Open jara001 opened 7 months ago
My flow to investigate further:
x, y, d, k
are clear, as the car is at that position; in addition the car is there at time t
.
That leaves us psi
, vx
, vy
, a
, omega
and delta
.
Heading psi
should be a difference in the position, as the car should track the trajectory precisely. I think that is should match in both cases.
Velocity v
(or vx
, vy
) is expressed with respect to the CoG. This should be an image of velocity placed in the center of the rear axle as;
F_y = m · dpsi · v_x = m · k · v_x^2
constrains the maximum velocity and is placed in the center of the rear axle. In addition, this is a velocity that is computed in the optimization. To create the image of velocity in the CoG (and its components) we use angle Beta:
Beta = atan(l_r · k)
Therefore, v_x = v · cos(Beta)
and v_y = v · sin(Beta)
. And I agree that for rear axle frame, v_x = v
and v_y = 0
.
In addition, Autoware Design says, that v_x, v_y
should be referred to in the CoG.
No differences here.
No differences here.
(Really) original version was: delta = L · k
which used some angle assumption and led to wrong values.
Currently used version is:
delta = atan(L · k)
and the suggested version is:
delta = atan(L / l_r · tan(Beta))
However, they are equal as:
Beta = atan(l_r · k) → tan(Beta) = l_r · k → k = tan(Beta) / l_r
delta = atan(L / l_r · tan(Beta)) = atan(L · (tan(Beta) / l_r)) = atan(L · k)
Added in 1702cf4 as a comment from Tomáš.
Purely rear axle should be:
Purely CoG should be: