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 but steady...). That, way you are going to have a trajectory for your robot to follow.
Then the most basic Controller type you can try would be a classical PID Controller. A PID controller will iteratively calculate the configuration error of your robot (position, and/or orientation), and then create control signals for your robot by multiplying, differentiating, and integrating this error. I will check my sources and may add some resources/articles for you to look.
Sometimes a PID Controller may not perform well. Given your robot type, you may need to try different Controller Algorithms, maybe you can look at some simpler methods; such as Stanley, Pure-Pursuit Controller.
For the precise detection of the robot location; this a gigantic area, with many different methods and approaches. You can use IMU sensor's accelerometer data to calculate the linear acceleration of the vehicle (be careful; the data you read directly from the accelerometer is not the pure linear acceleration), then double integrate it to have the position. Be warned that result of this operation will be nowhere near accurate. You may search for how to fuse different sensors' reading to improve this data. Or, if you have a small arena for your robot; you may use a LIDAR-like sensor or maybe a camera, which can perform precise localization.
As I mentioned, both localization and control fields have many different methods which vary in computational need. If you are new to this field, I would recommend you to study PID Controllers first.