Vamos Automotive Simulator

Sam Varner snick-a-doo@comcast.net

Vamos is an automotive simulation framework with an emphasis on thorough physical modeling and good C++ design. Vamos includes a real-time, first-person, 3D driving application.

This file documents Vamos version 0.7.0.

1. Let's Go

The ‘vamos’ application lets you experience the simulation first hand. Its main purpose is to be a test bed for the libraries. It is not intended to be a polished end-user application. However, you can drive on a number of tracks and try to beat your best time. Or you can just have fun driving on, and over, the ragged edge.

1.1 Getting Started

When you start the application with no arguments you will be looking out over the hood of your car, down the front straight of a simple, fictitious circuit. Give the car a little gas and shift into first by pressing and releasing the first joystick button. The clutch is engaged gradually, so you will need to increase the throttle to keep the engine revs up. If you stall, shift back to neutral (second button) and press the <s> key to restart the engine. See section Controls.

Once you get going you will need to shift into second. When you press the button to shift, the clutch is disengaged. It is re-engaged when you release the button. You will need to back off the throttle when the clutch is disengaged in order to make your shifts smooth. As with shifting to first gear, the clutch is engaged gradually, although much more quickly.

The first turn on the circuit is a sharp left-hander at the top of a hill. This is a good place to practice sliding the car through a turn. You will probably hear the tires slide as you enter the turn. Don't worry, the tires actually have more grip when they're sliding a little. However, you do lose some directional stability. So you point the nose a little toward the center of the turn and use the throttle to hold the car in the turn. If you slide the car more than a little, you will lose grip and probably find yourself in the gravel.

When driving on the edge, the throttle and brake do as much as the steering wheel to control the trajectory of the car. In general, accelerating tends to straighten out the car and braking tends to turn the car more. To demonstrate this, try backing off the throttle midway through a turn. You'll find that the back end steps out a little causing the car to turn in.

1.2 Robot Cars

You can race against computer-controlled opponents. Use the o option with a numeric argument to race against other cars. Use the d if you just want to watch.

1.3 Controls

The car can be driven with a joystick, keys, or even a mouse. A joystick is highly recommended.

Keys, buttons, and joystick axes are mapped to functions in an XML file in the data directory (usually ‘/usr/local/share/vamos/controls’). By default the file ‘default-controls’ is used. You can specify a different file with the -a or --controls= options. The default control bindings are as follows:

The `*' symbol indicates that the action is performed gradually after the key or button is pressed.

When shifting, pressing the key or button causes the clutch to be disengaged before the new gear is selected. Releasing the button releases the clutch. The clutch is engaged slowly when shifting from neutral, and more quickly for other gears. The clutch is always disengaged quickly.

1.4 Control File Format

Here's the format of a controls file.

<controls name="Name">
  <!-- Key Binding -->
  <bind>
    <function>function name</function>
    <key>k</key>[<up|down/>]
    [<time>t</time>]
  </bind>

  <!-- Button Binding -->
  <bind>
    <function>function name</function>
    <button>b</button>[<up|down/>]
  </bind>

  <!-- Axis Binding -->
  <bind>
    <function>function name</function>
    <axis>a</axis>
    [<factor>f</factor>]
    [<offset>o</offset>]
    [<minimum>m</minimum>]
  </bind>
</controls>

The function tag gives the name of the function to bind. Any member funciton of Gl_Car_World that takes two double arguments and returns a bool can be bound. The case of the name inside the function tag must match the actual function's name, and underscores must be replaced with single spaces.

The down tag binds the function to a key (or button) press; up binds it to a key release. If neither is specified, the function is bound to a key press.

The time tag sets how long it takes for setting to be ramped up to its target value. It is used for controling continuous values, like throttle, from the keyboard. The default time is 0.

For joystick axes, vaules range from -1 to 1. This number is multiplied by the value in the factor tag and then the value in the offset tag is added. The result is clipped at minimum. The defaults are 1, 0, 0, respectively.

1.4.1 Bindable Functions

These are the functions that can be bound to controls.

pause

Pause the simulation.

quit

Quit the program.

cycle view

Change the point-of-view from car to trackside to overhead.

read car

Read the car definition file.

read track

Read the track definition file.

read world

Read the world definition file.

restart car

Put the car at the starting line.

reset car

Put the car back on the track.

fill tank

Fill the car's gas tank.

gas

Operate the throttle.

brake

Operate the brakes.

steer

steer left

steer right

Operate the steering wheel. The 'steer left' and 'steer right' functions are useful for binding to keys.

shift up

shift down

Select an adjacent gear, except when in neutral.

shift up disengage

shift down disengage

Select an adjacent gear and operate the clutch, except when in neutral.

initial shift up

initial shift down

Select an adjacent gear when in neutral.

initial shift up disengage

initial shift down disengage

Select an adjacent gear and operate the clutch when in neutral.

clutch

Operate the clutch.

engage clutch

disengage clutch

Operate the clutch, except when in neutral

initial engage clutch

initial disengage clutch

Operate the clutch when in neutral

A function can be bound to more than one control. However, when the simulation is running, the joystick is read after the keys. If, for example, you bind the throttle to the up arrow key and to a joystick axis, the joystick (if present) will override the keyboard.

