Hi all,

we are solving an NLP with acados using a LINEAR_LS cost function. The model is a minimum lap time problem (MLTP) for a given race track including constraints describing vehicle- and thermo-dynamics of a race car with an electric powertrain. The race track is fed into the solver using parameters, which describe the track curvature for every discretization point.

Solving the problem for one lap on different tracks works fine. But solving the problem for multiple subsequent laps (i.e., an entire race with a temperature increase of the components of the electric powertrain) causes trouble: For some tracks, the solver converges to a solution within less than 60 SQP iterations, for other tracks it doesn’t find a solution but reaches the maximum number of NLP-iterations (1000). If we initialize the solver for the same problem that didn’t converge with some intermediate results we obtain after only 100 SQP-iterations, the solver converges within approx. 40 SQP-iterations.

It looks like the solver gets “lost” somewhere. Can this problem be caused by any step size parameter we need to set differently? Or are there different options to prevent the solver from getting lost and to solve the multiple-laps problem within one run?

Here are some solver parameters we have used: HPIPM, partial condensing, Hessian approximation with Gauss-Newton, Q = 0 (cost on states), R = 1e-3 (cost on driving/braking force input), P = 1e4 (cost on algebraic variable describing the time delta between two subsequent discretization points). We’ve used the IRK integrator. The number of discretization points for a single lap is approx. 200 with a step size of around 8 meters.

Thanks a lot in advance for your support,

Maximilian Bayerlein