Path following control robot kinematics and dynamics

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theBlue
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Hello,

I have a general question regarding what is the best controller (PI, PD, etc.) to control the position of a mobile robot in order to follow a known path.

The mobile robot at hand is a mechanism (a 4 bar linkage with its two base gliding on two parallel but not straight rails) and I want the end effector to follow the center-line between the two rails.

I have a path following controller working perfectly with the kinematics using just a P controller.

The problem occurs when I introduce the Dynamics. The Dynamics controller I am using is a PD.

I am controlling the Dynamics based on the kinematics path following control.

I do not know if this kind of control has a name ?

Thank you for your answer.
 
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Most control loops work with just P or PI. PID is seldom needed. PD sounds like a mistake to me. I can't believe that PD is appropriate.

Most critical is not the controller itself. Most critical is selecting where the controller output goes, and what the feedback is.