Acados for Humanoid Gait Generation

User Questions
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1

Hi,

I am employing acados to compute the optimal inputs for humanoid gait generation in a NL-MPC framework.

Input signals are the solution of an optimization problem and are assumed to be piecewise-constant.
My nonlinear constraint involves the values of the input signals in each time interval ( up to the end of the prediction horizon ). In particular, it is a summation of terms where the i-th term involves the value that the input to be optimized takes in the interval [t_{k+i}, t_{k+i+1}).
It seems to me then that SX.sym(‘input’) does not fit my problem. Is there a way to model this in acados/casadi?

Thank you,
Barbara

2

Hi Barbara,

first of all, welcome to the forum :tada:

As discussed, e.g. here: Implementing rate constraints and rate costs
It is only possible to couple stages via the dynamics, not via cost and constraints.
One way to implement your kind of cost function is to add a dummy state, which integrates the control input, such that the last value of this state is the sum of the control inputs weighted with the time steps.
Then you can just put a constraint on this state.

Please let me know if that works for you.

Cheers,
Jonathan