Advance Modeling of a Skid-Steering Mobile Robot for Remote ...
Share Embed Flag
Download ePaper

Advance Modeling of a Skid-Steering Mobile Robot for Remote ...

Advance Modeling of a Skid-Steering Mobile Robot for Remote ... Advance Modeling of a Skid-Steering Mobile Robot for Remote ...

rwu.edu
13.07.2015 Views

3.2 Characterization of the Vibrations 40order Taylor expansion, i.e. cos x ≈ 1, sin x ≈ x, so that we can rewrite (3.6) as follows:a x = ˙v x + gψa y = ˙v y − p ax ˙ω z − gθ(3.7)a z = ˙v z + p ax ˙ω y − gThe data are acquired from the accelerometers at a sample rate of 1 kHz by using LabVIEWand then exported and saved in an Excel format, ready to be loaded and analyzed in Matlab.The Matlab functions that are used for the frequency analysis of the signals are defined inAppendix A. For every value of the control input ω ∗ z contained in the variable rangeW, themain program first parses the data by calling the function parseData(), which loads thedata from the Excel file, computes their Fast Fourier Transform (FFT), converts them fromVoltage values to acceleration values and eventually plots them and their FFT. To improvethe accuracy and reduce the computation time of the FFT function implemented in Matlab,the FFT should be computed on the closest lower power of 2 of samples [20]. In our case, asthe data are acquired for 20 seconds, only the central 2 14 over 20000 samples are consideredfor the FFT. Then, by calling the function filterData(), the program low-pass filters thedata at 50 Hz by using a 10 th order Butterworth filter in order to cut off the noise due to alternatecurrent which works at 60 Hz. Such a choice of the cut-off frequency is also motivatedby the fact that, by taking a first look to the FFT of all the data, there never appear significantfrequency components higher than 50 Hz, except for the alternate current frequency around60 Hz. After low-pass filtering, the amplitude of the signal is calculated as difference betweentheir maximum and minimum value, the FFT of the low-pass filtered data is computedand the three highest peaks in the FFT are found by calling the function findPeakFreq().The findPeakFreq() function also band-pass filter the data by a narrow band, generally2 Hz, centered on the maximum peak frequency. Finally, the original data are plotted togetherwith the low-pass and band-pass filtered data, in order to check the reliability of themaximum peak frequency obtained, and all the amplitudes and peak frequencies are plottedwith respect to the robot angular velocity.Let us consider the data acquired while swiveling the robot in place at different desired angularvelocity ω ∗ z, separately on concrete, tile and carpet. In order to check the repeatabilityof the data, the accelerations are also acquired three times for each angular velocity ω ∗ z. Becausethe wheels start lifting from the floor generally when ω ∗ z > 64 deg , making the robots

3.2 Characterization of the Vibrations 41continuously hopping on its wheels and eventually making the motors stalling, we will beconsidering only the data acquired for ω ∗ z ≤ 64 degs .Some example graphs of the low-pass filtered data with their FFT are provided in AppendixB. The graphs representing the average of the data amplitudes and the average of the threehighest peak frequencies with respect to the angular velocity ω ∗ z and the type of ground arealso provided in Appendix B.Although the data acquired during different trials present a sort of irregularity in their peakfrequencies, due to the irregularity of the ground, there are some features which characterizethem. In particular, by looking at the graphs depicted in Appendix B, the main features canbe listed as follows:• There are, usually, two main frequency components (generally the two highest peak inthe FFT), which can be clearly identified for every angular velocity ω ∗ z and for all thethree types of ground.• The two main components are, usually, one at ¨low¨ (< 10 Hz) and the other at ¨high¨frequency (> 20 Hz), when swiveling the robot with relatively low angular velocities(ω ∗ z < 30 degs ).• The two main components are both at ¨low¨ frequency (< 10 Hz), when swiveling therobot with relatively high angular velocities (ω ∗ z > 30 degs ).• When running the robot on carpet, the ¨low¨ frequency component is always the dominantcomponent.• When running the robot on concrete and tile, the ¨high¨ frequency component is, usually,the dominant component for relatively low angular velocities (ω ∗ z < 30 deg ), whilesthe ¨low¨ frequency component is, usually, the dominant component for relatively highangular velocities (ω ∗ z > 30 degs ).• The ¨high¨ frequency components seem to increase when increasing the robot angularvelocity until 30 degs .• When running the robot on carpet, the amplitude of the oscillations increases almostlinearly with respect to the angular velocity.• When running the robot on concrete and tile, the amplitude of the oscillations is relativelysmall and constant for low angular velocities (ω ∗ z< 30 deg ), while it becomess

3.2 Characterization <strong>of</strong> the Vibrations 41continuously hopping on its wheels and eventually making the motors stalling, we will beconsidering only the data acquired <strong>for</strong> ω ∗ z ≤ 64 degs .Some example graphs <strong>of</strong> the low-pass filtered data with their FFT are provided in AppendixB. The graphs representing the average <strong>of</strong> the data amplitudes and the average <strong>of</strong> the threehighest peak frequencies with respect to the angular velocity ω ∗ z and the type <strong>of</strong> ground arealso provided in Appendix B.Although the data acquired during different trials present a sort <strong>of</strong> irregularity in their peakfrequencies, due to the irregularity <strong>of</strong> the ground, there are some features which characterizethem. In particular, by looking at the graphs depicted in Appendix B, the main features canbe listed as follows:• There are, usually, two main frequency components (generally the two highest peak inthe FFT), which can be clearly identified <strong>for</strong> every angular velocity ω ∗ z and <strong>for</strong> all thethree types <strong>of</strong> ground.• The two main components are, usually, one at ¨low¨ (< 10 Hz) and the other at ¨high¨frequency (> 20 Hz), when swiveling the robot with relatively low angular velocities(ω ∗ z < 30 degs ).• The two main components are both at ¨low¨ frequency (< 10 Hz), when swiveling therobot with relatively high angular velocities (ω ∗ z > 30 degs ).• When running the robot on carpet, the ¨low¨ frequency component is always the dominantcomponent.• When running the robot on concrete and tile, the ¨high¨ frequency component is, usually,the dominant component <strong>for</strong> relatively low angular velocities (ω ∗ z < 30 deg ), whilesthe ¨low¨ frequency component is, usually, the dominant component <strong>for</strong> relatively highangular velocities (ω ∗ z > 30 degs ).• The ¨high¨ frequency components seem to increase when increasing the robot angularvelocity until 30 degs .• When running the robot on carpet, the amplitude <strong>of</strong> the oscillations increases almostlinearly with respect to the angular velocity.• When running the robot on concrete and tile, the amplitude <strong>of</strong> the oscillations is relativelysmall and constant <strong>for</strong> low angular velocities (ω ∗ z< 30 deg ), while it becomess

logo

products

Resources

Company

Terms of service
Privacy policy
Cookie policy
Cookie settings
Imprint
Change language
Made with love in Switzerland
© 2024 Yumpu.com all rights reserved

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!