Similarly, more than one function can be bound to a control. Each function is called in turn until one of them returns true.

For shifting, you will likely bind two functions to each shifting control, one for shifting from neutral (e.g. initial shift up) and the other for shifting from other gears (e.g. shift up). If you bind the clutch to a key or button, rather than a continuous contral, you will also bind two functions to the clutch controls. The reason is that you may want different behavior from the clutch in these two situations.

When shifting from neutral to first, you will let the clutch out slowly to get the car started without stalling. When shifting to other gears you will operate the clutch more quickly. You can make this happen by binding both initial shift up disegnage and shift up disengage to the same key or button, and using a larger value in the time tage for initial shift up disengage.

1.5 Dashboard

Several rows of text are printed along the bottom of the screen to provide some information about the car, similar to the gauges on a car's dashboard. You also get some information that you would not normally see on a dashboard. Here's what is shown, going down the columns, starting on the left.

RPM

The engine speed in revolutions per minute.

Torque

The current engine torque in Newton-meters.

Speed

The car's speed in kilometers per hour.

Gear

The currently selected gear. ‘N’ stands for neutral and ‘R’ is for reverse.

Break and Throttle

The cyan bar shows the current brake setting. The magenta bar shows the throttle setting. These bars are useful for evaluating robot cars.

Slip Ratios

The slip ratios for each of the tires as a percentage. A slip ratio is the difference between the speed of the contact patch and the road moving beneath it, divided by the speed of the wheel's hub. Rolling without sliding yields a slip ratio of zero. Locking the wheels results in a slip ratio of 100%. Slip ratios are useful for seeing how close you are to the limit of adhesion. A ratio of 9% or 10% is usually close to optimal.

Fuel

Amount of fuel remaining in liters.

Air Density

The current density of the air that the car is driving through. This number decreases in another car's slipstream.

Lap Time

The elapsed time for the current lap.

Last

The time taken to complete the previous lap and the difference between this time and the best time.

Best

The shortest lap time so far.

frame/s

The current frame rate.

Sector

The number of the current timing sector and the elapsed time for that sector.

Best

The best time for the current sector.

Last Sector

The time taken to complete the previous sector and the difference between this time and the best time for that sector.

Distance

The distance from the start/finish line in meters.

1.6 Cars

A number of different car definitions are provided. The car can be selected with -c <car> or --car=<car>, where <car> is one of the following

‘F1’

A modern Formula One car.

‘F1-1967’

A late sixties Formula One car. For reasons I don't yet understand, this car is very difficult to control.

‘front-drive’

A front wheel drive car.

‘GT’

‘default-car’

A rear wheel drive sports car.

‘trainer’

An under-powered car for beginners.

1.7 Car File Format

The car definition goes inside a car tag. You can assign a name to the car with the name attribute.

<car name="GT">
  ...
</car>

The sections below show how the various subsystems are defined.

1.7.1 Robot Parameters

These settings define the target performance of the robot car. The robot will use the specified slip ratio for acceleration. Deceleration and lateral acceleration give the performance targets for braking and cornering on a flat and level road with no aerodynamic assistance. The actual targets are adjusted in real time for the slope of the track and aerodynamic downforce.

Note that these are just targets. If they are set to values that can't be achieved by the car the robot will drive the car off the road.

  <robot>
    <slip-ratio>9.0</slip-ratio>
    <deceleration>1.4</deceleration>
    <lateral-acceleration>1.5</lateral-acceleration>
  </robot>

1.7.2 View

The driver's point-of-view is set with the position tag. You may use whatever units you like, as long as you're consistent. See section Units. The horizontal field-of-view is set with the field-width tag. The vertical field-of-view is calculated automatically from the current window geometry.

  <view>
    <position>[ 1.3, 1.0, 0.8 ]</position>
    <field-width>60.0</field-width>
  </view>

1.7.3 Steering

The maximum steering angle is set with the max-angle tag. The exponent detemines how linear the steering response is. A higher number makes the steering less sensitive at small angles.

  <steering>
    <max-angle>10.0</max-angle>
	<exponent>3.0</exponent>
  </steering>

1.7.4 Drivetrain

The drivetrain section defines the engine, clutch, transmission and differential.

  <drivetrain>
    <engine>
      ...
    </engine>

    <clutch>
      ...
    </clutch>

    <transmission>
      ...
    </transmission>

    <differential>
      ...
    </differential>
  </drivetrain>

The subsections of the drivetrain are described below.

    <engine>
	  <position>[ 1.5, 1.0, 0.2 ]</position>
	  <mass>200.0</mass>
      <max-power>3.0e5</max-power>
	  <peak-engine-rpm>8000.0</peak-engine-rpm>
	  <rpm-limit>10000.0</rpm-limit>
	  <inertia>0.10</inertia>
	  <idle>0.05</idle>
	  <start-rpm>1000</start-rpm>
	  <stall-rpm>500</stall-rpm>
	  <fuel-consumption>0.0001</fuel-consumption>

      <sound>
        <file>engine.wav</file>
		<pitch>0.01</pitch>
		<volume>0.8</volume>
		<throttle-volume-factor>1.0</throttle-volume-factor>
		<engine-speed-volume-factor>0.001</engine-speed-volume-factor>
	  </sound>
    </engine>

The position and mass parameters affect the weight distribution of the car. The torque curve is calculated from max-power and peak-engine-rpm using a polynomial expression given in Motor Vehicle Dynamics, Genta (1997), where peak-engine-rpm is the engine speed at which the maximum power output (max-power) is achieved. A rev limit can be set with rpm-limit. The rotational inertia of the moving parts is inertia. idle is the throttle position at idle. Starting the engine initially sets the engine speed to start-rpm. Letting the engine speed drop below stall-rpm makes the engine stall. The rate of fuel consumption is set with fuel-consumption.

