How to control a DC Motor with absolute encoder using Arduino and Motor Driver?
This is a quite high-level question, so I will answer in general terms,
skipping the fine details. You can ask here more specific questions once
you are implementing the stuff.

Yours is a 10-bit absolute encoder. It can tell you its shaft position
with a resolution of 1/1024 revolution. It's way overkill for your
application. I suggest you connect only the four most significant bits
(pins 9 – 12), which will give you a resolution of 1/16 revolution.

It's better to read the four bits simultaneously. This can be done using
direct port
manipulation. I
would connect pins 9 – 12 of the encoder to pins 4 – 7 of the Arduino
respectively. As the encoder outputs are open-collector, you have to
enable the pullups in setup():



PORTD |= 0xf0;  // enable pullups on pins 4..7


and you can read the encoder simply as

uint8_t ecoder_value = PIND &amp; 0xf0;


Notice that this will give you a result that is left-aligned. This way
you can treat it as an 8-bit Gray code.

Next step is to decode the Gray code. I let you research how to do that,
as you can probably find examples, or even ready-made libraries for
that.

Next, you have to extend the value to a wider bit length in order to
know the absolute position of the cable-cam. The encoder only tells you
where you are within a revolution, but it doesn't tell you how many
revolutions you did. The extension is done by comparing the current
encoder position with the previous one, taking the difference (which can
be positive or negative), and adding it to the previously computed
absolute position. Something like this:

int32_t absolute_position;

void update_absolute_position(uint8_t encoder_position)
{
    uint8_t old_position = absolute_position;  // extract LSB
    int8_t delta = encoder_position - old_position;
    absolute_position += delta;
}


Beware of the types of the variables. The type of delta, for instance,
ensures that the result of the subtraction is wrapped the correct way to
yield a number between −128 and +127. Thus, the sign will tell you which
is the shortest path (clockwise or counterclockwise) from the previous
to the current position.

Note also that you have to call this function frequently enough: more
than once per half revolution. Otherwise it won't know which direction
the wheel turned. If your loop() runs fast enough (you don't use
delay(), right?), you just have to call this function once in
loop(). Otherwise you would have to setup a timer interrupt to ensure
the updates are frequent enough.

Lastly, you have to define the limits:

int32_t left_limit = INT32_MIN;
int32_t right_limit = INT32_MAX;

// To set the left limit to the current position:
if (user_pressed_the_relevant_button()) {
    left_limit = absolute_position;
}
// and likewise for the right limit.


and condition the maximum speed on the distance to the closets limit.
Assuming you store the speed as a signed number (the sign being the
direction), you would constrain it to always be between a negative
min_speed and a positive max_speed, which could be updated as
follows:

// Slow down if close to a position limit.
if (absolute_position - left_limit &lt; BREAKING_DISTANCE) {
    min_speed = map(absolute_position,
        left_limit, left_limit + BREAKING_DISTANCE,
        0, -ABSOLUTE_MAX_SPEED);
} else {
    min_speed = -ABSOLUTE_MAX_SPEED;
}
if (right_limit - absolute_position &lt; BREAKING_DISTANCE) {
    max_speed = map(absolute_position,
        right_limit - BREAKING_DISTANCE, right_limit,
        +ABSOLUTE_MAX_SPEED, 0);
} else {
    max_speed = +ABSOLUTE_MAX_SPEED;
}
speed_to_apply = constrain(requested_speed, min_speed, max_speed);


Note that this makes the speed limit a linear function of the position.
You may want to look into easing functions to have a smoother breaking.