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UAB School of Engineering - Mechanical Engineering - Early Career Technical Journal, Volume 15 25

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UAB School of Engineering - Mechanical Engineering - Early Career Technical Journal, Volume 15 Page 126


Journal of UAB ECTC Volume 15, 2016

Department of Mechanical Engineering The University of Alabama, Birmingham

Birmingham, Alabama USA

COMPARISON OF STOP SIGN DISTANCE DETECTION USING 2D AND 3D CAMERAS

Mahbubul Islam Kennesaw State University

Marietta, GA, USA

Dr. Kevin McFall Kennesaw State University

Marietta, GA, USA

ABSTRACT In this paper we illustrate traffic sign detection and

distance measurement by monocular and stereo camera. We have introduced this method to detect traffic signs and calculate their distance by applying a Haar cascade classifier which is unambiguous and obtains optimally calculated results. We have obtained distance by mathematical calculations from 2D images obtained from a monocular camera. 3D traffic stop signs can be detected using a Point Feature Histogram descriptor from a point cloud map. The distance to the detected traffic signs can be measured by a depth map obtained from a stereo camera. After proper calculation, we can draw a clear idea comparing stop sign detection in 2D and 3D cameras or stereo cameras.

INTRODUCTION This paper introduces the detection of traffic stop signs and

compares the distance measurements obtained by 2D and 3D cameras. Conventionally we can detect traffic signs or any object from captured image data as per our given reference or given classifier. But if we determine the distance from the object to the camera, then it will be much easier for us to use the result in any real-life application and so on. We can get mathematical results of distance from a 2D image, and we get analytical values for distance from 3D images by measuring a depth map in a point cloud environment. By comparing values for stop sign distance detected by 2D and 3D cameras, we can make a clear point that a calculated depth map result can be more accurate than a theoretical result in a real environment.

2D OBJECT DETECTION Two dimensional images contain RGB color values for

every pixel. To detect a sample object from an image, we need to contain the 2D colored picture RGB values in every single pixel, and the computational intensity of feature calculation makes the detection process slow, complex and computationally expensive. This kind of problem was addressed by Paul Viola [5], who introduced Haar-like features, a method of rapid object detection from digital images.

Haar-like Features: The Haar-like features process is divided by three key contributors.

Integral Image: Allows the process to compute in a quicker and optimized way by detector sampling. To integrate an image, a rectangle feature is used to compute very rapidly using an intermediate representation for image.

Figure 1: Representation of Haar-like feature

W(D)= L(4) + L(1) – L(2) – L(3) (1) Equation (1) represents W(D) as a weight of the image and

L as specific point area. The sum within D is computed using four lookups, as it contains the sum of all pixels on its upper-left region.

Learning Classification: Allows the system to select a minimum number of visual features from a large set of pixels and yields the process to compute the detection optimally [2]. OpenCV can be used for object detection using a cascade classifier that uses the following Haar-like features:

1. Edge Feature

2. Line Feature

3. Center-surround Feature


The feature used in a particular classifier is specified by its shape and position within the region of interest and by the scale (this scale is not the same as the scale used at the detection stage, though these two scales are multiplied). For example, in the case of the third line feature (2c) the response is calculated as the difference between the sum of image pixels under the rectangle covering the whole feature (including the two white stripes and the black stripe in the middle) and the sum of the image pixels under the black stripe multiplied by 3 in order to compensate for the differences in the size of areas. The sums of pixel values over rectangular regions are calculated rapidly using integral images

Cascade: Allows background regions to be discarded based on the integral image and the learning process. The overall form of detection process generates a decision tree by boosting process that we call a ‘cascade’ [1]

Figure 2: representation of a cascade decision tree A positive result introduces the evaluation of the second

classifier, which is adjusted to achieve high detection rates. A negative result leads to immediate rejection of images. Currently the process uses Discrete Adaboost, and the basic classifier is a decision tree with at least 2 leaves.

Training Cascade classifier

A classifier is trained with a few hundred sample views of a particular object, called positive example images containing traffic stop sign, that are scaled to the same size (say, 20x20), and negative examples - arbitrary images of the same size to distinguish from a particular object. In this way, the classifier can build a decision tree of the classifier for the image environment.

Cascade stages are built by training classifiers using Discrete AdaBoost. Then the system needs to adjust the threshold to minimize false negatives. In general, a lower threshold yields higher detection rates from positive examples and high false position rates from negative examples. After several stages of processing, the number of sub-windows reduces radically.

After cascade classifier training is fully accomplished, it can be applied as a given reference to detect an object of interest from input images. The classifier shows as “detected” if the region is likely to show the object, and “not detected” otherwise. Classifier is also designed in such a way that it can be easily “resized” in order to find the objects of interest at different sizes, which is more efficient than resizing the image itself.

2D OBJECT DISTANCE The central imaging model of cameras projects a point P in

real space to point p in the image plane using the focal length f, as appears in Figure 1. Points in space map from (X,Y,Z) to (x,y) according to

and X Yx f y fZ Z

= = (2)

Figure 3: Geometry for projecting a point P in XYZ space to its location p on the xy camera image plane.

Assuming a stop sign is parallel to the image plane, the sign height ∆Y in real space and ∆y in image space measured in length units are related by

pix

r

yYy f hZ N

∆∆∆ = = (3)

The corresponding height ∆ypix measured in pixels involves the vertical resolution in pixels Nr and the image height h in length units. Knowledge of the focal length f is required, which varies among cameras and is not always documented. Alternatively, the diagonal angle of view ψ, defined as the angle between lines from opposite corners of the image to the XYZ origin, is approximately 50° for most cameras. From geometry, image height can be expressed as

Z

Y

X

y

x

P(X,Y,Z)

p

f


( )12

2

2 tan

1

fh

R

ψ=

+(4)

where R is the aspect ratio of image width over height. Stop signs are detected in the image and enclosed in a circle of radius rpix where ∆ypix = 2rpix. Combining this with Equations (2) and (3) results in

( )2

1pix 2

14 tan

rN Y RZr ψ∆ +

= (5)

where ∆Y is 30 in. for a standard stop sign. The distance Z to a detected stop sign is therefore determined by measuring the sign size in the image rpix and applying the image size in Nr and R, and constants ∆Y and ψ.

3D OBJECT DETECTION

The task of 3D object detection is to find a set of corresponding values of point clouds between two different clouds with a given or reference or feature point cloud object. The system compares points that store XYZ coordinates, RGB Color value etc., which takes too much time and is computationally ambiguous[3].

For optimal 3D recognition of an object, there are 3 conditions given below:

1. Robust transformations: Rigid transformations (theones that do not change the distance between points)such as translations and rotations must not affect thefeature. Even if we move the cloud a bit, there shouldbe no difference. In any place the object is taken orput, it should be recognized by the system, rather thanrequiring that the features have the same size or angleof view.

2. Robust noise: Measurement errors that cause noiseshould not change the feature estimation much. Evenif the 3D point cloud creates noise with a feature, thenit should be detected.

3. Resolution invariant: If sampled with differentdensity (like after performing down sampling), theresult must be identical or similar.

Descriptor: A descriptor is a complex and precise signature of a point

that stores information about the surrounding environment’s geometry. It identifies a point across multiple point clouds for multiple point clouds, robust noise or resolutions and viewpoints.

There are many 3D descriptors for 3D object detection. Each has its own method for computing unique values for point clouds. Some use the difference between the angles of the normal of the point and its neighbors, etc.

Point Feature Histograms (PFH) descriptors: Surface normal and curvature estimations are basic in their

representations of the geometry of a specific point. To get a better result and optimal detection, a descriptor should not capture too much detail, as they approximate the geometry of a point’s k-neighborhood with few values [6].

The purpose of PFH is to encode a point’s k-neighborhood geometrical properties by generalizing the mean curvature around the point in a multi-dimensional histogram of point clouds, which provides an informative signature for feature representation. It is an invariant to 3D presentation of the surface and performs well with different densities or noise levels or any resolution. It attempts to capture the best possible sampled surface variations by all interactions between the directions of estimated normal.

Figure 4: representation of PFH computation Figure 4 is a diagram of PFH computation for a query

point (Gq) whose radius is r and and that has k neighbors (where the distances are smaller than radius r) interconnected with a mesh. The PFH descriptor computed a histogram of relationships between all pairs of points of the neighborhood anthe d computational complexity O(K2)

To compute the relative difference between two points Gi and Gj and their associated normal ni and nj , we define a fixed coordinate frame at one of the points (see the figure below).

x= ns (6)

y= 𝑥𝑥 × (𝐺𝐺𝐺𝐺−𝐺𝐺𝐺𝐺)||𝐺𝐺𝐺𝐺−𝐺𝐺𝐺𝐺||2

(7)

z= y × 𝑥𝑥 (8)


Figure 5: representation of descriptor measurement in xyz frame

Using Figure 5’s xyz frame, the difference between the two normals 𝑛𝑛𝐺𝐺 and 𝑛𝑛𝐺𝐺 can be expressed as a set of angular features as follows: 𝛼𝛼 = 𝑦𝑦.𝑛𝑛𝐺𝐺 (9) ∅ = 𝑥𝑥.

(𝐺𝐺𝑡𝑡−𝐺𝐺𝑠𝑠)

𝑑𝑑 (10)

𝜃𝜃 = arctan (𝑧𝑧.𝑛𝑛𝐺𝐺, 𝑥𝑥. 𝑛𝑛𝐺𝐺, ) (11)

where d is the Euclidean distance between the two points Gs and Gt, d=||𝐺𝐺𝐺𝐺 − 𝐺𝐺𝐺𝐺||2. The quadruplet ( 𝛼𝛼,𝜃𝜃,∅) is computed for each pair of two points in k-neighborhood

Set of quadruplets is binned into a histogram. The binning process divides the feature values range into subdivisions. The process counts the number of occurrences in each subinterval. The measured angles between normals can easily be calculated to the same interval on a trigonometric circle.

RESULT & EXPERIMENT We have established an experiment regarding this topic.

We have run a program using OpenCV, PCL (Point Cloud Library) and a stereo camera. The results are given in Table 1:

Table 1: Experimental Results Case 2D Distance

(meter) 3D distance (meter)

Difference (%)

1 17.23 17.5 0.015 2 24.52 25.3 0.031 3 8.41 9.77 0.162 4 34.05 36.84 0.082

As we have seen from the result, the results obtained by of 2D camera and 3D camera differ by about ~0.02%.

FUTURE RESEARCH We are also thinking about extending this research by using

different parameters and real life situations, like weather conditions, image noise reduction to recognize traffic signs, low light recognition of traffic signs etc. We hope to find more accurate and successful experiments using different parameters and real life conditions.

REFERENCES

[1] Zhao, Y., Gu, J., Liu, C., Han, S., Gao, Y., & Hu, Q. (2010).License Plate Location Based on Haar-Like Cascade Classifiersand Edges. 2010 Second WRI Global Congress on IntelligentSystems. doi:10.1109/gcis.2010.55[2] Lienhart, R., Kuranov, A., & Pisarevsky, V. (2003,September). Empirical analysis of detection cascades ofboosted classifiers for rapid object detection. In Joint PatternRecognition Symposium (pp. 297-304). Springer BerlinHeidelberg.[3] Huang, J., & You, S. (2013). Detecting Objects in ScenePoint Cloud: A Combinational Approach. 2013 InternationalConference on 3D Vision. doi:10.1109/3dv.2013.31[4] Huang, J., & You, S. (2013, June). Detecting objects inscene point cloud: A combinational approach. In 2013International Conference on 3D Vision-3DV 2013 (pp. 175-182). IEEE.[5] Viola, P and Jones, Michael. (2001). Rapid Object DetectionUsing a Boosted Cascade of Simple Features, Conference OnCOMPUTER VISION AND PATTERN RECOGNITION 2001,1-9.[6] Kim, I., Kim, D., Cha, Y., Lee, K., & Kuc, T. (2007). An

embodiment of stereo vision system for mobile robot for real-time measuring distance and object tracking. 2007International Conference on Control, Automation and Systems.doi:10.1109/iccas.2007.4407049[7] Li, C. T. (Ed.). (2009). Handbook of Research onComputational Forensics, Digital Crime, and Investigation: Methods and Solutions: Methods and Solutions. IGI Global.





APPLICATIONS OF LIDAR IN AUTONOMOUS VEHICLES Allen J. Stewart, Jonathan Burden, Kevin McFall

Kennesaw State University Marietta, Georgia, United States

ABSTRACT This paper explores the applications of multidirectional

LIDAR in autonomous vehicles. Such devices map their field of vision in a two dimensional outline. It summarizes the use of LIDAR in current autonomous vehicles in industry, such as the Google self driving projects. This paper also reviews the functionality of autonomous vehicles that could be enhanced with the inclusion of LIDAR systems. The scope of this project involves investigating how existing functionality could be replicated with similar performance given less expensive hardware, and how these developments can impact future applications within autonomous vehicles. A major focus of this project is to ensure that the analysis software will be compatible with as many platforms as possible. To this end, Python, an open source scripting language with a major focus in data analysis, is used as the programming language for the research and development. A major focus of this project was to use Python to reverse engineer the serial communication protocol between the UBG-05LN and a computer.

INTRODUCTION The National Oceanic and Atmospheric Administration

(NOAA) defines LIDAR, Light Detection and Ranging, as a range perception system that uses pulsed laser light to map environments [8]. LIDAR is prevalent in autonomous vehicles as a result of its unique ability to produce a 1:1 scaled 3-D model of the environments surrounding the sensor [3]. This functionality comes at a price. As stated by Fisher, “at $75,000 to $85,000 each, Google's lidar costs more than every other component in the self-driving car combined, including the car itself.” While the utility that these LIDAR units provide is valuable, a cheaper alternative is necessary if the general public is to ever see autonomous vehicles on a large scale [3].

Thus far, Google has set the standard when it comes to self-driving technologies [3]. The vehicles that Google is capable of producing do not require any input from their user. They are able to accelerate, brake, and steer themselves completely autonomously [4]. However, by Google’s own admission “The project is still far from becoming commercially viable” [5]. While many systems are working in conjunction to make this a reality, the vehicles get a non-trivial amount of their information from the LIDAR sensory systems (Hillel et al). As

a result, reducing the cost to implement LIDAR into autonomous vehicles, for a wide range of applications, is a top priority [3].

LIDAR serves a plethora of functions in autonomous vehicles. As discussed previously, LIDAR allows for a vehicle to generate a detailed map of its surroundings [3]. The Google vehicles use this map to do all of the following: detect non-vehicle objects that may cause a disturbance to navigation, work in conjunction with radar and sonar devices to assist in adaptive or intelligent cruise control, assist in lane keeping and station keeping calculations by observing and documenting the moment of other vehicles, and interrupt the various other systems of the vehicle in the event of an emergency [3].

Current systems leverage high cost LIDAR hardware for accurate mapping. This project aims to investigate the feasibility of a low cost LIDAR system that is capable of replicating the functionality of existing systems by means of more sophisticated software.

PROCEDURE The LIDAR sensor for this project is the UBG-05LN

manufactured by Hokuyo. This device is intended for use case scenarios that require only a binary value indicating whether an object is within a certain region of the sensor’s view, such as for use in an automatic door [6]. The binary sensor regions are to be programmed with the included software. This is the intended use of the hardware by the manufacturer [6].

Work began by establishing a physical connection between the sensor and a Windows based computer via a DB-9 cable using the RS-232 communication standard in order to interface with the first-party software. As it was shipped, the sensor did not come with a DB-9 serial connection installed, so a makeshift connector was constructed to correctly interface the data lines of the sensor with the serial port of the computer system. This was done by jumping the rx, tx, and ground connections of the sensor to a standard serial cable based upon the data sheet specifications. The first-party software recognized and began to communicate with the sensor. It then produced a continually refreshing point cloud map of all the data in its 180° field of view. An example of this is shown in Figure 1.


Figure 1. Sensor Demo Software

It was noted from the data that was presented by the example software that the sensor hardware was capable of far more functionality than the manufacturer specified. The software was able to return relatively high resolution range measurements over its serial link. However, out of the box, the sensor did not provide ready access to this numeric data.

At this point, the method by which the sensor communicated with the software was unknown. In order to better understand the communication protocol, a serial port monitoring program was used. This program logs all data traffic passing through a specified serial port. By observing the data traffic in the logs, the control codes and data stream structure could be determined. All communication done by the sensor is via ASCII encoded characters. The sensor responds to control commands, which start with the “$” character, a command character or characters, then is terminated by a linefeed or newline character. The control command used primarily for this research was “$G”. When this command was received by the sensor, the sensor sent back a stream of 1548 bytes. Inside this 1548 byte “datastream” was all the range data for the current “frame” the sensor was seeing.

In order to access this data, a Python script was written to automate the jobs of connecting to the sensor, requesting and receiving data, as well as decoding the data into a human usable form. The general flow of the script’s function is as follows:

1. The script binds to the COM port of the computer.2. A “request data” packet ($G) is sent over the serial

port.3. The data stream returned over the COM port is loaded

one byte at a time into a list object4. The data list object is decoded using the appropriate

encoding scheme5. The decoded data is graphed onto a plot window6. Steps 2 through 5 are repeated until the operator stops

the script.

The sensor uses a slightly odd 18-bit encoding scheme to represent the range data from the sensor. Only the 6 least significant bits in each byte are used. Every point measurement from the sensor is represented by 3 ASCII characters in the datastream. The first 6 characters were dropped from the datastream, as they contained an echo of the command that was received, then 3 status bytes. The remaining 1542 characters were converted from ASCII into the representative integer numbers. The next step in decoding was to subtract 48 (30 in hexadecimal notation) from each number, then convert the integers to binary form. After that, the six least significant bits in each character were concatenated, three at a time to form one 18-bit binary number.