The engine sound is set in the sound section. file is the name of a WAV file in the ‘data/sounds’ directory. throttle-volume-factor and engine-speed-volume-factor determine how the loudness of the sound changes.

    <clutch>
      <sliding>0.5</sliding>
	  <radius>0.25</radius>
	  <area>0.2</area>
	  <max-pressure>1.0e4</max-pressure>
    </clutch>

The torque on the clutch is found by dividing the clutch pressure by the value in the area tag and multiplying by the radius and sliding (friction) parameters.

The gear ratios can be defined in two different ways inside the transmission tag. The ratios can be defined individually as in the example below. The first number inside the brackets is the gear (-1 is reverse), and the second is the clutch speed divided by the driveshaft speed.

    <transmission>
	  <gear-ratio>[ -1, -2.69 ]</gear-ratio>
	  <gear-ratio>[ 1, 2.53 ]</gear-ratio>
	  <gear-ratio>[ 2, 1.71 ]</gear-ratio>
	  <gear-ratio>[ 3, 1.42 ]</gear-ratio>
	  <gear-ratio>[ 4, 1.19 ]</gear-ratio>
	  <gear-ratio>[ 5, 1.04 ]</gear-ratio>
	  <shift-delay>0.2</shift-delay>
    </transmission>

Alternatively, the number of gears and the highest and lowest ratios can be specified. The other gears will be calculate such that the reciprocals of the ratios are equally spaced.

    <transmission>
	  <forward-gears>5</forward-gears>
	  <first-ratio>3.21</first-ratio>
	  <last-ratio>1.10</last-ratio>
	  <shift-delay>0.2</shift-delay>
    </transmission>

The shift-delay tag tells how long it takes to change gears. For a paddle-shifter, like a modern Formula One car, shift-delay can be set to zero.

1.7.5 Fuel Tank

The fuel tank's position, the current volume of fuel and the density of the fuel affect the car's weight distribution. The capacity tag sets the maximum volume of fuel that the tank can hold. The initial volume is set with the volume tag. The density of the fuel is set with fuel-density.

  <fuel-tank>
    <position>[ 1.00, 1.00, 0.25 ]</position>
	<capacity>100.0</capacity>
	<volume>100.0</volume>
	<fuel-density>0.8</fuel-density>
  </fuel-tank>

1.7.6 Wheels

The wheel section contains information about the suspension, tire, and brakes as well as the wheel itself. The side and end attributes tell where the wheel is located. The values of these attributes are important.

The steered tag tells that the wheel responds to steering input. The driven tag tells that torque from the engine is applied to the wheel. Only two wheels may have a steered tag, and only two may have a driven tag.

  <wheel side="right" end="front">
    <steered/>
    <driven/>
    <position>[ 3.0, 0.05, -0.1 ]</position>
	<mass>30.0</mass>
	<restitution>0.1</restitution>
    <suspension>
      ...
    </suspension>
    <tire>
      ...
    </tire>
    <brakes>
      ...
    </brakes>
  <wheel>

Values set in one wheel section are persistent; if you want the same value for another wheel, you do not need set it.

The suspension, tire, and brakes sections are described below.

1.7.7 Suspension

    <suspension>
	  <position>[ 3.0, 0.35, -0.1 ]</position>
	  <hinge>[ 2.0, 0.35, 0.3 ]</hinge>
	  <spring-constant>22000.0</spring-constant>
	  <bounce>2000.0</bounce>
	  <rebound>2000.0</rebound>
	  <travel>0.4</travel>
	  <max-compression-velocity>10.0</max-compression-velocity>
	  <camber>-2.0</camber>
	  <caster>5.0</caster>
	  <toe>-2.0</toe>
	</suspension>

The hinge is the center of the wheel's path as the suspension moves. The location of the hinge is determined by suspension geometry, and may be outside of the car itself. Currently, this parameter has no effect of performance. It may be used in the future for configuring anti-dive and anti-squat suspension geometries.

bounce and rebound are the damping coefficients for compression and expansion of the suspension, respectively. If the speed at which the suspension is compressed, or expanded exceeds the value in max-compression-velocity, the dampers “lock up.”

Wheel alignment is set with the camber, caster, and toe tags. All angles are in degrees.

1.7.8 Tires

The longitudinal, transverse, and aligning section each contain a vector of “magic formula” coefficients as presented in Motor Vehicle Dynamics, Genta (1997). The two elements of rolling-resistance are the constant and velocity-squared terms, respectively.

