Dynamics model for Racecars mpc example

nirajbas94 · February 18, 2020, 9:44pm

I am trying to implement MPC for F1/10 car racing in real time. Your racecars example with hpipm is what I am almost trying to do. However, I am not able to make complete sense of the dynamic bicycle model used. Can you explain the parameters and equations used for the model?

FreyJo · February 19, 2020, 11:33am

Hi @nirajbas94,

There will be a publication on this application soon.
Unfortunately, it will not be public before the final submission.
I will update this, if/when it can be made public.

Freddy · April 27, 2020, 8:23am

Hello FreyJo,

I tried to understand the unscaling of the weight matrices for the stage and the terminal costs.
Would you mind to give me some hints, or comments on that?

github.com

acados/acados/blob/master/examples/acados_python/race_cars/acados_settings.py#L97


R = np.eye(nu)
R[0, 0] = 1e-3
R[1, 1] = 5e-3


Qe = np.diag([ 5e0, 1e1, 1e-8, 1e-8, 5e-3, 2e-3 ])


ocp.cost.cost_type = "LINEAR_LS"
ocp.cost.cost_type_e = "LINEAR_LS"
unscale = N / Tf


ocp.cost.W = unscale * scipy.linalg.block_diag(Q, R)
ocp.cost.W_e = Qe / unscale


Vx = np.zeros((ny, nx))
Vx[:nx, :nx] = np.eye(nx)
ocp.cost.Vx = Vx


Vu = np.zeros((ny, nu))
Vu[6, 0] = 1.0
Vu[7, 1] = 1.0
ocp.cost.Vu = Vu

Thank you a lot!
Best regards,
Freddy

FreyJo · April 27, 2020, 10:09am

Hi Freddy,

this term is due to a change in the interface (few months ago).

Now, the costs at each shooting node (but the terminal) one are weighted with the corresponding discretization time. To keep the weighting matrix from the previous formulation I multiplied with N/Tf.
Dividing by unscale for the terminal cost is probably related to a bug in the early stage of the template interface, but I cannot tell for sure.

Best,
Jonathan

Freddy · May 1, 2020, 6:11pm

Hi Jonathan,

okay, thank you for the short explanation.

Best regards,
Freddy

alexbuyval · May 5, 2020, 2:35pm

Hi Jonathan,
Is there any update regarding the publication?

Best regards,
Alex

FreyJo · May 8, 2020, 2:13pm

The publication is submitted and accepted for IFAC 2020 and will be publicly available after the conference I guess, so July 20th.

Best,
Jonathan

AlexWin · July 18, 2020, 2:40pm

@FreyJo would you mind posting it here / sharing a link of the publication? I am curious.

Thanks, Alex

FreyJo · July 21, 2020, 8:55am

Yes, the paper is finally publicly available

Cheers!

alexbuyval · August 12, 2020, 1:53pm

@FreyJo thank you for the sharing

The authors wrote in the paper “We implement n(s) and n(s) as piecewise cubic polynomials ηj with respect to the track progress s”.
I wonder if any examples how to implement it by acados?
As I understood it should be similar the kappa along track here, however, I cannot figure out how to implement it for constraints by runtime.

Regards,
Alex