For example, a three character measurement might bereceived in the datastream as “0Wk”

Figure 2. Measurement Example (Jonathan Burden)

This three-character set represents a range of 2,555 to the sensor.

That number, converted back into an integer was the range for a single measurement point from the sensor, given in millimeters. This process was repeated for the remainder of the datastream to form a single “frame”. Each frame is made up of 513 point measurements, starting at the sensor’s 3 o’clock position and sweeping leftwards across its field of vision, ending at the sensor’s 9 o’clock position. The script plots these data points onto a graph and displays them, updating as new data is available.

CONCLUSIONS Comparing the collected data both in real time, and offline,

allows for a variety of LIDAR based applications. A particular application relevant to autonomous vehicles, and achievable with this data, is station-keeping. With the information collected by the sensor, the vehicle can monitor its surroundings and constantly check for changes in the environment and react accordingly in order to maintain a desired driving path.

Figures 3 displays the results of simulating an obstacle approaching a vehicle from the front, while the obstacles to the sides remain relatively unchanged. This behavior is achieved by placing the sensor inside a box. The sensor begins at the back of the box facing the front. It is then moved toward the front of the box, stopping at the midpoint. The range information is


represented in millimeters. The box has physical outer dimensions of about 400mm deep and about 450mm wide. Note that since the sensor is within the box, the physical size of the sensor affects the measured values, taking roughly 30 mm off of the effective depth and 20mm off of the width (10 on each side). Making the expected measured value from the back of the box about 370 mm deep and about 430 wide. From these measurements, the distance from the sensor to the either corner, from the back of the box, should be roughly 427mm.

Figure 3. Results from simulating an obstacle approaching a vehicle with the obstacle first farther away

(top) and then moving closer (bottom). Note: distance scales on top and bottom images are not the same. The measured valued are about 6.32% lower than the

expected values. This error likely comes from the sensor not being completely flush with the back of the box. It is also worth noting that the sensor is intended for use up to 5 meters, in

which case an error of about 30 mm would be completely acceptable for applications in autonomous vehicles.

This kind of analysis is directly applicable to adaptive cruise control algorithms where the distances between a vehicle and the vehicle in front of it must be constantly monitored, while proper lateral distance is maintained with vehicles in adjacent lanes.

This project demonstrates the importance of LIDAR in self-driving applications. It set out to show that a less sophisticated LIDAR sensor is capable of collecting ample data to recreate some of the functionality of much higher priced systems. The software developed for this project is capable of poling new data from the sensor at a rate of about 15 times a second. Solutions like these are vital to the success of autonomous vehicles. Steps such as these are what will make autonomous vehicles an achievable goal.

REFERENCES [1] A. B. Hillel, R. Lerner, D. Levi, and G. Raz, “Recentprogress in road and lane detection: a survey,” Machine Visionand Applications, vol. 25, no. 3, pp. 727–745, Feb. 2012.[2] Distance Measuring Type Obstacle Detection Sensor UBG-

05LN. (2006, May 18). Retrieved fromhttp://www.robotshop.com/media/files/PDF/UBG-05LN-Specs.pdf[3] Fisher, A. (2013, September 18). Inside Google's quest to

popularize self-driving cars. In Popular Science. Retrievedfrom http://www.popsci.com/cars/article/2013-09/google-self-driving-car[4] Gannnes, L. (2014, May 14). Google's new self-driving car

ditches the steering wheel. In re/code. Retrieved fromhttp://recode.net/2014/05/27/googles-new-self-driving-car-ditches-the-steering-wheel/[5] G. Erico, “How Google’s Self-Driving Car Works,” IEEE

Spectrum, vol. 18, 2013.[6] Scanning Range Finder UBG-05LN. (2009, August 3).

Retrieved from https://www.hokuyo-aut.jp/02sensor/07scanner/ubg_05ln.html[7] S. Yenikaya, G. Yenikaya, and E. Düven, “Keeping theVehicle on the Road - A Survey on On-Road Lane DetectionSystems,” ACM Computing Surveys, vol. 46, no. 1, p. 2, Oct.2013.[8] What is LIDAR. (2015, May 29). In National Ocean

Service. Retrieved fromhttp://oceanservice.noaa.gov/facts/lidar.html

http://www.robotshop.com/media/files/PDF/UBG-05LN-Specs.pdf

http://www.robotshop.com/media/files/PDF/UBG-05LN-Specs.pdf

http://www.popsci.com/cars/article/2013-09/google-self-driving-car

http://www.popsci.com/cars/article/2013-09/google-self-driving-car

http://recode.net/2014/05/27/googles-new-self-driving-car-ditches-the-steering-wheel/

http://recode.net/2014/05/27/googles-new-self-driving-car-ditches-the-steering-wheel/

https://www.hokuyo-aut.jp/02sensor/07scanner/ubg_05ln.html

https://www.hokuyo-aut.jp/02sensor/07scanner/ubg_05ln.html

http://oceanservice.noaa.gov/facts/lidar.html





MINIMUM STORAGE SPACE MODELING BY MAXIMUM INDEPENDENT SET FOR ANTENNA SYSTEMS

Serkan Güldal, Ph.D. , Murat M. Tanik, Ph.D. Department of Electrical and Computer Engineering,

UAB Birmingham, Alabama, USA

Ibrahim Bilgin Department of Mechanical Engineering, UAB

Birmingham, Alabama, USA

ABSTRACT Advanced communication is fast becoming a signature

property of humankind. The latest development is the widespread use of wireless communication. In this study, we assumed a need for storage in antenna systems and studied how to minimize the required storage space to reduce to cost and increase the security. We generated antenna systems randomly for different antenna ranges, number of antennas, and unit area. We repeated the process 5000 times while modeling antenna systems connectivity by Maximum Independent Set (MIS). Based on our simulation results, MIS modeling increases efficiency up to at least 30%. This paper does not address any antenna design criteria. It is an exercise in application of information theoretic least action principle to already designed antennas.

INTRODUCTION Let 𝐺𝐺 = (𝑁𝑁,𝐸𝐸) be an undirected graph that has 𝑁𝑁 number of

nodes and 𝐸𝐸 number of edges. Nodes 𝑢𝑢 and 𝑣𝑣 are called independent if they do not share an edge. An independent set is a collection of these nodes. The Maximum Independent Set (MIS) is the set with the largest cardinality among independent sets. The MIS contains the maximum number of nodes that are not adjacent [1]. Finding MIS is classified as an NP-hard problem [2].

In the IEEE standard definitions, an antenna is defined as “part of a transmitting or receiving system that is designed to radiate or to receive electromagnetic waves” [3]. Different types of antennas such as wired, aperture, microstrip, array, reflector, lens antennas are widely used [4].

In this study, we model the connectivity of antenna systems as MIS. As such, we convert antenna systems to graphs, so MIS could be computed. Application of MIS divides antenna systems to two groups. One group is composed of the members of the MIS, while the other group is composed of the immediate neighbors of the MIS. For purpose of our analysis we labeled the members of the MIS as the master antennas. The master antennas have storage units to increase efficiency and security.

MAXIMUM INDEPENDENT SET APPLICATION IN ANTENNA SYSTEMS DESIGN

There are various applications of MIS such as, coding theory and wireless communication [5]. We discuss how MIS can be a useful tool in the analysis of certain properties of antenna systems. In antenna systems, storing information is costly and can make the system vulnerable to external unauthorized access.

Our approach is to label some antennas as masters of its immediate neighbors and use MIS as a modeling tool. In Figure 1, a randomly generated antenna system is shown. Antennas are labeled by numbers and areas of the disks represent the range of each antenna.

Figure 1. A randomly generated antenna system with 20 antennas (axes’ units are the normalized length)

Conversion of an antenna system to a graph is based on the overlapping antenna ranges. For example, antenna 18 and antenna 14 are overlapping, so in the graph, it represents an edge. There are antennas which are not overlapping with other


antennas such as 6. These antennas are edge free antennas in the corresponding graph. The graph representation of antenna system in Figure 1 is shown in Figure 2. An MIS of the graph is highlighted with red vertices, {1, 2, 3, 5, 6, 8, 10, 11, 16, 17, 18, 20}. Cardinality of this MIS is 12. Thus, for this particular antenna the system’s efficiency is

𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 =(20 − 12) ∗ 100

20= 40%

Figure 2. Graph representation of an antenna system shown in Figure 1

There are non-overlapping antennas such as {1, 4, 5, 6, 10, 16} which do not share the available information. This antennasystem imitates rural areas with bad wireless communicationnetworks. However, in urban areas, one can consider thatantennas are more connected represented by increased numberedges as shown in Figure 4. The increase in the number of edgeslowers the cardinality of MIS.

In Figure 3, a redundant antenna system is represented. Redundancy prevents interruption and strengthens the signal. This antenna system includes 50 antennas with different ranges. The graph model of this system is shown in Figure 4.

Figure 3. A randomly generated antenna systems with 50 antennas

In Figure 4, the graph has 50 nodes representing the antenna system shown in Figure 3. One of the MIS is highlighted with red vertices, {1, 2, 3, 8, 9, 11, 14, 16, 17, 19, 25, 31, 41, 42, 47}. When the MIS is used to store information to be distributed between antennas, every antenna in our model will have one immediate neighbor to gather information. The overall efficiency of this system is as follows:

𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 =(50 − 15) ∗ 100

50= 70%

Figure 4. Graph representation of the antenna system shown in Figure 3

SIMULATION OF MAXIMUM INDEPENDENT SET MODEL OF ANTENNA SYSTEMS

Initially, in our study, we generate random antenna systems. Our randomized algorithm takes two parameters as input. Our first parameter is the number of antennas in the system. The number of antennas is affected by different natural phenomena such as mountains, population, or industrialization. The second input parameter is the range of the antennas. There are various antennas for different purposes. We have used a normalized scale throughout this study with maximum antenna ranges as 0.1, 0.3, 0.5, 0.7, and 0.9 unit. After input parameters are given, the calculation is repeated 5000 times. Results are shown by histogram in the following section.

Our Mathematica implementation is shown in the appendix.

RESULTS AND DISCUSSION We have simulated our model for different numbers of

antennas and antenna ranges. Our simulations were repeated for 5000 times. In Figure 5, we show the simulation result for an antenna system that has 10 antennas for different ranges between 0.1 and 0.9. In Figure 5.a, maximum antenna range is 0.1 with the small number of antennas. In Figure 5.b, while we kept the number of antennas constant, the maximum antenna range is


increased to 0.3, with efficiency of 20% in the overall system. We had increased the antenna ranges to approximate the urban

areas. In Figure 5.e, the maximum range is increased to 0.9, so it covered most of the area. Thus, efficiency is increased to 60%.

a) Maximum range is 0.1 b) Maximum range is 0.3

c) Maximum range is 0.5 d) Maximum range is 0.7

e) Maximum range is 0.9

Figure 5. Simulating antenna systems that have 10 antennas with increasing coverage

We repeated simulations for different numbers of antennas to test the effect of changes in the number of antennas. In Figure 6, the antenna system has 20 antennas with different ranges. In Figure 6.a, randomly generated 20 antennas with the maximum antenna range 0.1 generates 5% efficiency. This is a considerable success since these 20 antennas are cost effective small range antennas. Additionally, modeling MIS reduces the cost ,which is

already low additional to the security layer. In Figure 6.b, maximum antenna range increased to 0.3, so most probable cardinality of MIS is reduced from 19 to 13. Increase in the maximum antenna range reduced the cardinality of MIS. By increasing the maximum antenna ranges to 0.9, cardinality reduced down to 7 which means 65% efficient antenna system.

0 0 0 0 0 0 13 212

1413

3362

1 2 3 4 5 6 7 8 9 10

FREQ

UEN

CY

NUMBER OF STORAGE ANTENNAS

0 0 0 4 47

423

1340

1796

1144

246

1 2 3 4 5 6 7 8 9 10

FREQ

UEN

CY


0 0 11207

924

17271446

570

104 11

1 2 3 4 5 6 7 8 9 10

FREQ

UEN

CY


0 3186

1015

1789

1356

550

92 9 0

1 2 3 4 5 6 7 8 9 10

FREQ

UEN

CY


0 46

677

17581631

721

144 23 0 0

1 2 3 4 5 6 7 8 9 10

FREQ

UEN

CY


UAB School of Engineering - Mechanical Engineering - Early Career Technical Journal, Volume 15 7




Figure 6. Simulating antenna systems which have 20 antennas with increasing coverage We simulated the number of antennas up to 30 to identify

the relation between MIS and number of antennas. Figure 7.a presents the antenna system which has 30 antennas in the unit area with the maximum antenna range is 0.1 unit. It brings 10% efficiency in the antenna system if the cardinality is 27. Unlike previous analysis, most probable cardinality cannot be chosen clearly; most probable cardinality changes between 26 to 28 for the maximum range 0.1. This is an expected result of increment of edges. Different antennas are overlapping while they are distributed in the area.

0 4 34188

647

14331736

958

13 14 15 16 17 18 19 20

FREQ

UEN

CY


0 2 37 113

405

923

12761148

700

29684 15 1 0

7 8 9 10 11 12 13 14 15 16 17 18 19 20

FREQ

UEN

CY


0 3 24154

548

1072

1331

1037

565

19754 12 3 0

4 5 6 7 8 9 10 11 12 13 14 15 16 17

FREQ

UEN

CY


0 5 93

427

1092

1359

1101

600

23476 11 1 1 0

3 4 5 6 7 8 9 10 11 12 13 14 15 16FR

EQU

ENCY


0 1 93

537

11991440

1027

500

156 35 11 1 0

2 3 4 5 6 7 8 9 10 11 12 13 14

FREQ

UEN

CY






Figure 7. Simulating antenna systems which have 30 antennas with increasing coverage

CONCLUSION In this paper, we model the antenna systems using the

Maximum Independent Set approach. Our model has identified the hierarchy in the antenna systems to reduce the cost and increase the security by adding another level in the available antenna system.

We implemented our model in Wolfram Mathematica package and presented results by histograms. Increments in number of antennas and maximum range reduced the required master antennas. We also noticed that better coverage of the area

by wireless communication systems, such as urban areas, creates more efficient antenna systems.

ACKNOWLEDGMENT We would like to thank to one of the referees indicating that

if we are interested in antenna design, we should include a discussion of existing antenna systems especially in the area of IoT applications. Since the focus of the paper is to introduce a simple coverage calculation assuming the existing of antenna systems, we abstain from any discussion of antenna design.

0 4 20 78263

591

10561265

1087

522

114

20 21 22 23 24 25 26 27 28 29 30

FREQ

UEN

CY


0 1 11 46138

372

725

1012 1017

790

512

24893 28 7 0

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

FREQ

UEN

CY


0 12 68234

582

9471101

913

640

331

12436 10 2 0

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

FREQ

UEN

CY


0 1 17112

373

825

1116 1099

776

415

18762 12 5 0

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18FR

EQU

ENCY


0 2 42209

568

1053

1278

956

542

23283 27 7 1 0

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

FREQ

UEN

CY



REFERENCES

[1] C. Berge, Graphs and Hypergraphs, Elsevier SciencePublishing Co Inc., 1976.[2] R. M. Karp, "Reducibility among Combinatorial ProblemsIn Complexity of Computer Compu-tations," R. E. Miller and J.W. Thatcher, eds., Plenum Press, New York, p. 85–103, 1972.[3] "IEEE Standard for Definitions of Terms for Antennas,"

IEEE Std 145-2013 , doi: 10.1109/IEEESTD.2014.6758443, 2014. [4] C. A. Balanis, "Antenna Theory: Analysis and Design," JohnWiley & Sons, 2015.[5] S. Butenko, "Maximum Independent Set and RelatedProblems, with Applications," University of Florida, Gainesville,Florida, 2003.

APPENDIX A. The Simulation implementation of MIS Modeling

In the following code, implementation of the simulation of antenna system has 30 antennas with maximum antenna range 0.9 ispresented.

antenna = 30; range = 0.9; area = 1; storageAntennas = Table[ x = Table[RandomReal[{-area, area}], {antenna}]; y = Table[RandomReal[{-area, area}], {antenna}]; radious = Table[RandomReal[range], {antenna}];

disk = Table[Disk[{x[[i]], y[[i]]}, radious[[i]]], {i, antenna}];

graph = {}; For[i = 1, i <= antenna, i++, For[j = i + 1, j <= antenna, j++, If[Sqrt[(x[[j]] - x[[i]])^2 + (y[[j]] - y[[i]])^2] <= radious[[i]] + radious[[j]], AppendTo[graph, i <-> j]]; ]; ]; g = Graph[graph]; g = VertexAdd[g, Range[antenna]]; (*Adds antennas which are not connected any other antenna*) storage = Length@FindIndependentVertexSet[g][[1]], {k, 5000}];

histogram = Table[Count[Flatten@storageAntennas, i], {i,antenna}]; (*For MS Word*) Export["antenna=" <> ToString@antenna <> "range=" <> ToString@range <> "area=" <> ToString@area <> ".txt", storageAntennas, "CSV"]; Export["antenna=" <> ToString@antenna <> "range=" <> ToString@range <> "area=" <> ToString@area <> " histogram" <> ".txt", histogram, "CSV"]; Histogram[storageAntennas]





HEAT TRANSFER MODELLING AND BANDWIDTH DETERMINATION OF SMA ACTUATORS FOR ROBOTICS APPLICATIONS

Tyler Ross Lambert, Austin Gurley, and David G Beale Auburn University Department of Mechanical Engineering

Auburn, AL, United States of America

ABSTRACT Shape Memory Alloys (SMA) are special alloyed metals

that, when heated or cooled, undergo a large change in the crystalline structure that causes them to expand and contract with large force. Because ambient cooling conditions are slow compared to the electric heating, the speed of heat transfer determines the speed at which the actuator can be cycled from hot to cold (contracted to extended), called the ‘bandwidth’ of the device.

