[ODE] Bike Balancing!

[James Steele]

Eike I suspect uch of the balancing behaviour that your experiencing is 
from the sphere themselves?  Not sure if just altering the steering 
angle will do what I want as I'm casting rays against the world for 
wheel collisions.
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This is OT :- but maybe people here might benefit from how I approached 
my tire model. Maybe I can be persuaded to do a ODE example when I have 
some free time :)

The tire model is very simplistic and comes in two parts :-

1) the engine/transmission simulation which deals with the torque/revs 
of the engine and gearing
2) the forces produced by the tires

The first part is just numbers, and not really that hard to do. It just 
calculates the engine and rive torque bases on the throttle input and 
current drive gear.

 The second part really does nothing more than cast a ray for each wheel 
against the scene.  When a wheel is colliding with something it produces 
the wheels forces in this way :-

1) Caclulate the world matrix of the wheel (this will include any 
steering angle on the wheel)

2) Project the wheel matrix on to the contact normal The At and Right 
vectors of the matrix will now give you the longitudinal and lateral 
force vectors

3) If the wheel is a drive wheel, calculate the desired force from the 
drive torque and multiply this by the longitudinal patch vector from step 2

4) If the wheel is braking, then produce calculate the brake force 
produced by the wheel

5) Get the velocity at the wheel contact point, and normalize it (call 
this vector patchVel)

6) Perform a dot product between the patch vel and the patch right 
vector and multiply this by the wheel load (I get this from the 
suspension force) and also the tires friction coeffiicient.

7) Calculate the maximum load the tire can take.  I calculate this by 
taking the wheel load (again from the spring force) and multiplying it 
by the tire friction coefficient and the surface friction coefficient. 

At this point you wil have three things :-
 i. The desired longitudinal force of the tire ( a scalar value called 
forceLong)
ii. The desired lateral force of the tire ( a scalar value called forceLat)
iii. The maximum force the tire can produce ( a scalar value forceMax)

8) Check to see if the tire is braking the force limits. If it does, 
workout the total amout of force the tire produces and flag the wheel as 
braking traction.  An exmaple of the code is :-

forceMaxSqr = forceMax * forceMax;
totalForceSqr = (forceLong*forceLong) + (forceLat*forceLat)

if (forceMaxSqr < totalForceSqr)
{
    float k = totalForceSqr / forceMaxSqr
    forceLong *= k;
    forceLat *= k;
 
   // You may want to set flags in your wheel structure to indicate the 
wheel has lost traction

}

9) Combine the forces into one vector with something like

forceVec = (patchLat * forceLat) + (patchLong + forceLong)

10) Apply the force at the contact point for the wheel

11) Update your wheel rotation velocities.  It's a bit complicated to 
explain everything I do here, but in a nut-shell; the wheel rotation 
velocities are updated depending on thier drive/brake/traction state.  
i.e. if a drive wheel is slipping, it's rotational velocity is that of 
the rpm of the axle, if not, then it's the same as the longtudinal patch 
velocity.  If the brakes are pressed and the wheel has lost traction, 
then the angular velocity of the wheel is just assumed to be zero (locked)

11) There is also a feedback loop for the engine revs to be constrained 
to the wheel rotations, but just taking the average of all of the drive 
wheels rotational velocities in contact with the ground and not slipping.

The tire model isn't complete though.  I haven't added 
lateral/longitudinal tire deformation and the maximum force calculation 
should really use something like Pacejka curves, but as a basic model it 
works very well.  I prototyped the tire model using a car with similar 
parameters to a Opel/Vauxhall/Holden VXR8 and it was pretty fun to drive.

I added some additional things to the tire model for more arcade 
handing. Things like :-

i) simple/complex load calculation flag
ii) simple/complex patch matrix calculation flag
iii) fake global downforce multiplie which acted on the max force 
calculation

The car is pretty fun to drive and exibits very realistic behavours like 
brake lock up, wheel spin, traction loss as the tires reach thier 
limits.  The lack of tire deformation make loss of traction happen very 
suddenly though, sort of like driving on very bad tires at high speed.

It worked on the bike first time too using engine and gearing parameters 
from a Yamaha, apart from the falling over bit :)

I hope this was informative!