NMPC time minimization problem

Hello,

I am using the "Truck and Trailer Automatic Parking Using Multistage Nonlinear MPC" example to get familiar with the MPC toolbox.

My question is, how should I define the cost function if I want to minimize the time, i.e., the duration of the maneuver?

Thank you

[Almudena Buelta Méndez]

Thanks! That's what I thought. However, in the example it says "You can use different ways to define the cost terms. For example, you might want to minimize time, fuel consumption, or parking speed", so I assumed there might be a straightforward approach to do so.

Answer 1

[Akshat Dalal]

Hi Almudena,

In typical MPC formulations, the cost function is designed to penalize deviations from desired states and/or control efforts. Minimizing time, however, is not directly about penalizing these deviations but about achieving a goal in the shortest possible time. This requires a slightly different setup because the objective (time) does not naturally fit into the state or control input vectors.

However, you can define a surrogate objective that correlates with time in your cost function. For instance, you could optimize the 'speed' in your cost function as a higher average speed would lead to a shorter time. You could use combine multiple such variable's as an alternate way of minimizing the duration of the manoeuvre.

Hope this helps!