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tl;dr: don't worry about it Your system really operates in continuous time, described by differential equations. It's a convenient, even necessary, approximation to use discrete time and difference equations. The dynamics solution would result from integrating the differential equations; the difference equations approximately solve the problem by doing ...


This problem can be solved by various types of controllers. Firstly, I would suggest you to create intermediary points in between two consecutive points your Path Planning Algorithm calculates. Try to make the intermediary points frequent. The frequency of these intermediary points will also define the movement characteristic of the robot (agressive, slow ...


With problems like this, you will need apriori knowledge of your operating area. Since you know that it is a fixed-size arena, you could build a map and use localization within the map to know where you are / if you stray away from your path. There are several visual methods to create such a map. I'd suggest you start with ORB_SLAM.


If you want to have a model that will behave closely to a real-life one, I would definitely believe that you should also have a look at the dynamic modeling of a differential drive robot, as Kinematic equations do not include the forces and torques acting on your robot. In fact during the simulation part of a real-world control problem, you should use the ...

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