Integrating CBF constraints with Acados

MPC Discussions
1

I want to integrate CBF based constraints with Acados. I need to use state of next shooting node in the horizon. while applying constraints for Xi, I want to use state Xi+1. Is this possible in Acados, cause this is possible with Casadi.

2

Hi :waving_hand:

Yes this is possible via state augmentation if you are using the discrete dynamics module. With an augmented system model of the form \tilde{x}_{n+1} = \begin{bmatrix} f(x_n, u_n)\\ x_n \end{bmatrix}
you can then defined constraints on \tilde{x}_n which includes both the current and the previous state of the original dynamic system.

Hope this is helpful!
Katrin

3

Hi Kaethe,

Thanks for the prompt reply! But, here Xn+1 is my predicted state for i the shooting node, however I need Xn+2, that is predicted state of i+1 shooting node. But, here Un+1 is not available to calculate Xn+2. In casadi, I can access u for any time slot within the horizon. Is that possible here? With the state augmentation approach, I can maintain last state and current state, but I need to maintain current state and Next state. I hope this clarifies my scenario. Is this possible in acados?

4

I’m not super familiar with CBFs, but I guess you need x_n, u_n, x_{n+1}, is that correct?

In that case you simply need to augment with the control as well, i.e.
\tilde{x}_{n+1} = \begin{bmatrix} f(x_n, u_n)\\ x_n\\u_n \end{bmatrix}