	<tire>
      <friction>
        <longitudinal>
          [ 1.65, 0.0, 1690.0, 0.0, 229.0, 0.0, 0.0, 0.0, -10.0, 0.0, 0.0 ]
        </longitudinal>
	    <transverse>
	      [ 1.80, 0.0, 1690.0, 800.0, 6.03, 0.0, -0.359, 1.0, 0.0, -6.11e-3, -3.22e-2, 0.0, 0.0, 0.0, 0.0 ]
	    </transverse>
	    <aligning>
	      [ 2.07, -6.49, -21.9, 0.416, -21.3, 2.94e-2, 0.0, -1.20, 5.23, -14.8, 0.0, 0.0, -3.74e-3, 3.89e-2, 0.0, 0.0, 0.639, 1.69 ]
	    </aligning>
	  </friction>
	  <radius>0.310</radius>
      <rolling-resistance>[ 1.3e-2, 6.5e-6 ]</rolling-resistance>
	  <rotational-inertia>10.0</rotational-inertia>
    </tire>

1.7.9 Brakes

    <brakes>
	  <friction>0.8</friction>
	  <max-pressure>2.0e6</max-pressure>
      <front-bias>0.55</front-bias>
	  <radius>0.2</radius>
	  <area>0.01</area>
    </brakes>

front-bias is the fraction of braking pressure applied to the front brakes.

1.7.10 Particles and Contact Points

Particles affect the mass distribution of the car.

  <particle>
    <position>[ 2.0, 1.0, 0.5 ]</position>
	<mass>100.0</mass>
  </particle>

Contact points are particles that participate in collisions. The material specified in the material tag (either “metal” or “rubber”) determines the sound made when contact is detected. The coefficients of friction and restitution are set with the friction and restitution tags, respectively.

  <contact-point>
    <mass>40.0</mass>
    <position>[ 0.0, 0.0, 0.0 ]</position>
	<material>metal</material>
	<friction>0.5</friction>
	<restitution>0.1</restitution>
  </contact-point>

1.7.11 Drag and Wings

The aerodynamic properties of the car are determined by the drag and wing sections. The frontal area and coefficient of drag, set it frontal-area and drag-coefficient, are used to calculate the drag force.

  <drag>
    <position>[ 2.0, 1.0, 0.25 ]</position>
	<frontal-area>2.0</frontal-area>
	<drag-coefficient>0.3</drag-coefficient>
  </drag>

Downforce can be added with wings. The amount of downforce is determined by the value in the lift-coefficient tag. If the lift coefficient is positive, upforce is generated. This is usually undesirable for cars. The efficiency determines how much drag is added as downforce increases. The surface-area is the surface area of the wing. This value is also used in the drag calculation.

  <wing>
    <position>[ 0.0, 0.9, 0.5 ]</position>
	<frontal-area>0.2</frontal-area>
	<surface-area>0.5</surface-area>
	<lift-coefficient>-4.0</lift-coefficient>
	<efficiency>0.5</efficiency>
  </wing>

1.8 Tracks

Once you get bored with the default, you might want to try driving on some different tracks. The track can be selected using command line arguments. Use either vamos -t <track> or vamos --track==<track>, where <track>, is the name of one of the XML files in the ‘data/tracks’ directory. There are files for almost all of the Formula One circuits for the past couple of decades, plus a few more. These include

‘drag’

A striaight flat strip of road.

‘Monza’

The high-speed Italian circuit.

‘Peanut’

‘default-track’

A simple track.

‘Road_Atlanta’

The Georgia-shaped track in Georgia.

‘Silverstone’

The home of the British grand prix.

‘skid_pad’

A cirular track for testing handling.

‘Spa’

The Spa-Francorchamps track in Belgium.

‘Suzuka’

The track for many Japanase Grands Prix.

You can use the trk-convert program to turn a track file for RARS (Robot Auto Racing http://rars.sourceforge.net) into a C++ track file for Vamos. The converted files usually need some adjusting, so you'll have to learn a little about Vamos track files.

1.9 Track File Format

Tracks are defined in XML files. Here's the beginning of a track file.

<track name="Peanut">
  <racing-line show="0">
    <iterations>800</iterations>
    <stiffness>1.0</stiffness>
    <damping>0.01</damping>
    <margin>1.6</margin>
    <resolution>14.0</resolution>
  </racing-line>

1.9.1 Racing Line

The racing line section is optional. A good line is calculated for almost all tracks using the default parameters (shown). Changing the show parameter to 1 will cause the racing line to be drawn on the track. However, the -l option is a more convenient way to do this.

Use more iterations if the racing line does not converge to something reasonable. You can try fewer to reduce the calculation time.

The racing line is calculated by simulating a chain of masses with springs that tend to straighten the chain. Stiffness sets the spring constant. Damping prevents runaway oscillation.

The margin is how close to the edge of the road the line is allowed to get.

Resolution is the distance between masses. This parameter defaults to the width of the road at the starting line.

The racing line can be modified by the tags racing-line-adjustment and curvature-factor in the road. See below.

1.9.2 The Sky Box

  <sky>
    <sides>textures/sky_sides.png</sides>
	<top>textures/sky_top.png</top>
	<bottom>textures/sky_bottom.png</bottom>
	<smooth/>
  </sky>

The sky section describes the sky box, which is a cube onto which a background is mapped. The sides image is wrapped around the front, right, back, and left sides of the sky box. The optional smooth tag can improve the quality of the sky box images.

