.kubacki, adam.j.owczarkowski, Abstract. The article shows the kinematic model and the construction concept of the Quadrotor. Furthermore, it exhibits the way of steering four rotor flying vehicle and performs basic movements such as rotation, inclination and change altitude of flight. Much effort has gone into selecting the proper filtration algorithm to reduce the noise from machine vibes. This article presents the fusion of the FIR and Kalman algorithms. A few graphs show a comparison of the fast Fourier transform for both filters. The main objective was to calibrate the filters to achieve low noise level and sufficiently fast response time, which are crucial in the flying machines. Keywords. Quadrotor, FIR filter, Kalman filter 1 Introduction Nowadays, we can often hear information about unmanned, remote-controlled vehicles of various types. All of them are able to cross way to setpoint without the participation of human intervention. Historically, the first construction of unmanned vehicles were involved in the military. Now, a lot of elements was adapted in a civilian area. They serve primarily as a hobby of many people. Among all the vehicles remotely controlled the most popular are flying vehicles, especially, multi rotors vehicles. Multi rotors flying vehicles are divided due to numbers of rotors which were used to construction. In most cases we are dealing with an even number of rotors. The four-rotor flying vehicle has four engines based on the cross framework. On each axis there are two motors rotating in the same direction but in opposite relation to the second axis. In such construction it is possible to compensate the resulting torque [2].

2 Fig. 1. Schematic representation of the structure of the Quadrotor along the direction of rotation of the propeller 2 The method of control of Quadrotor To control of the vehicle we use only speed changes of the rotors, and thus the change of thrust of the propellers. This is carried out in such way that the total torque should be compensated. These type of vehicles do not have any additional type of control actuators such as aileron. In the Quadrotor control system, we use three basic movements. The first and most important is to change the altitude of the vehicle. For this purpose, we change the speed of all the rotors at the same time. Fig. 2. Hovering (left side), falling (right side)

3 To tilt or displace the vehicle we have to decrease speed of one engine and increase by the same amount on the other one. Both engines must be on one axis. Fig. 3. Fly to the left (left side), fly to the right (right side) Another possibility is rotation of the vehicle around its axis. For this purpose, the capability of producing torque. On the one axle we reduce the speed of both motors, and on the other we increase the torque. Fig. 4. Vehicle rotation clockwise (left side), vehicle rotation counterclockwise (right side) 3 Construction of the vehicle The vehicle, on which carried out the study is built on the cross frame from tubes of carbon with a diameter of 12mm and a wall thickness of 1mm. Arm span is 58 mm and its weight is 98g together with the mounted battery cells. It is powered by three cells with a total voltage of 11.1V. The maximum engine speed is 132 rpm. There used biplane propeller with dimensions 9x4.7.

4 Fig. 5. Designed Quadrotor The control module is based on a microprocessor contained on the board STM32F4 Discovery, Freescale Semiconductor accelerometer MMA7455 and STMicroelectronics gyroscope L3G42D. Communication with the operator takes place via Bluetooth BTM-222. In addition, between the main processor and the sensors and between motors controllers are used Atmega8 auxiliary processors. Main CPU ATmega8 ATmega8 Fig. 6. A block diagram of the control system

5 Below shows already built vehicle flying. Fig. 7. The photografy of Quadrotor 4 Filtering the signal by the FIR filter A development of a shortcut FIR is finite impulse response filter. It is characterized in that it is not recursive digital filter which does not have a feedback loop so that the response to the finite excitation is also a finite in time. An important feature of this type of filter is a linear phase response. This means that all subsequent samples are equally delayed relative to the input signal and there is no phase distortion in the signal. To design such a filter we must correctly determine the vector of impulse response coefficients. These coefficients can be prepared by various methods. Filter structure is shown below. Fig. 8. The structure of FIR filter[1] Research on the FIR filter consisted of observing the effect of the cutoff frequency on the filtered signal. To determine the coefficients it was used MATLAB and fir1 function. The implemented filter is a sixth order. The following publication shown

6 only after two charts obtained in the course of many attempts to introduce the difference between properly and appropriately selected settings of the filter. Below is shown the input signal from acceleration and output signal for the cut-off frequency equal to 3 Hz and FFT chart. 1.5 Input signal Output from FIR filter a [g] t [s] Fig. 9. Course of acceleration during motion and the response of the FIR filter for cut-off frequency of 3Hz In the chart above we can see that the course is already partially filtered. Below is the FFT chart showing which frequencies are cut off..4.3 FFT of input signal FFT of output from FIR filter a [g] f [Hz] Fig. 1. FFT chart for input and output signals of the FIR filter for 3Hz cutoff frequency

7 The next graph shows the results of the filter used in the project. Cutoff frequency for this filter is 5 Hz. 1.5 Input signal Output from FIR filter a [g] t [s] Fig. 11. Course of acceleration during motion and the response of the FIR filter for cut-off frequency of 5Hz On the FFT graph, we see that the cut off frequency of start earlier, and part of noise in output signal is reduced by 75%..4.3 FFT of input signal FFT of output from FIR filter a [g] f [Hz] Fig. 12. FFT chart for input and output signals of the FIR filter for 5Hz cutoff frequency

8 5 The Kalman filter The Kalman filter is a method of dynamic filtering, which today is one of the most popular methods of estimation based on not only the input but also the output signal [6]. The study consisted of the Kalman filter to observe the impact of the effect of gain on the filtered signal. Below is shown too large gain factor which is.6. angle [rad] Input from FIR filter Output from Kalman filter t [s] Fig. 13. Kalman filter output in the setting of.6 for a selected time segment Too high gain results in rapid response to change in the signal, but it is so large that it reflects the noise from the input filter. The optimal setting turned out to be the value of The output waveform shows chart below. angle [rad] Input from FIR filter Output from Kalman filter t [s] Fig. 14. Kalman filter output in the setting of.9512 for a selected time segment

9 Appropriately selected setting allows to achieve optimal response of the filter. It is fast enough to show the waveform while not reflecting noise. 6 Conclusion The output of sensors is very noisy. It is necessary to use different method of signal filtering like use of FIR and Kalman filter, which allows along with PID controller for stable control of flight of vehicle. Introduced by the delay is so minimal that it does not interfere with the flight. It is possible to use these filters for filtering signals in a multi-rotors vehicle. The implementation of FIR filter is very simple for the driver and does not burden the CPU significantly. The Kalman filter is more difficult to implementation in CPU, but this filter provide very good results of filtered signals. References 1. Orfanidis S.J., Introduction to Signal Processing, PrenticeHall International, Inc P. Tomasik, M. Okarma, D. Marchweka, QUADROTOR - od pomysłu do realizacji, Pomiary, Automatyka, Robotyka 211, R. 15, nr 9, s G. M. Hoffmann, H. Huang, S. L. Waslander, and C. J. Tomlin. Published by the American Institute of Aeronautics and Astronautics, Inc., Lozano PCR, Dzul A. Stabilization of a mini rotorcraft with four rotors. IEEE Control Syst Mag 25: Bouabdallah S, Siegwart R. Backstepping and sliding-mode techniques applied to an indoor micro quadrotor. In: IEEE international conference on robotics and automation, Barcelona, Spain; 25. p D. Simon, Optimal State Estimation, Wiley-Interscience, 26