move layer constantly in a certain direction depending on 3d-Rotation?

TRY THIS 
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var rotationDuration = 60; // The duration of each rotation in frames
var maxRotationAngle = 180; // The maximum angle to rotate (in degrees)
var pauseDuration = 30; // The duration to pause in frames (1 second at 30fps)

var currentTime = time - inPoint; // Calculate the time relative to the layer's in-point

var cycleNumber = Math.floor(currentTime / (rotationDuration + pauseDuration));
var seed = Math.floor(time / (rotationDuration + pauseDuration)); // Create a seed for random rotation
seedRandom(seed, true);

var rotationAngle = random(0, maxRotationAngle);
var normalizedTime = currentTime % (rotationDuration + pauseDuration);
var rotation;

if (normalizedTime < rotationDuration) {
    // Animate the rotation during the rotation duration
    var progress = normalizedTime / rotationDuration;
    rotation = progress * rotationAngle;
} else {
    // Pause the rotation
    rotation = rotationAngle; // Hold the final rotation
}

rotation;

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both sides rotation

var rotationDuration = 1; // The duration of each rotation in frames
var maxRotationAngle = 180; // The maximum angle to rotate (in degrees)
var pauseDuration = .01; // The duration to pause in frames (0.5 seconds at 30fps)

var currentTime = time - inPoint; // Calculate the time relative to the layer's in-point

var cycleNumber = Math.floor(currentTime / (rotationDuration + pauseDuration));
var seed = Math.floor(time / (rotationDuration + pauseDuration)); // Create a seed for random rotation
seedRandom(seed, true);

var rotationAngle;

if (cycleNumber % 2 === 0) {
    // Rotate during the first half of the cycle
    var normalizedTime = currentTime % (rotationDuration + pauseDuration);
    if (normalizedTime < rotationDuration) {
        var progress = normalizedTime / rotationDuration;
        rotationAngle = progress * maxRotationAngle;
    } else {
        rotationAngle = maxRotationAngle; // Hold the final rotation
    }
} else {
    // Rotate the other way during the second half of the cycle
    var normalizedTime = currentTime % (rotationDuration + pauseDuration);
    if (normalizedTime < rotationDuration) {
        var progress = normalizedTime / rotationDuration;
        rotationAngle = -progress * maxRotationAngle;
    } else {
        rotationAngle = -maxRotationAngle; // Hold the final rotation
    }
}

rotationAngle;

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Meh! I see the issue.

This is the classic case where you need to use a previous calculated value for the current frame. This is not possible with expressions. Instead, you need to recalculate the value for each frame.

This ends in a for-loop, starting at 0 and counting up to your current frame, doing the math over and over again. The longer your comp is, the longer this for-loop will execute.

The for-loop will work for sure, but maybe you find a better approach. Why not creating the animation with keyframes (walks left for x seconds, turn around and walks right) in a long comp. The keyframes are placed in the middle of the timeline, so you have enough animation going on to boh sides. Then you use the comp, place it randomly with your expression and cut of start and ending point. With time remap, you can also use expressions for this.

*Martin

Try this:

angle = thisComp.layer("Null 1 Control").effect("Angle Control")("Angle") - 90;
ofSt = thisComp.layer("Null 1 Control").effect("Slider Control")("Slider");
strt = time - inPoint;
t = strt - ofSt;
freq = easeIn(t, 0, .5, 10, 0);
amp = easeIn(t, 0, .5, 100, 0);
RndmPos = wiggle(freq, amp);
if (strt < ofSt)
	moV = RndmPos	
else moV = value
xMove = t * angle;

[moV[0] + xMove, moV[1]]

(now that I look at the ease method for the wiggle I see set that up incorrectly. don't have time to fix it now but the expression should still work)

I don't know how you are generating your random movement but you should be able to just replace the wiggle method with that.  I based the start time for the end of the random motion on a slider control. Set the slider to 1 and the random motion will stop at 1-second and the movement in X will begin with the speed based on the value of the Angle Control with no movement at 90º.

Why not just separate the dimensionss for position and then just add the time expression tothe X position value?

E.g.

time*a

with a being whatever number you decide? 1 pixel per second is the default.so use math to get the speed you're after.

Could be as trivial as if()else{}, though the hold-up likely is on what your 180 deg determination is based. Moving relative to a camera and maintaining a consistent behavior might be trickier than jsut in a 2D comp. To be honest, though, since you plan on keyframing the rotation, what would be the issue with also animating the motion? This could even be as trivial as animating at once and then applying two different animation presets - one for the left side movement, one for the right side.

Mylenium