The bottom line is that they want to sell you a system, so they provide the controller.
PDF page 15 here
https://www.electro-tech-online.com/custompdfs/2012/02/AerotechLinear_Motors.pdf now makes some sense as to how they work.
This
https://www.electro-tech-online.com/custompdfs/2012/02/00857a.pdf might provide some insight.
With a BLDC motor, there are three coils and there is a sensor that basically feeds back the position of when only one of the coils in energized. So, there would be one of three positions.
To rotate a motor, you energize the coils based on which sensor(s) is active. You can determine the RPM by monitoring just one sensor. If you actually vary the current in each phase you could microposition the motor.
So picture 3 coils that repeat linearly for the length of the linear motor. Again picture 3 sensors that repeat. Now connect every 3rd sensor in parallel and every 3rd coil in parallal. Now as it moves, a new set of coils are used, but each repeating set of 3 has the same magnetic field. Since there is nothing to move except where the actuator is, the actuator moves. I could imagine that crude positioning could be determined by the sensors in the motor alone and past actions.
An encoder is a way of measuring position. It's nothing more than a disk with two optical sensors which generate pulses. You can determine the direction and speed based on this sensor.
I know you said map terrain, but you didn't give any real specs. Resoluton, height etc. Distance to be traveled etc. How accurate the x y and z position should be. etc.
Suppose I wanted to map an area 20' in diameter and 10' is the max depression. So I position my reference in the 10' depression and my rotating level is in the center.
So, let's use polar coordinates from the camera and we roll around this thing that looks like a medical I-V cart, but with some way of leveling it. Maybe you don't want to level it and use the sensor to determine the angle.
So, you set it down. Pull it taught. Push a button. The gismo moves the linear sensor into the field of view of the laser. It knows the height to the precision of the encoder. It could even find the angle (if shallow) using the linear position sensor. Then you move to the next position.
This could probably be totally automated. Move while keeping a certain amount of force on the cord. Find the laser beam. Level itself. Find the height. Move a distance theta and do it again. A position sensor would keep track of theta too.
When your done, convert everything back to Cartesian co-ordinates (x,y).