Can aligator solve a problem with different stage model?

[Zionshang]

The formulation of Aligator's optimal control problem is conventionally based on stage models, where the dynamical model typically remains consistent across all stages.

Recent advances have introduced a layered MPC approach that is gaining traction in robotics. This method employs full-order dynamics
at the initial of the prediction horizon, while transitioning to reduced dynamics in later phases.

This raises an implementation question:
is it possible to define different dynamics models (with different manifold spaces and different ndx) in one problem when building an Aligator problem?

I'm really looking forward to your answer!

[ManifoldFR]

Hello @Zionshang, thank you for your interest in aligator!

The formulation of Aligator's optimal control problem is conventionally based on stage models, where the dynamical model typically remains consistent across all stages.

This is incorrect. The dynamical model can change across stages. In fact, each stage model is just a container around dynamical models, costs, and constraints (all held by value in polymorphic containers), and each stage has independent copies of all of those. So you can change the dynamics across each stage - some of the examples in our recently-published T-RO paper (namely the quadruped examples and the ballistic motion on UR10).

The real question is whether two subsequent stage models can have different state spaces.
This is in fact supported in aligator. You just need to ensure that at stage $k \in \{ 0, \ldots, N-1 \}$, the input and output state spaces $X_k, X_{k+1}$ as in

$$\mathscr{X}_{k+1} \ni x_{k+1} = f_k(x_k, u_k), x_k \in \mathscr{X}_k$$

are consistent with those at stages $k-1$ and $k+1$.

[Zionshang]

Thank you so much for your insightful response! Aligator's capabilities truly exceed anything I ever imagined – this is absolutely phenomenal!