1.9.3 Materials

After the sky box, the properties of the various materials that make up the track are defined.

  <material name="track" type="asphalt">
	<friction>1.0</friction>
	<restitution>0.1</restitution>
	<rolling>1.0</rolling>
	<drag>0.0</drag>
	<bump-amplitude>0.01</bump-amplitude>
	<bump-wavelength>100.0</bump-wavelength>
	<texture>
	  <file>textures/track2.png</file>
	  <length>200.0</length>
	  <smooth/>
	  <mipmap/>
	</texture>
  </material>

The name is used to identify the material in other parts of the file. The type helps determine what sound is played. The type must be one of rubber, metal, asphalt, concrete, grass, gravel, or dirt.

The friction tag sets the relative friction of the surface. If, for example, you want to specify another surface that has half the friction of asphalt, you whould set the friction value to 0.5. The calculation of the actual frictional force involves the car. Similarly, relative values of the coefficient of restitution, rolling resistance, and velocity-dependent drag are set with the restitution, rolling, and drag tags.

The bumpiness of the surface is set with the bump-amplitude, and bump-wavelength tags. They define a sinusiodal variation in the track's elevation. You may use whatever units you like, as long as you're consistent. See section Units.

The texture image is set in the texture section. The file is the name of a PNG image file. The physical size that the image covers is set with the length and width tags. In this example, the width tag is omitted. As a result, the texture is stretched to fit the width of the track.

The smooth and mipmap tags improve the quality of the images, but they also reduce the frame rate.

1.9.4 Segments

The materials are grouped into “segments” that describe the materials for the track, kerbs, shoulders, and barriers.

  <segment name="left turn">
    [ wall grass kerb track kerb gravel tires ]
  </segment>

The name is used to identify the segment in other parts of the file. Inside the segment tag is an array of material names. The material of the right-side barrier (as seen from a car traveling forward around the track) is first.

1.9.5 Track Geometry

The track is made up of road sections. Here is a simple road section

  <road segment="left turn">
    <resolution>5.0</resolution>
	<length>130.0</length>
	<radius>160.0</radius>
  </road>

The segment attribute names a list of materials defined earlier in the file. The resolution sets the size of the quadrilateral divisions in the road section. The smaller the resolution, the more closely the section approximates a smooth curve. The length and width are given in meters. However, any system of units can be used as long as they are used consistently throughout the simulation for both derived and fundamental quantities.

The first road section must set the width of the track and shoulder, and also the height of the barriers. These dimensions are specified as (distance, width) pairs. Any number of pairs may be specified for a given width, the program will interpolate linearly between specified points.

  <!-- front straight -->
  <road segment="straight pit">
    <resolution>10.0</resolution>
	<length>100.0</length>
	<left-width>[ 0.0, 25.0 ]</left-width>
	<right-width>[ 0.0, 25.0 ]</right-width>
	<left-road-width>[ 0.0, 8.0 ]</left-road-width>
	<right-road-width>[ 0.0, 8.0 ]</right-road-width>
	<left-wall-height>2.0</left-wall-height>
	<right-wall-height>2.0</right-wall-height>
	<elevation>[ 20.0, 0.0 ]</elevation>
	<elevation>[ 200.0, 5.0 ]</elevation>
  </road>

Similarly, any number of elevation points may be specified. A spline is used to interpolate between elevation points to achieve smooth elevation changes.

The racing-line-adjustment adjusts the edges of the track left (positive) or right (negative) for the purpose of calculating the racing line. It is often useful to do this to shift the line toward the edge of the track so that the robot cars will run onto the kerbs.

If the cars go too fast or too slow for on a particular segment, the curvature-factor can be specified to make the robots think the racing line is curved more or less than it actually is. The actual curvature is multiplied by this number. If it's greater than one the cars will go slower; if it's less they'll go faster.

1.9.6 Braking Markers

Braking markers are signs that show the distance to an upcoming turn. For turns approached a high speed, markers at 150 m, 100 m, and 50 m are typically shown.

  <road>
    ...
	<braking-marker>
	  <file>textures/50.png</file>
	  <distance>50.0</distance>
	  <size>[ 1.4, 0.7 ]</size>
	  <offset>[ 2.0, 0.0 ]</offset>
	  <side>right</side>
	</braking-marker>
	<braking-marker>
	  <file>textures/100.png</file>
	  <distance>100.0</distance>
	</braking-marker>
	<braking-marker>
	  <file>textures/150.png</file>
	  <distance>150.0</distance>
	</braking-marker>
    ...
  </road>

Once the size and offset parameters have been set, they do not need to be specified again unless you want to use different values.

1.9.7 Kerbs

Concrete kerbs are often placed along the insides of curves, and on the opposite side at the curve exits. I'm not really sure why. Nonetheless, kerbs can be specified in the road sections.