The design and tuning of controllers that drive SMA actuators successfully can be difficult, and accurately predicting the temperature of an SMA actuator during operation is useful so that the correct voltage can be applied during heating in order to optimize the response time. This report models the heat transfer of fine wires in typical room conditions considering wire size, ambient temperature, and ambient air currents. The complete heat transfer equations are complex – to make this model useful for controls design, both the cooling bandwidth and transformation bandwidth are determined, and these characteristic values can be used to define a simple first order transfer function. This heat transfer model is then used to determine a simple equation that yields the system bandwidth from knowledge of the SMA actuator diameter.

INTRODUCTION SMA actuators are driven by a change in crystalline

geometry upon heating and cooling. Cooler temperatures and higher stresses correspond to the Martensitic crystalline geometry, while higher temperatures and lower stresses correspond to the Austenite crystalline geometry. This effect can be achieved through heating the actuator’s wire by passing a hot fluid over it, but a more prevalent method of wire heating is accomplished by passing a current through the wire. Cooling of the wire is primarily accomplished via convective heat transfer. When designing and tuning controllers to drive SMA actuators, accurately predicting the temperature of the wire is useful, so the correct voltage can be applied during the heating phase to get the optimal response time. Knowledge of the heat transfer rates can also reveal the system bandwidth, which helps in designing a control scheme. SMA actuators

that cool down using still, ambient air typically have low bandwidths, often below 1 Hz. Because of these characteristically low bandwidths, care has to be taken to design a controller that will not operate so fast as to attenuate the system response [1]. This knowledge of the system bandwidth and how it changes with the wire diameter can also help a designer select the appropriate diameter wire for the actuator in a variety of automated mechanical systems.

A variety of methods exist to raise this bandwidth into the range of 10 Hz to 20 Hz through the use of multiple actuators in agonist-antagonist pairs [2, 3, 4, 5, 6, 7]. An analysis of force tracking control was performed and displayed a system bandwidth of an SMA actuator of approximately 2 Hz [8]. An analysis of a robotic grip using a NiTi actuator using a 𝐻𝐻∞ control scheme revealed a system bandwidth of 0.48 Hz [9]. An anti-slack, rapid-heating, anti-overload differential PID control scheme acting on an antagonist pair of SMA actuators showed the ability to get 2 Hz tracking bandwidth [10, 11]. A neural network feedforward control scheme acting on an SMA actuator with an antagonist spring achieved a bandwidth of only 0.1 Hz [12]. Several takes on self-sensing with SMA actuators have been used in control schemes, yielding bandwidths between 0.15 Hz and 1 Hz [13, 14, 15]. An analysis on the frequency response of several SMA actuators of different diameters showed in detail how these actuators perform at frequencies ranging from 0.1 Hz to 100 Hz [16]. The system bandwidth of an SMA actuator has been shown to increase as the wire diameter decreases for passively cooled systems, because the rate at which energy is transferred away from the wire is the limiting factor to system bandwidth [17].

HEAT TRANSFER DIFFERENTIAL EQUATION The heat transfer model of a constant cross-section SMA

wire undergoing Ohmic heating from an electrical power source and cooling via convection from the surrounding air is typically given in the following form [18]:

𝑚𝑚�𝑐𝑐𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 + 𝛥𝛥𝐻𝐻𝜉𝜉̇̇� = 𝐼𝐼2𝑅𝑅(𝜉𝜉) − ℎ𝐴𝐴𝑠𝑠(𝑑𝑑 − 𝑑𝑑∞) (1)

The following notation is used: • m - mass of the wire


• 𝑐𝑐𝑝𝑝 - specific heat of the SMA• 𝛥𝛥𝐻𝐻 - change in energy associated with a phase

transformation• 𝜉𝜉̇̇ - the time derivative of the phase fraction (percent

martensite phase in the wire)• T - uniform temperature of the wire• t - time• I - current through the wire• 𝑅𝑅(𝜉𝜉) - resistance in the wire as a function of its phase

fraction • ℎ - convection coefficient between the wire surface and

the surrounding fluid• 𝐴𝐴𝑠𝑠 - surface area of the wire in contact with the

surrounding fluid• 𝑑𝑑∞ - temperature of the ambient fluid surrounding the

wire

The authors previously used this heat transfer model tomake an SMA module in multibody dynamics software under the assumption that the SMA actuator always stayed in a constant horizontal orientation [19]. This model can be simplified by making some significant assumptions regarding the convection coefficient, h. The 𝛥𝛥𝐻𝐻𝜉𝜉̇̇ term in the formulation represents the latent heat of transformation from one crystalline phase to another. This quantity is often ignored in order to obtain a simpler model. However, a shape memory alloy such as nickel titanium will have a latent heat of transformation of roughly 24.2 Joules per gram, which can be a non-negligible quantity [20]. Because this analysis is focused on cooling rate and not the transformation rate, the quantity is neglected so that a simpler model can be obtained. For this same reason, it can be safely assumed that there is no current (or at least negligible current) passing through the wire as it cools. The final assumption is to say that the wire can be treated as being at a uniform temperature, which will eliminate the effects of diffusion of heat from within the wire on the temperature at any point in the wire. This assumption has been shown to typically be a good one because the wires under consideration will be of small diameter, so radial heat diffusion is negligible [21]. They will also be expected to heat up quickly enough so that the diffusive effects can be decently stated to have little effect on the convection of heat to the ambient fluid. One consideration to note is that for shorter wire lengths, there will be thermal boundary effects to take into account that will prevent the wire from being at a uniform temperature. These boundary effects will also be neglected, as it has been shown that for wire lengths above 148.8 mm this thermal boundary layer can safely be neglected [22].

These assumptions lead to the homogeneous form of the heat transfer equation:

𝑚𝑚𝑐𝑐𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

+ ℎ𝐴𝐴𝑠𝑠𝑑𝑑 = ℎ𝐴𝐴𝑠𝑠𝑑𝑑∞ (2)

This takes the form of a simple ordinary linear first order differential equation and can be rewritten into the following form to reveal the time constant:

𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 + �

ℎ𝐴𝐴𝑠𝑠𝑚𝑚𝑐𝑐𝑝𝑝

�𝑑𝑑 = �ℎ𝐴𝐴𝑠𝑠𝑚𝑚𝑐𝑐𝑝𝑝

�𝑑𝑑∞ (3)

Because the SMA wire can be considered as having a uniform cross-sectional area throughout its length, the surface area available for convection (𝐴𝐴𝑠𝑠) and the wire mass (𝑚𝑚) can be expressed as a function of wire diameter (d) and wire length (𝐿𝐿):

𝐴𝐴𝑠𝑠 = 𝜋𝜋𝑑𝑑𝐿𝐿 and 𝑚𝑚 = 𝜌𝜌𝜋𝜋 �𝑑𝑑2�2

𝐿𝐿 𝜌𝜌 denotes the wire’s volumetric density. Substituting these values into Equation 3 causes the heat transfer model to take the following form:


ℎ𝜋𝜋𝑑𝑑𝐿𝐿 14 𝜌𝜌𝜋𝜋𝐿𝐿𝑑𝑑2𝑐𝑐𝑝𝑝

�𝑑𝑑 = �ℎ𝜋𝜋𝑑𝑑𝐿𝐿

14 𝜌𝜌𝜋𝜋𝐿𝐿𝑑𝑑2𝑐𝑐𝑝𝑝

�𝑑𝑑∞ (4)

Simplifying Equation 4 yields:


4ℎ 𝜌𝜌𝑑𝑑𝑐𝑐𝑝𝑝

� 𝑑𝑑 = �4ℎ 𝜌𝜌𝑑𝑑𝑐𝑐𝑝𝑝

�𝑑𝑑∞ (5)

The solution to this differential equation, with the initial condition that the wire starts at a uniform temperature of 𝑑𝑑0 takes the following form:

𝑑𝑑(𝑑𝑑) = 𝑑𝑑∞ + (𝑑𝑑0 − 𝑑𝑑∞)𝑒𝑒−� 4ℎ

𝜌𝜌𝑑𝑑𝑐𝑐𝑝𝑝� 𝑡𝑡 (6)

This simple, first order differential equation is only accurate to the extent that h, the ‘convection coefficient’, is known.

