Hi StackExchange fellows,
During my internship I have to work on a mobile robot and make it follow a path. As I was doing some researches, I found this article: Path Following Mobile Robot in the Presence of Velocity Constraints from Martin Bak, Niels K. Poulsen and Ole Ravn.
Despite several close readings, I still don't understand some points:
1) In equation 26 p.7, the controller expression use the vector $R_k$. Because it is normally dependant on the position of the robot and not directly on time, in p.8-9 a model $n$-step predictor is used to obtain $R_k$. But this model need to know the control law previously computed, which required to have $R_k$. So I don't understand how $R_k$ can be computed this way. Apparently the controller works, simulations have been done. But I really don't get it, so I would be glad that someone helps me to do so please.
2) Why matrices $A$,$B_\phi$ and $B_r$ in equation 19 p.6 are considered constant during the paper, while the velocity $v$ seems time-dependent (cf. equation 31 p.8 for example) ?
Thank you by advance !
I have not read the paper properly. But,
It seems at each sampling time they assume the velocity $v$ will remain constant during the entire prediction horizon to simplify the cost function calculation. Also angle sinuses are considered equal to their corresponding arcs.
The vector $R$ is the reference which is updated at each sample time before MPC optimization of control input. I do not see using n-step predictor to calculate $R$. Even if you use MPC to calculate $R$, it will be via a different process from the main MPC you use to calculate inputs.