  <road>
    ...
	<left-kerb>
	  <start>
        <distance>10.0</distance>
		<transition>
		  <length>4.0</length>
		  <width>1.0</width>
		</transition>
	  </start>
	  <end>
        <distance>100.0</distance>
		<transition>
		  <length>4.0</length>
		  <width>1.0</width>
		</transition>
	  </end>
	  <profile>[ 1.0, 0.1 ][ 3.0, 0.1 ][ 3.1, 0.0 ]</profile>
	</left-kerb>

    <right-kerb>
      ...
    </right-kerb>
    ...
  </road>

Each road section can have a left-side and a right-side kerb. A set of coordinates of the form [ distance-from-edge-of-track, elevation-above-track ] set the shape of the kerb in the profile tag. A [ 0.0, 0.0 ] coordinate is inserted automatically.

The start and end tags tell where and how the kerb begins and ends. If the distance is positive it is relative to the beginning of the road section. If it's negative it is measured from the end. The distance may be omitted for either or both ends. The default start and end distances are zero and the end of the track, respectively.

The transition section tells how the ends of the kerb are capped. In the example above, the kerb tapers down track level and a width of 1.0 m in a distance of 4.0 m. The transition does not add length to the kerb. The start and end tags specify the endpoints of the kerb including the transitions.

If the end tag is omitted on one segment and the start tag is omitted on the next, the kerb will run seamlessly across the segment boundary. If the kerb should run through the segment and connect with kerbs on the next and previous segments an empty tag (<left-kerb/> or <right-kerb/>) will do.

Once the transition length and width, and the profile are set they do not need to be specified again unless you want to use different values. You can use <transition/> to specify a transition with the previously set values. For example, this kerb runs the entire length of its road section and is capped with transitions at both ends.

    <right-kerb>
	  <start><transition/></start>
	  <end><transition/></end>
    </right-kerb>

If there's no start tag, the kerb starts at the beginning of the road section with no transition. If there's to end, the kerb ends at the end of the road section. To make the kerb join smoothly across two road sections, omit the end in the first section, and omit the start in the second.

Kerbs are typically serrated. Again, I don't know why. This can be simulated by setting the bump parameters on the kerb material defined near the beginning of the track file.

1.9.8 Closing a Circuit

Adjusting a track to make meet the beginning seamlessly is tedious. If a <circuit/> tag is included, the program will make the adjustments automatically. You can specify how many of the last segments will be adjusted with the segments attribute. For example, with <circuit segments="2"/> only the last two segments will be changed. Note the quotes around the value (required by the XML standard) and the trailing slash.

Allowed values for the segments tag are 0, 1, 2, and 3. The default is 3.

‘3’

Adjust the length of the next-to-last segment (which must be a curve), to make the last segment parallel to the first. Adjust the length of the third-to-last segment (which must be straight) to put the last segment in line with the first. Adjust the length of the last segment so that it meets the beginning of the first.

‘2’

Adjust the radius and length of the next-to-last segment to align the last with the first. Adjust the length of the last segment so that it meets the beginning of the first.

‘1’

Adjust the length of the last segment so that it meets the beginning of the first.

‘0’

Adjust nothing.

In all cases (including 0) the elevation curve is forced to close.

If the track can not be closed with the specified adjustments, or the requirements about what segments must be stright or curved, the exception Vamos_Track::Can_Not_Close is thrown.

1.10 Worlds

The “world” specifies various environmental factors. Here's the entire default world file.

<world name="Earth">
  <!-- Acceleration due to gravity -->
  <gravity>9.8</gravity>

  <maximum-time-step>0.01</maximum-time-step>

  <atmosphere>
    <!-- Air density -->
	<density>1.2</density>
	<!-- Wind velocity -->
    <velocity>[ 0.0, 0.0, 0.0 ]</velocity>
  </atmosphere>

  <lighting>
    <!-- Direction to the light source -->
    <source-position>[ 0.0, -1.0, 1.0 ]</source-position>
	<!-- RGB for ambient light -->
	<ambient>[ 0.7 , 0.7, 0.7 ]</ambient>
  </lighting>
</world>

Here is a description of the sections.

gravity

Acceleration due to gravity. The typical value for Earth is 9.8 m/s^2.

maximum-time-step

Each frame in the simulation will be sub-divided into time steps no larger than this value. If you see jitter when the car is stopped, try lowering the maximum time step. However, you may take a performance hit, if the value is too small.

atmosphere

Density of the air and wind velocity.

lighting

Light source position and ambient light level.

Other world files can be specified with the --world= or -w options. Just for fun, a world file for the moon is provided.

2. Units

A number that describes a physical quantity is meaningless unless the units of measure are given. If we have a length of 20, we don't know if it's 20 meters, 20 feet, or 20 light years. Despite this fact, there are no units specified in Vamos.

Consider the fundamental quantities to be time, length, and mass. From these, you can derive the units for any quantity used in the simulation. For instance, the units on velocity are a length unit divided by a time unit. Force units are mass times length divided by time squared. As long as the fundamental and derived units are consistent, it does not matter what base units are used.

There's one exception. Since the simulation relies on library functions for timing information, and these libraries use seconds, the unit of time must be seconds.

I always use SI (metric) units because it's easy to keep the base and derived units consistent. The SI base units are the meter (m) for length and kilogram (kg) for mass. Power is derived quantity with units of Watts. A Watt is a kg*m^2/s^3. If you use feet and slugs as your base unit, then your power will be in slug*ft^2/s^3; you can't simply use horsepower.

