Question regarding xref and trajectory tracking about mpc-matlab HOT 6 OPEN

MehdiIshac commented on August 14, 2024

Question regarding xref and trajectory tracking

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MIDHUNTA30 commented on August 14, 2024

Hi Mehdi, Thanks for your feedback. In setting the reference for MPC, we also needed to find the control reference ur_k for tracking the state reference values. Here the reference x1r_k=0.5kTs, and x2r_k=1. Inorder to find ur_k we have to solve the reference state equation xr_k+1=f (xr_k,ur_k) for ur_k, which results in [0.5(k+1)Ts 1]'=f ([0.5kTs 1]',ur_k). Since the reference is time-varying here, solving this for ur_k may be difficult. In NMPC, I have only worked with constant reference cases so far. You can look at path planning or trajectory planning algorithms for robots. You can also share the codes with me and I can give some suggestions. Regards, Midhun

…

On Fri, Mar 24, 2023 at 1:35 AM Mehdi Ishac ***@***.***> wrote: First of all, I would like to thank you for your amazing work that as helped me a lot in my MPC internship. I have a question, especially on the NMPC_2.m code file, if we would like to make trajectory following by changing the reference value over time (example x1 = 0.5*k*Ts, x2 = 1), How should we incorporate theses reference changes? I have tried to do so with a unicycle robot model adding some changes in the nlcon function to adjust the value of the reference with the Prediction horizon location in time but with no successful results. (i can send you my .py file if you want to check) If you have any code example, it would help me a lot Thank you Midhun — Reply to this email directly, view it on GitHub <#3>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AW4QRSQRCRRW273WVI3M2MLW5SUILANCNFSM6AAAAAAWFVT6UQ> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

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MehdiIshac commented on August 14, 2024

Thank you Midhun for your fast answer,
I have considered trying a point stabilization for the unicycle robot using your NMPC example,
it works pretty well, I have also found an interesting article where their modified cost function (formula 14) is quite the same as yours except that QN is way more important than Q in the cost function penalties. For the tracking I will consider various path planning algorithms as you mentioned, thanks.

Here is the article for point stabilization
ICMA.2005.1626717.pdf

And my python code, if you want to make me some feedback, is in my MPC repository, I have credited you.

Best regards

Ishac

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MIDHUNTA30 commented on August 14, 2024

Thanks Ishac for sharing the reference and your code. I'll look into it. Regards, Midhun

…

On Sat, Mar 25, 2023 at 2:23 PM Mehdi Ishac ***@***.***> wrote: Thank you Midhun for your fast answer, I have considered trying a point stabilization for the unicycle robot using your NMPC example, it works pretty well, I have also found an interesting article where their modified cost function (formula 14) is quite the same as yours except that QN is way more important than Q in the cost function penalties. For the tracking I will consider various path planning algorithms as you mentioned, thanks. Here is the article for point stabilization ICMA.2005.1626717.pdf <https://github.com/MIDHUNTA30/MPC-MATLAB/files/11068392/ICMA.2005.1626717.pdf> And my python code, if you want to make me some feedback, is in my MPC repository, I have credited you. Best regards Ishac — Reply to this email directly, view it on GitHub <#3 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AW4QRSVRXC27QGI46WYHUITW52XB7ANCNFSM6AAAAAAWFVT6UQ> . You are receiving this because you commented.Message ID: ***@***.***>

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MIDHUNTA30 commented on August 14, 2024

I had gone through your Python code and it works fine for stabilization problems. I also went through the reference paper which discusses stabilization problems for mobile robots using NMPC. Regarding tracking, I found an article by the same authors for which the link is given below:
http://www.ece.ufrgs.br/~fetter/sbai05_10022.pdf
I think if we know the state and control reference sequences over the prediction horizon: ( xr_k, xr_k+1,...,xr_k+N) and (ur_k,ur_k+1,...,ur_k+N-1) for the mobile robot, we can use the NMPC scheme from this paper.

Regards,
Midhun

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MehdiIshac commented on August 14, 2024

Hi Midhun
Thanks for you answer,
I have managed to try the NMPC tracking problem for the unicycle model and succeeded.
You are wright, we have to know the control reference over the prediction of horizon which means we have to compute {vr_k , vr_k+1 ,..., vr_k+N-1} and {wr_k , wr_k+1 ,..., wr_k+N-1} each time step.

This can be done for the unicycle with the following formula,

$$v_r(k) = arctan(\frac{\dot{y(k)}}{ \dot{x(k)}})\\$$

$$w_r(t) = \frac{ \ddot{y(k)}\dot{x(k)} - \dot{y(k)}\ddot{x(k)} }{ \dot{x(k)}^{2} + \dot{y(k)}^2 }$$

I uploaded an example in my MPC repo, dealing with an 8 track shaped trajectory

For those who wants to go further, i recommend the use of Casadi (which is available in python, matlab or c++) for NMPC
purposes and giving a lower computational time than Scipy .

Best regards

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MIDHUNTA30 commented on August 14, 2024

Ok. Great. Thanks for sharing the information. I'll look into the code. Regards, Midhun

…

On Tue, May 23, 2023 at 2:20 PM Mehdi Ishac ***@***.***> wrote: Hi Midhun Thanks for you answer, I have managed to try the NMPC tracking problem for the unicycle model and succeeded. You are wright, we have to know the control reference over the prediction of horizon which means we have to compute {vr_k , vr_k+1 ,..., vr_k+N-1} and {wr_k , wr_k+1 ,..., wr_k+N-1} each time step. This can be done for the unicycle with the following formula, $$v_r(k) = arctan(\frac{\dot{y(k)}}{ \dot{x(k)}})\\$$ $$w_r(t) = \frac{ \ddot{y(k)}\dot{x(k)} - \dot{y(k)}\ddot{x(k)} }{ \dot{x(k)}^{2} + \dot{y(k)}^2 }$$ I uploaded an example in my MPC repo, dealing with an 8 track shaped trajectory For those who wants to go further, i recommend the use of Casadi (which is available in python, matlab or c++) for NMPC purposes and giving a lower computational time than Scipy . Best regards — Reply to this email directly, view it on GitHub <#3 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AW4QRSU3WHSTQE6VMXNJMBLXHR24PANCNFSM6AAAAAAWFVT6UQ> . You are receiving this because you commented.Message ID: ***@***.***>

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Question regarding xref and trajectory tracking about mpc-matlab HOT 6 OPEN

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