Hi to all,
I would like to be able to write equations to model my tracked vehicle which has a mass m=200Kg
My skid-steering vehicle uses one track per side with a rubber belt made in 100% natural rubber, please refer to the next photo to get a more detailed idea.
Since I mounted an IMU in its geometric center, I can read both the angular velocites and the accelerations along the three axis plus the heading, the pitch and yaw angles in degrees.
I would like to be able to write a model for the vehicle in order to simulate and study its outputs depending on specific inputs.
Each track has a length L=1000 mm
, a width W=330 mm
and a lug height, H = 32 mm
The vehicle is Lv= 1000 mm
long and Wv=900 mm
There are no suspensions, but I consider the rubber track as the combination of a spring, coefficient K
, and a damper, coefficient b
. The rubber compression is about Dx =1,5 mm
By supposing a sinusoidal input below the track generated by the terrain profile, u(t) = Asin(wt), I was able to write the equation for the Z axis:
X(s)/Y(S)=(bs+k)/((m/2)*s^2 + bs+k) for the right track
X(s)/Y(S)=(bs+k)/((m/2)*s^2 + bs+k) for the left track
Now, I would like to consider the lateral force Ft
which acts on the robot during a turning motion.
Let's consider the vehicle during a steering maneuver on the left: while the YAW angle changes to reach the target heading, the tracks are subjected to the later force as result of the terrain resistance.
Is there any way to write an equation to define the relation between the heading of the vehicle and the force Ft?
I do not know if you should consider the force Ft as a sine wave or a costant since it changes on if the vehicle sinks into the terrain.
I would like to write something like: Z(s) = G(s)X(s).
Can you suggest me how to write this relation, please?