CONVECTION COEFFICIENT DETERMINATION The convection coefficient can be found by using its

relation to the surface averaged Nusselt number for a cylinder in a cross-flow (Nu𝐷𝐷��). By definition, the convection coefficient is taken to be [23]:

ℎ = 𝑘𝑘𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 Nu𝐷𝐷��

𝑑𝑑(7)

𝑘𝑘𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 is the thermal conductivity of the surrounding fluid.

An extensive set of empirical models has been developed in order to find the surface averaged Nusselt number for a cylinder in a cross-flow. One of the more widely used and accurate models are the Churchill-Bernstein relationship, typically considered valid for values of the product Re𝐷𝐷Pr greater than or equal to 0.2, typical of warm air moving at approximately 0.05 m/s [24]:

Nu𝐷𝐷�� = 0.3 +0.62Re𝐷𝐷1/2Pr1/3

�1 + �0.4Pr �

2/3�1/4 �1 + �

Re𝐷𝐷282000

�5/8

�4/5

(8)

In the above relationship, Pr denotes the Prandlt number, which is the ratio between momentum diffusivity and thermal diffusivity. Re𝐷𝐷 denotes the Reynolds number, which is the ratio of inertial forces to viscous forces. These are defined as


Pr ≡ 𝜐𝜐𝛼𝛼

= 𝑐𝑐𝑝𝑝𝜇𝜇𝑘𝑘

and Re𝐷𝐷 ≡ 𝑣𝑣𝑑𝑑𝜐𝜐

𝜐𝜐 is the kinematic viscosity, 𝜇𝜇 is the dynamic viscosity, 𝛼𝛼 is the thermal diffusivity, d is the wire diameter, and v is the fluid velocity as it passed over the wire. These material properties can vary greatly depending on temperature and pressure. Because the pressure stays roughly constant at atmospheric pressure, they all become strong functions of temperature. For common fluids such as air or water, their values are typically tabulated for a variety of temperatures, and using interpolation methods, can reveal fairly accurate values for any temperature.

Using air as the surrounding fluid, air property tables reveal data for a fairly large temperature range that allows this model to be of use at velocities above 0.025 m/s [25]. Below this speed, the relationship experiences a degree of error and models that use natural convection as the dominant form of heat transfer rather than forced convection are needed.

For very low air velocities (or still air), the Churchill-Bernstein relationship fails to accurately capture the Nusselt number because natural convection is the predominant mode of heat transfer rather than forced convection. For natural convection of an isothermal horizontal cylinder, the Nusselt number is given by the following empirical relationship [26, p. 18]:

Nu𝐷𝐷�� = �0.6 + 0.387Ra1/6

�1+ �0.559Pr �

9/16�8/27�

2

9)

Ra denotes the Rayleigh number, defined as:

Ra ≡ Pr �𝑑𝑑3𝑔𝑔∆𝑑𝑑𝑇𝑇

𝜐𝜐2� (10)

g denotes the acceleration due to gravity and 𝑇𝑇 represents the expansion coefficient, which is also a function of temperature and tabulated for air.

The empirical relationship for vertical cylinders is noticeably similar, being given by the following relationship for certain cases where the diameter satisfies the criteria 𝑑𝑑 > 35𝐿𝐿

(RaPr)1/4 [26, p. 19]:

Nu𝐷𝐷�� = �0.825 + 0.387Ra1/6

�1+ �0.492Pr �

9/16�8/27�

2

(11)

RESULTS The temperature response for three common cases was

determined via solution of the differential equation. The heat transfer model utilizes the following assumptions for the operation of the Nitinol wire in order to determine the convection coefficient and the system bandwidth:

a) The wire has a uniform temperature at all stages of cooling.b) The wire experiences constant stress during operation.c) The boundary conditions of the wire fixture are ignored.

d) Wire cooling does not move the ambient air so that the airvelocity stays roughly constant.

These three cases were all given for Nitinol wire starting heated at 100 degrees Celsius and cooled via convection to the ambient room temperature. The first case was cool room temperature (20 degrees Celsius) with the air being blown at 2 m/s over the wire. The second and third case analyzed natural convection with still air at 25 and 35 degrees Celsius, respectively. The response of the first case is then plotted in Figure 1.

Figure 1. Forced Convection on Nitinol Wire (Case 1) The response of the second case is also shown, as Figure

2. This plot reveals that natural convection is slower to coolthe wire than forced convection.

Figure 2. Natural Convection on Nitinol Wire (Case 2) The response of the third case is also shown, as Figure 3.


Figure 3. Natural Convection on Nitinol Wire (Case 3)

Similar responses can be generated using the model for a vertical cylinder. The convection coefficient, due to its dependence on wire temperature, ambient temperature, and wire diameter, can be found to be a function of these parameters. For the cases where natural convection is dominant, the convection coefficient can approximately be expressed by the following expression, where the temperatures are expressed in degrees Celsius (or Kelvin) and the wire diameter is expressed in millimeters:

ℎ(𝑑𝑑, 𝑑𝑑∞,𝑑𝑑) = 65.5𝑒𝑒−𝑓𝑓4(𝑑𝑑 − 𝑑𝑑∞)

16 �

Wm2K�

(12)

An SMA will have its internal crystalline geometry changed by the energy supplied to the material either in the form of heat or an applied external stress once either of these quantities passes certain thresholds that are characteristic of the specific alloy in use [27]. The primary crystalline phases of interest are the Martensite phase, which is found at lower temperatures and higher stresses; and the Austenite phase, which is found at higher temperatures and lower stresses. Nitinol’s temperature dependence on phase composition can be highlighted with a stress-temperature-phase diagram, as in Figure 4. From the diagram, it can be seen that the phase transformation occurs over bands, with specific start and finish temperatures for both the Martensite and Austenite transformations. The stress dependence on the transformation temperature is denoted by CM and CA for the Martensite and Austenite bands, respectively.

Figure 4. Temperature-Stress Phase Diagram To study the effect of heat transfer on the actuator

bandwidth, the conditions in which the SMA response decreases to -3 dB of its DC response time must be understood. By keeping the stress constant, the Martensitic phase transition temperature can be approximated using the line labelled M. From this line, the bandwidth can be determined based on the time it takes to cool to this transition temperature using the following relationship:

𝐵𝐵𝐵𝐵 = 1

2𝑑𝑑𝑀𝑀 (13)

𝑑𝑑𝑀𝑀 is the minimum 100% transformation time, defined as the time it takes on the temperature response curves for the wire to reach the Martensitic transformation temperature. This definition allows for the bandwidth to be determined for any situation in which the stress does not significantly change during cooling and if the heat supplied to the SMA actuator during heating carries twice as much energy into the system as is being lost to the surrounding air. This second consideration makes heating times and cooling times comparable. The bandwidths for the three cases above for the given stresses are given in Table 1. The wire orientation affects the heat transfer rate, and therefore the transformation bandwidth, in cases where the air is not moving, so formulas have been derived expressing these bandwidths in terms of 𝜃𝜃, which is the angle of the SMA actuator with respect to horizontal ranging from 0 to 90 degrees.

Table 1. Approximate Transformation Bandwidths of SMA Actuator Systems

For the second case, a transformation bandwidth can be determined to approximately fit the following form by using a


power series fit and by taking the wire diameter to be in millimeters:

𝐵𝐵𝐵𝐵𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑠𝑠𝑓𝑓𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑓𝑓𝑡𝑡𝑡𝑡 = 0.0099 + 0.0068 sin𝜃𝜃

𝑑𝑑2(14)

The bandwidths for the general heat transfer equations, neglecting the crystalline transformation, are also found by finding the time constant for the cooling responses and using the relationship of the bandwidth and the time constant, 𝜏𝜏 [28]:

𝑓𝑓−3 𝑓𝑓𝑑𝑑 = 1

2𝜋𝜋 𝜏𝜏(15)

These bandwidths for the cooling response are tabulated for the three cases in Figure 5.

Figure 5. Cooling Bandwidths of SMA Actuator Systems

For cases where natural convection dominates over forced convection, this cooling bandwidth can be approximated as a function of the wire diameter, in millimeters, by using a power series fit:

𝐵𝐵𝐵𝐵𝑐𝑐𝑡𝑡𝑡𝑡𝑓𝑓𝑓𝑓𝑡𝑡𝑐𝑐 = 0.0086𝑑𝑑2

(16)

EXPERIMENT A 0.125 mm Nitinol wire actuator was driven via an

electrical current being passed through it at room temperature. The current, supplied from a PWM signal provided by a microcontroller, heats the wire and causes it to contract. This current was applied over a spectrum of frequencies in order to determine the system bandwidth. The measured change in position of the SMA actuator is the system gain, and this value was normalized so that the DC gain was equal to unity, and the constricted length characteristic of a total phase transformation into Austenite was equal to 0. The measurements of wire position were performed using a robust dual measurement self-sensing technique as previously outlined by the authors [29]. The experimental setup is shown in Figure 6.

