Different QP solvers for MPC

[Ahmadreza-Shahrokhshahi]

Hi,

I am trying to have a better understanding about the QP solvers that can be used to solve the MPC problem. There are five different solvers in COPRA that is suggested for solving the QP for MPC:

• LSSOL
• GUROBI
• QLD
• OSQP
• QuadProg

Two solvers QuadProg and QLD can readily be used in the codes. I want to know about the other solvers' behavior in terms of computation time, and dependency on the number of prediction horizon steps (e.g., is it O(N^2) or something else based on the sparsity of the matrices, etc.). Since GUROBI and LSSOL are not free and I have not installed osqp-eigen on my system yet, I was curious if you have compared different solvers so far.
There might be other QP solvers such as qpOASES, qpswift, which are not included in COPRA.

1. Do you think that we can use solvers like qpOASES and qpswift? (based on the structure of our problem here)
2. My ultimate goal is to find the solver which fits our MPC problem, and its computation costs increases the least by increasing N.

P.S. I have seen this QP solvers copmarison, but I thought that you might have done a more particular comparison for the LIPM walking control MPC problem, which typically has N≈10-30, and the problem-specific constraints.

[stephane-caron]

That's a good question! I was curious so I tested on this prototype: model_predictive_control.py Results are in the third table of this benchmark.

• OSQP and qpOASES perform roughly the same on these problem parameters.
• You can try varying the problem parameters in the script to test for yourself 😉
• There's an issue with qpSWIFT. Edit: it has been addressed 👍

A couple of things to note as well:

• The code does not run Copra but a Python version of the same function.
• The "quadprog" solver in the benchmark is this one, not eigen-quadprog.

[abhishek-pandala]

Hi,
We have tried to resolve the issue pertaining to qpSWIFT in the previous comment here

[stephane-caron]

The issue has been addressed 👍 On this example qpSWIFT performs 4–6× faster than qpOASES and OSQP.

Another thing to note: this is a cold-start example, whereas one would warm-start in a practical scenario. Feel free to adapt the example to dig further.