Our project focuses on using fuzzy logic to make a car drive by itself. Autonomous cars are nothing new nowadays, but the path that we took difers from what is commonly implemented in such cases. When searching for a self-driving car, most of the results rely on a neural network, that learns how to navigate through the track. The issue with this approach is that the network only knows this one particular track and any other track would require training the network all over again. Our idea was to make a car, that would be able to navigate through any given track without the need to learn how to do it. To better describe the technologies that we used first we need to talk about the history of games and AI, then move focus to the more technical aspects of this project, including how the car gathers input and how it is being analyzed, to then cover all of the tests conducted on diferent car settings consisting of weight, drivetrain and maximum torque, finally reaching our small contest between AI and two diferent players.
77–84
interesting approaches to game theory and its
applications. For instance, virtual reality [6] was improved by
using the convolutional neural networks and many
diferent sensors for increasing the inversion in virtual reality.
Machine learning solutions was also applied in many
different real scenario [[7, 10]. Games are used for diferent
purposes, not only in entertainment but also in
educational areas. It was shown in [
One of the biggest diferences between humans and computers is the ability to use abstract concepts to describe reality. We can say for example that something is small, short, blue or that it is far away from us. While doing it, we do not assign a certain value to it, like 2cm3 2 seconds, #007EFF or 100km. Instead, we perceive those values as a scale - a certain range of values can be assigned to a certain word. For example, one person can perceive something as light when it weighs up to 2 kg, while another person may think that 5kg is still light and their scale Figure 2: Measuring the distance using raycast in Unity for the definition of the word ’light’ is more like 1-6kg because something under 1kg is perceived as ’very light’.
But how does it apply to computers? Computers do not 2. the number of input values determines the count understand abstract concepts, they use exact values to of rules - having 7 input values and 3 possible lindescribe things. While in some cases it is the preferred guistic values gives us 3 7 possible situations and approach, in others it might be a real issue. Imagine us- all of them need a rule. Decreasing the number of ing a brake only when the distance between the driven input values to 3 the count of rules changes to 33 car and the car in front of it is smaller than 1.5m and , making it possible to manage and less resource in addition always using only the full force of the brake. consuming.
Standing in trafic would be unbearable, would it not?
One of the solutions for this type of issue is using fuzzy Every input value needs to be fuzzified - a linguistic
logic. Fuzzy logic is a type of logic, where input contain- value is being assigned depending on the range the input
ing exact values is converted into linguistic values called value suits best.
antecedents, which can be then processed using rules, The mathematical equation (eq. 1) used for fuzzyfying
giving us diferent linguistic values describing the output the input:
called consequents, which are then defuzzyfied giving us
new exact values for the final output. This may sound
dificult or complicated, but actually, it is not that hard
to achieve. Using the example of our project, we will try
to show this process as simply as possible. Our car mea- (1)
sures the distance to the nearest obstacle in 7 directions: In the eq. 1 the values a bvand c depend on the
linto the front, 15∘ , 30∘ and 75∘ to the left, similarly to the guistic value the equation is used for. If we write those
right. Next, those falues are being used to calculate the values as linguisticValue=[a,b,c] then:
weighted average for 3 directions: left, front, and right. red=[
Finally, as we described earlier we compute the final Figure 3: rules output - horizontal and vertical values. Later it came to our attention, that those values needed to be slightly modified, so we added some more factors to the multipligreen. When all of the input values have those linguistic cation (Fig.5) values assigned, we can move on to the rules. When all This certainly is not the most optimal way to do it, but of the input values have those linguistic values assigned, for our needs was good enough we can move on to the rule shown in Fig. 3
As we said before, we need 27 rules to cover every 4. Raycast in Unity possible situation that may occur. Every rule consists of linguistic values for the input and linguistic values Raycast is a technology that allows you to determine the for the output. Using values of how well the inputs fit distance of a casting point projecting from a mesh that the red, yellow and green range, rule values are being has crossed its path (Of course, if this mesh has a collider). calculated simply by multiplying the values assigned to In order to properly project a raycast, it is necessary to the linguistic values in the rule. For example rule a con- provide it with a starting point and a direction relative sists of all red, so the rule value will be: = to the object associated with it, for example, a car or a * * ℎ rifle. This technology is successfully used in fps and RPG This way we determine which rule is the most accurate games to detect whether the target of a specific character for the given input - we simply take the one with the is in its field of view and is not obstructed by anything highest rule value. In our case the simplest way to de- (for example, enemies looking for the main character). In fuzzyfy was to assign certain values to the consequent the case of the former, raycast is also very often used to values and compute the output by multiplying the rule’s determine where the shot fired from the weapon will hit. consequent and its ruleValue (Fig.4) Although this method is slowly being abandoned as it is to create a track. Our first idea was simple: pick any premade area. This could be enough if the car would be driven by a user, but not for AI because a standard Figure 6: Flowchart of the AI’s algorythm track would not give the AI any information about its’ boundaries. The next guess was to upgrade the course for our car, upgraded version should have some kind of barriers to create a path to the finish line. This plan was not realistic enough - in the real world, the projectile’s quickly discarded and the next concept was to create a lfight path is not a perfectly straight line and additionally, track using prepared parts like turns or u-turns. The its speed is limited, so where the raycast would register biggest issue with this solution was the fact, that if the a hit, the real bullet could miss the target if it is mov- substrate was not perfectly flat, AI did not work properly. ing. Therefore, the gaming industry is slowly starting to The last idea, other than forcing our car to fly, was to use a diferent method, which is to generate additional create a route ourselves from scratch. We decided on bullets with a given initial velocity and mass. Of course, recreating one of the most famous auto and motorcycle however, there are exceptions where the raycast