Figure 6. SMA Actuator with Self-Sensing Probe The results of the analysis show that at a frequency of

approximately 0.65 Hz, the gain has shifted –3 dB (to about 70.7%) of its DC value. The frequency response from an increasing sinusoidal input with frequencies ranging from 0 to 1.4 Hz is provided in Figure 7, with the cutoff frequency being marked with the star. A bandwidth of 0.65 Hz falls inside of the range of predicted system bandwidths provided in Table 1, and would correspond to an SMA actuator with an orientation that is very close to horizontal.

Figure 7. SMA Actuator Frequency Response at Room Temperature

Equation 16 would predict a system bandwidth of 0.5504 Hz, which carries fifteen percent error when compared to the experimental results. This is because Equation 16 is derived for the cooling bandwidth of the system, neglecting changes in the crystalline structure of the SMA actuator. Equation 13 predicts a transformation bandwidth of 0.6304 Hz, assuming the wire remains horizontal during operation. This is much closer to the experimental value, but still contains a small degree of error which is attributed to the experiment being non-ideal. Equation 13 is derived for ambient, still air with a temperature of 25 degrees Celsius. If the ambient temperature is significantly different than room temperature, or there is air movement around the wire, then this approximation will experience some degree of error. If the speed at which the wire

Microcontroller

Self-sensing Probe

SMA Actuator

Moving Hinge


heats up is significantly different than the speed at which it cools, this will also lead to a degree of error, because the transformation bandwidth formulation assumes comparable rates of heating and cooling. The difference in the cooling and heating responses is evident in the experiment, as at frequencies higher than the predicted cooling bandwidth of 0.55 Hz, the cooling response was greatly attenuated as the actuator did not have adequate time to cool, and the SMA actuator always remained at or close to its constricted length. Another source of error comes from the self-sensing measurement technique, which provides a resolution of 1.5 degrees out of 90 degrees of travel, or about 0.0167 on the normalized plot of position, limiting the accuracy at which the system bandwidth can be obtained.

CONCLUSIONS This paper has shown the use of two sets of empirical

models for the surface averaged Nusselt number that are of general use and promise errors of less than twenty percent in the determination of the convection coefficient and the bandwidth of an SMA actuator. These Nusselt numbers are used to compute the convection coefficients and solve the first order differential equation that governs the temperature response of the wire. By comparing the temperature response to the phase transformation temperatures, the time taken for the wire to transform from Austenite phase to Martensite phase can be determined. This time can be used to determine the bandwidth of the system. The model that emerged from this analysis accurately predicts the system bandwidth to within three percent of the experimental value. This ability to accurately predict the system bandwidth can aid in the selection of specific diameter SMA actuators for use in different robotic systems, because depending on how quickly the actuator will need to cycle and how strong the actuator will need to be, one size wire may be more suitable than another.

Future work will include the derivation of bandwidth predicting models for situations where heating of the wire is achieved through the passing of a fluid over the wire instead of through electric heating. More complex actuator systems will also be analyzed, such as how the system responds when paired with an antagonist in the form of a spring or another SMA wire. Through the use of a robust self-sensing method and the knowledge of which SMA actuator is appropriate, mechanisms that utilize SMA actuators will be created and tested.

REFERENCES

[1] T. Evdaimon and M. a. D. P. T. Sfakiotakis, "A Closed-Loop Position Control Scheme for SMA-Actuated Joints," in 2014 22nd Mediterranean Conference on Control and Automation (MED), Palermo, Italy, 2014.

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[5] L. Odhner and H. Asada, "Scaling up shape memory alloy actuators using a recruitment control architecture,"in Robotics and Automation, Anchorage, AK, 2010.

[6] J. Ditman and L. Bergman, "A Comparison on theEffectiveness of Two Shape Memory Alloy Based Actuators," in Intelligent Materials, Second International Conference Proceedings, Colonial Williamsburg, VA, 1994.

[7] S. Nakshatharan, D. Kaliaperumal and D. Ruth, "Effectof stress on bandwidth of antagonistic shape memory alloy actuators," Journal of Intelligent Material Systems and Structures, vol. 27, no. 2, pp. 153-165, 2016.

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[14] T.-M. Wang, Z.-Y. Shi, D. Liu, C. Ma and Z.-H. Zhang,"An Accurately Controlled Antagonist Shape Memory Alloy Actuator with Self Sensing," Sensors, vol. 12, pp. 7682-7700, 2012.

[15] R. Josephine, N. Sunja and K. Dhanalakshmi,"Differential resistance feedback control of a self-sensing shape memory alloy actuated system,"International Society of Automation Transactions, vol.53, pp. 289-297, 2014.

[16] Y. Teh and R. Featherstone, "Frequency ResponseAnalysis of shape memory alloy actuators," in International Conference on Smart Materials and Nanotechnology in Engineering, Harbin, China, 2007.

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GESTURE RECOGNITION USING ULTRASONIC SENSORS AND AN RGB CAMERA

Minchul Shin Department of Mechanical Engineering

Georgia Southern University Statesboro, Georgia, United States

Stephen Zeigler Department of Mechanical Engineering

Georgia Southern University Statesboro, Georgia, United States

ABSTRACT This paper provides a new Head Mounted Device (HMD)

design including a standard RGB camera and an ultrasonic transducer. The RGB camera tracks objects in the latitudinal and longitudinal directions (2D images) while the ultrasonic transducer tracks the depth of the object in relation to the HMD. The transducer contains a single transmitter that sends a burst of waves at predetermined increments and three receivers that vibrate at the frequency of the returning waves. Using a charge amplifier, a Sallen-Key low pass filter, and a Sallen-Key high pass filter, a frequency range can be determined so that background interference is limited. A distance can be calculated using the time-of-flight (TOF) method along with the measurement of time between the signal produced from the transmitter and the received signal. Using three receivers allows for a more accurate location. An HMD of this design is more accurate, subjected to less interference from background noise, and not reliant of external hardware for user input such as gloves or remotes.

INTRODUCTION With the increase in technological innovations, new and

innovative ways to control and operate these innovations are needed. With the creation of wearable devices such as Google Glass and Kinect sensor, a way to operate these systems is needed [1]. Since the first appearance of 3D image mapping technology in the early 21st century, various gesture recognition methods, including multimodal vision-based and 2D imaging+depth, have been introduced for easy access to information. However, because of inaccuracy of signal processing, conventional inputs – such as haptic, vision-based, voice recognition and typing on a hand-held keyboard – limit broad applications for certain tasks, such as document preparation and extended web browsing [2-4]. Voice recognition is the most advanced and natural way for human-computer-interaction (HCI) but requires acoustically clean environments, and often requires the user to repeat commands multiple times. Haptic or touch-based input is familiar and comfortable to users but requires the driver to take attention away from the road to reach the device(s) and search for the

right place to touch. Figure 1 is an example of 3D gestural control in real time. It contains multiple applications that can be accessed using gestures such as tapping in the air or swiping in different directions.

Figure 1. Example of fast and precise 3D gestural control in cluttered environments using realtime signal processing.

Many gesture recognition systems using imaging+depth modalities have been developed since they first appeared as research curiosities in the 1980s [5]. Various methods using infrared, ultrasonic, and RGB (Red, Green, Blue) cameras have been developed and used successfully to render images in three dimensions [6-11]. Generally, infrared cameras use time-of-flight (TOF) methods in which a power source emits an electromagnetic (EM) wave and the device calculates the time it takes for the EM wave to reflect off a target. The infrared camera has benefits of high depth rate and accuracy. However, infrared cameras have two critical challenges: strong sunlight sensitivity and high power consumption. In particular, light interference severely limits 3D camera performance outdoors [8-14]. To compensate for these limitations, researchers have developed the ability to suppress background light [15-16], but the practical efficacy remains uncertain. As an alternative, the use of ultrasound, or acoustic, sensing for performing 3D imaging has


advantages over other methods: low price; no daylight sensitivity; and low power consumption.

In order to combat these limitations of other forms of device controllers, a new form needed to be developed. Using an RGB camera to control the longitudinal and latitudinal directions of gestures (2D images) along with a chip containing an ultrasonic transmitter along with three receivers to control depth, a new theoretical form has been developed.

METHODOLOGY AND RESULT SYSTEM OVERVIEW

The design of the system is subjected to minimal background noise because the ultrasonic chip only identifies sound waves at frequencies around 40 kHz using filters. The RGB camera produces an image, but it is limited in its capability to determine which object in the image is the focus. The chip isolates a certain depth so that only objects at that range are detected instead of objects that are in the field of view, but farther away. This allows the RGB camera to ignore all other data except the data at this depth, and then image processing allows for gesture recognition. The chip along with the camera used can be seen in Figure 2.

Figure. 2: Ultra sonic sensor design (left) and the RGB camera (right).

Figure 3. Finger positioning using ultrasonic TOF method.