Derived units used in the simulation are

• area (distance^2)
• volume (distance^3)
• speed (distance/time)
• acceleration (distance/time^2)
• force (mass*acceleration)
• torque (force*distance)
• engine power (force*distance/time)
• spring constant (force/distance)
• damping (force/speed)
• density (mass/volume)

There are some places where non-SI units are used. All angles are specified in degrees. Engine speeds are specified in rotations per minute (RPM). The coefficients for tire friction have their customary units.

3. Code Reference

The code is devided into four modules that reside in four namespaces, Vamos_Geometry, Vamos_Body, Vamos_Track and Vamos_World. Each namespace contains the code for a library. These libraries are libvamos-geometry, libvamos-body, libvamos-track, and libvamos-world. The geometry library has classes for vectors, matrices and curves. The body library has a class for a rigid body and classes for a car and its parts. It also has other classes that are needed by more than one of the other libraries. The track library has the classes needed for building a track. The world library handles a rigid body's interaction with the track.

The geometry library is used by both the body and world libraries. The body library is used by the world library. The dependency graph looks like this:

           libvamos-geometry
              /    |
             /     |
  libvamos-media   |
             \     |
              \    |
               ----+----          
              /    |    \
             /     |     \
  libvamos-track   |   libvamos-body
             \     |     /
              \    |    /
            libvamos-world

Libraries farther down the graph depend on the libraries above them. If you only need the services of the geometry library, then you only have one library to link. If you use the body library, then you need to link the geometry and media libraries as well. If you use the world library, then you need to link all five. When linking multiple libraries you may need to make sure that libvamos-geometry is linked first, followed by libvamos-body, and then libvamos-world. If you get errors from the linker about undefined references to functions defined in one of these libraries, then you may have to adjust the link order.

Care was taken to avoid a dependency of libvamos-track on libvamos-body and vice versa. This allows cars and tracks to tested independently.

3.1 The Geometry Library

The geometry module is a collection of mathematical constants, functions, and objects. There are also a few less mathematical classes that are required by more than one other module. This is done to avoid dependency problems.

3.2 Three_Vector

A Three_Vector represents a vector in three dimensions. Some supported operations are

• subscripting using []
• vector addition and subtraction using + and -
• multiplication and division by a scalar using * and /
• left and right matrix multiplication using *
• dot and cross products using the dot() and cross()methods
• projection onto another vector using the project() method
• magnitude using the abs() method

Matrix multiplication is done with a Three_Matrix.

3.3 Three_Matrix

A Three_Matrix represents 3x3 matrix. It's suitable for representing a three-dimensional rotation matrix or inertia tensor. Some suported operations are

• subscripting using []
• matrix addition and subtraction using + and -
• multiplication and division by a scalar using * and /
• left and right vector multiplication using *
• matrix multiplication using *
• eigenvalue and eigenvector determination
• inversion

3.4 Inertia_Tensor

An inertia tensor is a matrix that describes a rigid body's responce to torques. The Inertia_Tensor generates the tensor from the locations of masses on a body. The masses and positions are specified using the add() method. The inertia() method returns the moment of inertia for a force applied at a particular point on the body.

3.5 Two_Point

A Two_Point describes a point in a plane. It is a struct with two data members, x and y. A constructor is provided for initializing the members. No vector operations are supported, and some of the supported operations are undefined for vectors. That's why this class is called Two_Point and not Two_Vector. The supported operations are scalar and member-wise addition, subtraction, multiplication, and division. For the scalar versions, the operation is performed on each member.

Spline is the only user of Two_Point. Perhaps it should be defined in Spline's header so that there's less temptation to use Two_Point inappropriately.

3.6 Spline

Spline is a class for a parametric cubic spline interpolation between points. A vector of Two_Points through which the curve passes and angle of the curve at the first and last points are passed to the constructor.

Splines are used to make smooth road elevation changes and banking transitions.

3.7 Surface

A Surface describes the friction, rolling resistance, restitution and texture image of a surface such as pavement, grass or gravel.

3.8 Texture_Image

The Texture Image class provides a convenient way of reading a ‘*.ppm’ image file from the disk and for getting information about the image.

3.9 Conversions

The header file ‘Conversions.h’ contains a few functions for performing frequently-used unit conversions. Currently, there are conversions for radians and degress, radians per second and revolutions per minute, and meters per second and kilometers per hour.

3.10 The Media Library

3.11 The Track Library

A Track is a collection of straight and curved pieces of road. These pieces are described by classes derived from Road_Segment. Currently, we have a straight segment class (Straight_Road), and a circle arc segment class (Arc_Road). The track is assembled so that there are no corners where two segments join.

If you look at the code you'll find a class for a segment that smoothly curves through a set of given points (Spline_Road). This class has been commented out because I don't know how to do the transformation from world coordinates to track coordinates for a spline.

The elevation and banking at any number of points on a segment can be specified. The specified points are interpolated with a cubic spline so that the transitions are smooth.