has an raceways: Laguna Seca Raceway. To better suit our needs advantage over simulated ballistics. One such exception it was shrunk (to spend less time on every lap) and the is dynamic fps games with relatively small maps. After driving surface was increased to make the turns simpler. all, the ballistics and the velocity of a projectile at short The base structure of the road was made in Blender. Due distances are not that significant, and raycast consumes to problems with mesh colliders, the walls are reinforced much fewer hardware resources. This is because it is only with additional blocks made from basic cubes in Unity. active for one frame (short hit test immediately after the This way the raycast could finally work properly. There shot), while the position of the bullet with active ballis- are two turns that turned out to be dificult both for AI tics must be counted until the hit and, additionally, many and the players. such bullets can appear in the memory at the same time. The left one (a) looks simple at first glance but with In our case, raycast was the best option for gathering data a long straight road before the turn where the car can about the surroundings, because it is a simple and fast drastically accelerate, it was enough to make the car way to do it. When driving a car we need as little delay unable to pass through without hitting the wall. The right as possible, so the simpler and less resourceconsuming one (b) is a u-turn which requires some skill from the method the better. players to drive without a collision, so it was too dificult
To make our car move, we needed a simple script and for AI regardless of the car’s speed when entering the a bit of Unity’s physics. We added round colliders into turn. The title of this paragraph still seems to be unrelated the car’s wheels and we by rotating them we move the to the topic, so let us explain. Accidentally we recreated car. one of the scenes from the series ’Initial D’, because the
The car also has a rigidbody attribute, so the Unity’s car one of the members of our group picked from Unity physics engine can apply gravity to it and detect colli- Asset Store is a model of Toyota AE86 (main character’s sions. car) and the turn (a) was also dificult for the characters It is very unlikely for cars to float in space so we needed of this series. Unfortunately AI we created does not drift very well. At the moment of writing this article, the model is no longer available, because the package has been deprecated from the Asset Store. 5. Experiments With this knowledge we focused on selecting the friction and drag parameters for the physics of the vehicle In order to optimize the vehicle so that it would lap the wheels. Until the expected results were obtained, we track in the best time possible and without collisions, e modified both the sliding and the static friction. Ophad to conduct a series of tests consisting of changing timal efects were acquired only when the extreme of selected parameters in Unity and checking which config- static friction was about twice as high as the sliding urations would give the best results. Before conducting friction. We also needed to adjust the weights of the more constructive tests, we began with random parame- wheels and of the car itself to more reasonable amounts. ters and started testing how MaxTorque and the wheel WheelFrictionCurve is used by the WheelCollider to drive impact a car’s ability to maneuver (simultaneously describe the friction properties of the wheel tire. The we were trying to find room for the code’s improvement). curve takes a measure of tire slip as an input and gives
We found that as the expected time needed to lap the a force as output. The curve is approximated by a twotrack decreased as MaxTorque increased until the point, piece spline. The first section goes from (0,0) to (exwhere the car could no longer respond fast enough and tremumSlip,extremumValue), at which point the curve’s started to hit a wall. Some of the values stayed unmea- tangent is zero. The second section goes from (extremumsured because we found them insignificant. In the table Slip,extremumValue) to (asymptoteSlip,asymptoteValue), where curve’s tangent is again zero. Wheel collider com- relation to the center of mass of the wheel with a radius putes friction separately from the rest of the physics of 30 centimeters. As a result, we achieved not only the engine, using a slip based friction lack of the vehicle overturning but also the curb weight model. It separates the overall friction force into a and the engine torque was significantly reduced. After ”forwards” component (in the direction of rolling, and establishing which friction and drag parameters were the responsible for acceleration and braking) and ”sideways” most efective, we moved onto the next text in which we component (orthogonal to rolling, responsible for keep- wanted to see how changing the maximum torque paraming the car-oriented). Tire friction is described separately eters will afect the time the car will finish the race. The in these directions using WheelCollider.forwardFriction table below shows the dependence of max torque on time. and WheelCollider.sidewaysFriction. In both directions Changing max torque values from 500 to 1000 in steps it is first determined how much the tire is slipping. Then of 100 with the Front Wheel Drive. Then we decided the slip value is used to find out the tire force exerted on to check which drivetrain setting would be the most efthe contact. Finally, after making many adjustments to fective for the fastest track completion. In this test, the the parameters, we came to the conclusion that the best maximum torque remained 800 for both the front-wheelresults were obtained when both of the drag parameters drive and the rear-wheel drive, but 400 for the all-wheel were set to the minimum. Then the center of friction drive. It was measured for 3 attempts. The table below force application acting on the wheels was lowered in shows the dependence of diferent drive layouts on time
In conclusion, AI works properly up to a certain velocity.
However, after reaching higher speeds, it is not able to respond fast enough, which results in a collision with the wall. The car is also not capable of coping with an obstacle placed closely in front of it, falling into the path selection loop of going slightly forwards and slightly Table 1 backward. Not surprisingly, when it comes to checking Obtained results whether the player or artificial intelligence is doing a better job, as long as the best technique to achieve the best time will be drifting, AI will fall far behind the players or even not finish the lap. Despite the dificulties Table 2 encountered, the following situation was achieved: the Max torque value and obtained time car, regardless of its starting point, is able to move and complete the given track without major issues. However, the results achieved by a human driver are still noticeably
To summarize, by setting the max torque value to 800, better than those achieved by artificial intelligence. Ultithe best time to complete the track was achieved. As mately, the chosen goal was accomplished because the for the drivetrain, the front wheel drive turned out to car can indeed successfully drive without human interbe the best choice, also achieving the fastest completion vention and without the need to be trained beforehand. times. Taking into consideration all the tests performed,