Embeded realtime 40x20 problem 200Hz

[ceserik]

Hello, I am trying to use OSQP to solve a 40x20 problem. The problem is torque allocation for four wheel drive Formula Student vehicle. I need to get the frequency under 200Hz on STM32G4 so I am using floats and i am NOT using long int. Right now the problem is linear but I wanted to use OSQP to have ability to add quadratic functions in the future. At the moment I have troubles getting the speed to be fast enough. Currently the frequency is around 3kHz on i5-8th gen, but STM32 will be slower. For the last few days I have tried changing different solver settings: alpha, rho, eps_abs, eps_rel. I have disabled adaptive rho as very often got failed rho update. I have loosened the tolerances as much as possible to still get a viable output. As for the scaling all matrices and inputs are in the range of -100 to 100. I have found that limiting max iterations to 200 shortened the time significantly and still gave practically the same result.

I have analysed the data from 6000 problems which are varying only in two variables and found that solver spends a lot of time solving a few probems (reaches max iter). For other problems it finds the solution 140 times faster, see picture.

So I think I must have the solver improperly configured for this type of problem, or problem is poorly defined. My current settings are

osqp_set_default_settings(settings); settings->polishing = 0; settings->verbose = 0; settings->alpha = 1.0; settings->adaptive_rho = 0; settings->warm_starting = 1; settings->rho = 0.1; settings->eps_abs = 1e-3; // Absolute tolerance settings->eps_rel = 1e-3; // Relative tolerance settings->eps_prim_inf = 5e-2; // Primal infeasibility tolerance settings->eps_dual_inf = 1e-2; // Dual infeasibility tolerance settings->max_iter = 200;
I have the problem defined also in matlab where the solver used is dual simplex and it is solved in 25 iterations. Also I know that I have some unnecessary constraints. Preprocessing in matlab, which is using this solver told me this: LP preprocessing removed 10 inequalities, 0 equalities, 4 variables, and 24 non-zero elements. But the problem in matlab solver is defined as follows

min 1/2xTQx+cTx
s.t.L≤Ax≤U;l≤x≤u

x lower and upper bounds are constrained indepenedtly.
I would like to ask what can be done to improve the convergence of solver, should I further scale the problem to have all variables between 1 to -1, are there any solver settings which I should change to sovle the linear problem faster, should I remove the unnecesary variables rows, will dual simplex be faster for this problem, or what else can be done to improve the convergence?

The problem is defined like this
OSQPInt A_nnz =112; OSQPInt m = 44; OSQPInt n = 20; OSQPFloat A_data[112] = { //0 1 2 3 4 5 6 7 8 9 1.000000, -1.000000, -1.000000, 1.000000, 1.000000, -1.000000, 101.000000, -101.000000, 1.000000, -1.000000,//0 1.000000, 1.000000, -1.000000, -1.000000, 1.000000, -1.000000, 1.000000, 102.000000, -102.000000, 1.000000,//1 -1.000000, 1.000000, 1.000000, -1.000000, -1.000000, 1.000000, 1.000000, -1.000000, 103.000000, -103.000000,//2 1.000000, -1.000000, 1.000000, 1.000000, -1.000000, -1.000000, 1.000000, -1.000000, 1.000000, 104.000000,//3 -104.000000, 1.000000, -1.000000, 1.000000, 1.000000, -1.000000, 1.000000, -1.000000, 1.000000, -1.000000,//4 1.000000, -1.000000, -1.000000, 1.000000, -1.000000, -1.000000, 1.000000, 1.000000, -1.000000, 1.000000,//5 -1.000000, -1.000000, 1.000000, -1.000000, -1.000000, 1.000000, -1.000000, 1.000000, 1.000000, -1.000000,//6 -1.000000, 1.000000, -1.000000, -1.000000, 1.000000, -1.000000, 1.000000, -1.000000, 1.000000, -1.000000,//7 -1.000000, -1.000000, -1.000000, -1.000000, -1.000000, -1.000000, -1.000000, -1.000000, -1.000000, -1.000000,//8 -1.000000, -1.000000, -1.000000, -1.000000, 1.000000, -1.000000, -1.000000, -1.000000, 1.000000, -1.000000,//9 -1.000000, -1.000000, 1.000000, -1.000000, -1.000000, -1.000000, 1.000000, -1.000000, -1.000000, -1.000000,//10 -1.000000, -1.000000 }; OSQPInt A_row_indices[112] = { 0, 1, 28, 29, 30, 31, 36, 37, 38, 39, 40, 2, 3, 28, 29, 30, 31, 36, 37, 38, 39, 41, 4, 5, 28, 29, 30, 31, 36, 37, 38, 39, 42, 6, 7, 28, 29, 30, 31, 36, 37, 38, 39, 43, 8, 9, 16, 17, 18, 19, 20, 21, 32, 10, 11, 16, 17, 22, 23, 24, 25, 33, 12, 13, 18, 19, 22, 23, 26, 27, 34, 14, 15, 20, 21, 24, 25, 26, 27, 35, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 0, 1, 8, 9, 2, 3, 10, 11, 4, 5, 12, 13, 6, 7, 14, 15, 28, 29, 30, 31 }; OSQPInt A_col_ptrs[21] = {0, 11, 22, 33, 44, 53, 62, 71, 80, 82, 84, 86, 88, 90, 92, 96, 100, 104, 108, 110, 112}; OSQPFloat q[20] = { 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.200000, 0.200000, 0.200000, 0.200000, 0.200000, 0.200000, 1.000000, 1.000000, 1.000000, 1.000000, 3.000000, 4.000000 }; OSQPFloat u[44] = { 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 40.000000, -40.000000, 30.000000, -30.000000, 20.000000, -20.000000, 10.000000, -10.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, -30.000000, 30.000000, -69.000000, 69.000000, 0.000000, 0.000000, 0.000000, 0.000000, 80000.000000, 30000.000000, 30.000000, 0.000000, 40, 30, 20, 10 }; OSQPFloat l[44] = { -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -OSQP_INFTY, -40, -30, -20, -10 };;