Track o---Road_Segment
           ^     ^
          /       \
Straight_Road    Arc_Road

3.12 The Body Library

A Body describes a three-dimensional rigid body made up of point particles. These particles are described by Particle and its subclasses. Position and orientation for both Bodys and Particles is provided by the Frame base class. The Car class is derived from Body

     Frame
     ^   ^
    /     \
 Body o---Particle
  ^
  |
 Car

3.12.1 Frame

3.12.2 Particle

3.12.3 Body

3.12.4 Car

3.12.4.1 Drivetrain

3.12.4.2 Wheel

3.13 The World Library

To avoid dependencies, Track, Atmosphere, and Body were each designed so that they know nothing about the others. It is the purpose of the World class to mediate any interactions among those classes. Because Track, Atmosphere, and Body are independent, it is neccessary that World depend on each of these classes. A subclass of World that provides an interface to the input methods of Car is provided. It's called Car_World. (Apologies to Marcus Hewat, creator of the Carworld program, http://perso.club-internet.fr/hewat/carworld/carworld.htm. Aside from some bits of code I stole for reading textures from files and drawing text on the screen, this project is unrelated to Carworld.)

        World
       o ^ o o---.
      /  |  \     \
 Track   |  Body  Atmosphere
         |   ^
  Car_World  |
          o  |
           \ |
            Car

The World base class doesn't do any graphics. If you want to see the results of the simulation on screen, you must derive an appropriate class and define the draw() method. An example of such a class that uses OpenGL, Gl_Car_World, is provided. You must also use subclasses of Track and Car (such as Gl_Track and Gl_Car) that use the same graphics system if you wish to see instances of those objects.

A typical application will construct a Track, Atmosphere, and Car, and then construct a World by passing pointers to those objects. The simulation is started by calling the World's start() method. The World is responsible for initializing the graphics system (if used) and starting the event loop.

3.13.1 Atmosphere

To be written.

A. Building Vamos

A.1 Downloading

You can get the latest release by going to the Vamos home page, http://vamos.sourceforge.net, and following the “Download” link. Another way to get there is to go through the SourceForge project page, http://sourceforge.net/projects/vamos.

A.2 Dependencies

Vamos makes use of some external libraries. These libraries need to be present in order to compile Vamos.

OpenGL-compatible libraries, including the OpenGL Utility Library (GLU) and the OpenGL Utility Toolkit (GLUT) must be installed. Mesa http://www.mesa-3d.org works fine. In addition, you need accelerated video hardware. Some video cards require specific GL implementations.

SDL http://www.libsdl.org is used for event handling (keys, mouse, and joystick). Sound is handled by OpenAL http://connect.creativelabs.com/openal.

You will also need a reasonably up-to-date C++ compiler. Specifically, it must handle namespaces. Gcc version 2.96 and later, including 3.x, and 4.x should do. See http://gcc.gnu.org. The code is intended to be portable, standard C++, so other compilers should work as well.

A.3 Compiling

After downloading the source archive (the ‘tar.gz’ file), unpack it with the tar command, or some other utility. All of the files in the archive are placed in a subdirectory. If the archive is ‘vamos-1.2.3.tar.gz’, the files are placed in ‘vamos-1.2.3’.

Vamos uses the GNU Autotools (automake, autoconf, and libtool) to check for prerequisites and handle different architectures. Change to the directory created by un-archiving and type ./configure. Type ./configure --help to see the options accepted by configure. I have only tried to compile Vamos on GNU/Linux and Cygwin/Win32 platforms. Please write me if you find an architecture that is not handled correctly.

The configure script generates the ‘Makefile’s needed to compile the program. Issue the make command to start the compilation. If you encounter errors, or warnings that you think I should know about, please contact me.

If the compilation succeeds, you can install the libraries, headers, and application by typing make install. You may need to be a privileged user to install software on your system. You do not need to install the program to run the application. Switch to the ‘vamos’ directory and run ./vamos to try the application without installing.

B. Copying

Vamos may be copied according to the terms of the GNU General Public License (GNU GPL). The license is in the file COPYING in the top-level directory of the source code.

This documentation may be copied according to the terms of the GNU Free Documentation License (GNU FDL) which is printed below.

B.1 GNU Free Documentation License

Version 1.1, March 2000

Copyright © 2000 Free Software Foundation, Inc.
59 Temple Place, Suite 330, Boston, MA  02111-1307, USA

Everyone is permitted to copy and distribute verbatim copies
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If you have no Invariant Sections, write “with no Invariant Sections” instead of saying which ones are invariant. If you have no Front-Cover Texts, write “no Front-Cover Texts” instead of “Front-Cover Texts being list”; likewise for Back-Cover Texts.

If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.

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About This Document

This document was generated by Sam Varner on January, 18 2012 using texi2html 1.78.

The buttons in the navigation panels have the following meaning:

where the Example assumes that the current position is at Subsubsection One-Two-Three of a document of the following structure:

• 1. Section One
  • 1.1 Subsection One-One
    • ...
  • 1.2 Subsection One-Two
    • 1.2.1 Subsubsection One-Two-One
    • 1.2.2 Subsubsection One-Two-Two
    • 1.2.3 Subsubsection One-Two-Three     <== Current Position
    • 1.2.4 Subsubsection One-Two-Four
  • 1.3 Subsection One-Three
    • ...
  • 1.4 Subsection One-Four

This document was generated by Sam Varner on January, 18 2012 using texi2html 1.78.