ERK vs. DISCRETE + RK4

User Questions
1

Hi,

I’m trying to understand the differences between using the Explicit Runge-Kutta (ERK) integrator provided by ACADOS and implementing a discrete-time model where the system dynamics are integrated externally using the RK4 method (Runge-Kutta 4).

In my case, I implemented the discrete-time dynamics using RK4 as shown below, and I noticed that it is computationally faster compared to using the ERK integrator in ACADOS:

k1 = self.model.fc_func(acados_model.x, acados_model.u)
k2 = self.model.fc_func(acados_model.x + self.dt / 2 * k1, acados_model.u)
k3 = self.model.fc_func(acados_model.x + self.dt / 2 * k2, acados_model.u)
k4 = self.model.fc_func(acados_model.x + self.dt * k3, acados_model.u)
f_disc = acados_model.x + self.dt / 6 * (k1 + 2 * k2 + 2 * k3 + k4)

acados_model.disc_dyn_expr = f_disc

However, I wonder if using the sim_method_step_size with the ERK integrator allows for more accurate integration over subintervals, and whether this explains the difference in behavior.

Could you clarify the exact differences between these two approaches? Also, if the differences are minimal, are there specific solver options or settings I should pay attention to when using the discrete-time implementation?

Thank you in advance for your guidance!

2

Hi :wave:

the two should be exactly the same if you use the following settings in your OCP solver:

  • dt in your custom RK4 implementation equals solver_options.tf/solver_options.N_horizon
  • solver_options.sim_method_num_stages = 4, solver_options.sim_method_num_steps = 1

Not sure what you mean with sim_method_step_size.

Best, Katrin