In order for this concept to work, the following needs to occur. A single transmitter produces sound waves at a certain frequency in given intervals of time. The chip records the time it takes for the sound wave to travel to the object and back one of the receivers. The signal produced from the sound

wave is then filtered to ignore any frequencies other than the target frequencies. Once the data is collected, the depth of the object can be calculated. After the depth is determined, the object that has been detected can be used in gesture recognition using image processing with the RGB camera. The depth of objects will be detected with wave phase differences to each receivers as seen in Figure 3.

A. ULTRASONIC SENSOR DESIGNThe purpose of the chips design is to verify depth in a field

of view. A single transmitter sends a burst of sound waves at a predetermined increment of time. A program is used to record the time it takes for the sound wave to be produced, strike an object, and return to one of the three receivers (TOF method) as shown in Figure. 2. Using the time and the frequency of the sound wave, a distance can be calculated.

In order to begin the construction of the design, a theoretical simulation of the circuit was needed. A resonant frequency of system is designed at 40 kHz, based on the resonant frequency of the ultrasonic transmitter.

Using information gathered from the frequency response from the model, the target value of 40 kHz was verified. The circuit needed to be designed in such a way that the bandwidth of the circuit was centered around 40 kHz. This was achieved through the use of charge amplifiers, low pass filters, and high pass filters. A charge amplifier is needed in order for the receiver’s signal can be processed. A charge amplifier converts a collected charge from a piezoelectric sensor to a voltage that can be used in signal processing. An active low pass filter and high pass filter were initially used, but more efficient filters were discovered. Utilizing a Sallen-Key high pass filter and Sallen-Key low pass filter, a higher magnitude was achieved at the target frequency. The overall circuit design modeled using Multisim is seen in Figure 3 and was implemented by the PCB circuit, as shown Figure 4. The final chip design utilizes three of these receiver circuits in conjunction with a single transmitter. The theoretical frequency response of the circuit is seen in Figure 5. Based on the graph, the quality factor (Q) of the system is around 24.

Figure 4: The overall design of the circuit for the receivers. The first Op-Amp is the charge amplifier, the second is the Sallen-Key high pass filter, and the third is the Sallen-Key

low pass filter.


Fig 5. System block (a) and frequency response (b) of receiver circuit.

B. IMAGE PROCESSINGThe purpose of the image processing is to allow the

device to register skin tone and recognize gestures such as the ones seen in Figure 6.

Figure 6. Examples of motion for gesture recognition. The image processing was designed using a Microsoft

LifeCam Studio webcam and MATLAB. To begin the image processing, the LifeCam was set to a resolution of 320x240. Once that was completed, the input video feed was set to color images, and the interval between frame-grabs was set to 5 frames. The video feed was initiated after the settings were completed. A while loop was created to run for a set number of intervals so the program knows when to stop running. An image was collected using the “getsnapshot” function in MATLAB. A function that was created was initiated in order to detect skin tones found in the collected image. This function used a bin file that contained samples of skin tones. This bin file allows the function to isolate RGB intensities to form colors that are within the skin pigment spectrum. Once the image is acquired and the bin file read, the image is run through a filter and grey thresholding in order to eliminate background objects. Finally the image is converted into a binary representation of the image in order for the red box to distinguish the area of interest. An example of image filtering based on skin color can be seen in Figure 7. Once that is completed, a rectangle box is constructed around the detected area as seen in Figure 8.

Figure 7. Skin color detection and filtering The issue with this program currently is that it cannot

differentiate between depths. If two objects that satisfy the function that detects skin tones are connected by pixels, the two objects will be merged together. An example of this is seen if Figure 8. The red rectangle signifies the area that satisfies the function. The right hand is closer to the camera and the face is farther away. Despite the difference in distance from the camera, both the face and hand are detected and registered. This issue is fixed by using depth information by the ultrasonic transmitter/receiver and implemented along with the code as shown in Figure. 9.

Figure 8: Skin detection program limitation.

Figure 9: Skin detection program. For gesture recognition to occur, a separate program from

the skin detection program is needed to detect and track motion between frames of the video feed. To begin, the camera settings need to be set similar to the skin detection program. Once the video is started, an initial image is acquired. A while loop is constructed, and a second image is acquired after the


predetermined interval between frames, in this case 5 frames. The initial image and the second image are converted from RGB images into grayscale images. The MATLAB function “imsubtract” is used to detect the differences between the two images and form a single image of these differences. These differences represent where the movement occurred. The image of the differences is run through a filter and then converted to a binary image. A red rectangle is then constructed around where the motion occurred. Another image is acquired after the image is processed and the process is repeated. This process is repeated based on the number of iterations specified at the beginning of the while loop. Figure 10 shows the operator moving his fingers up and down in a waving motion to demonstrate this program. This image was captured in real time using a live feed.

Figure 10. Motion tracking example.

The overall image processing layout used can be seen in Figure 11. The steps that have currently been completed are the motion tracking and skin detection steps. The depth information along with combining all three programs are being established.

Figure 11: Overall Image Processing.

The goal of the proposed sensor is to monitor hand gestures produced by a driver. The sensor will be accompanied by a software interface that allows application designers to

choose the gesture vocabulary they wish to use for their application. A computer vision module capable of recognizing such gestures will be developed.

CONCLUSION The theoretical chip design model and its simulation provide

an example for how the chip will determine depth in a field of view. The RGB camera along with image processing programs will allow the HMD to detect and track hand gestures using skin detection and motion tracking. The combination of the chip and camera allow the device to differentiate between background objects and the target object. This design will allow for a more accurate and more reliable form of control over HMDS.

REFERENCES [1] Han, J., Shao, L., Xu, D., & Shotton, J. (2013). Enhancedcomputer vision with Microsoft Kinect sensor: A review. IEEETransactions on Cybernetics, 43(5), 1318-1334.[2] Rümelin, S. & Butz, A. “How to make large touch screensusable while driving.” In Proceedings of the ACM 5thInternational Conference on Automotive User Interfaces andInteractive Vehicular Applications (pp. 48-55). October, 2013.[3] Geiger. “Ber Luhrungslose Bedienung von Infotainment-Systemen im Fahrzeug”. PhD thesis, TU MLunchen, 2003[4] Pfleging, B., Schneegass, S., & Schmidt, A. “Multimodalinteraction in the car: combining speech and gestures on thesteering wheel.” In Proceedings of the ACM 4th InternationalConference on Automotive User Interfaces and InteractiveVehicular Applications. pp. 155-162. October 2012.[5] F. Blais, “Review of 20 years of range sensor development”,J. Electron. Imaging., vol. 13(1), pp. 231-243, Jan. 2004.[6] S.-J. Kim, J. D. K. Kim, B. Kang, and K. Lee, “A CMOSimage sensor based on unified pixel architecture with time-division multiplexing scheme for color and depth imageacquisition,” IEEE J. Solid-State Circuits, vol. 47, no. 11, pp.2834–2845, Nov. 2012.[7] Leap Motion. Leap Motion Controller. https://www.leapmotion.com/. [8] R. Przybyla, H.-Y. Tang, S. Shelton, D. Horsley, B. Boser,“3D Ultrasonic Gesture Recognition” in 2014 IEEE Int. Solid-State Circuits Conf. (ISSCC) Dig. Tech. Papers, pp. 210-211,2014.[9] T. Kopinski, S. Geisler, L. Caron, A. Gepperth and U.Handmann, “A real-time applicable 3D gesture recognitionsystem for Automobile HMI” in 2014 IEEE Int. Conf. IntelligentTransportation Systems. (ITSC), pp. 2616-2622, 2014[10] E. Ohn-Bar and M. Trivedi, “Hand Gesture Recognition inReal-Time for Automotive Interfaces: A Multimodal Vision-based Approach and Evaluations” in Intelligent TransportationSystems, IEEE Transactions on, vol. PP, no. 99, pp. 1–10, 2014.[11] F. Parada-Loira, E. González-Agulla, J. Alba-Castro, “HandGestures to Control Infotainment Equipment in Cars” in IEEE Intelligent Vehicles Symposium (IV), pp. 1-6, 2014. [12] Y. Oike, M. Ikeda, and K. Asada, “A 120 110 positionsensor with the capability of sensitive and selective lightdetection in wide dynamic range for robust active range finding,”

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2012 IEEE Int. Solid-State Circuits Conf. (ISSCC) Dig. Tech. Papers, 2012, pp. 396–398. [15] T. Ringbeck, T. Möller, and B. Hagebeuker,“Multidimensional measurement by using 3-D PMD sensors,”Adv. Radio Sci., vol. 5, pp. 135–146, 2007.[16] C. Niclass, M. Soga, H. Matsubara, S. Kato, and M.Kagami, “A 100-m range 10-frame/s 340 96-Pixel time-of-flightdepth sensor in 0.18- m CMOS,” IEEE J. Solid-State Circuits,vol. 48, no. 2, pp. 559–572, Feb. 2013.

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