GameObject is vibrating throughout the movement - unity3d

Question

I have a GameObject that takes position coordinates from a file. This GameObject moves with vibration rather than smoothly. (as if moving back and forth.)
Here is the code that provides the movement:
int counter = 0;
void Update()
{
var maxDistance = speed_* Time.deltaTime;
var oldPosition = transform.position;
var newPosition = Vector3.MoveTowards(transform.position, positions[counter], maxDistance);
var actualDistance = Vector3.Distance(newPosition, oldPosition);
var distanceRemainder = maxDistance - actualDistance;
if (distanceRemainder > 0.0001)
{
newPosition = Vector3.MoveTowards(newPosition, positions[counter], distanceRemainder);
counter++;
}
transform.localPosition = newPosition;
}
NOTE: The data read from the file is in the "positions" array (x,y,z coordinates).
When I lower the 300f value in the variable maxDistance, the vibration stops and the motion becomes more fluid. However, Gameobject speed is also slowing down. How can I ensure a fast and smooth movement?
SOLUTION:
While looking for a solution of the problem, I came across the this topic. It helped me learn the source of the problem.
I have observed that the GameObject is not vibrating in Scene view, it was moving smoothly. But the object seemed to be vibrating in GameView. The problem is not the moving object, it's the camera function I write to follow it.
The camera function that was written to follow the object has been updated and the problem has disappeared.
One can see more of the solution by going to Post #13 in the link above.
Thanks to everyone trying to help.

Answer 1

This is caused cause you are using your distanceRemainder as your maxDistanceDelta, which I think is incorrect, if you want a smooth movement, you should multiply it for the Time.deltaTime, try:
newPosition = Vector3.MoveTowards(newPosition, positions[counter], distanceRemainder*Time.deltaTime);
Or simply declare speed variable and do:
newPosition = Vector3.MoveTowards(newPosition, positions[counter], speed*Time.deltaTime);

Answer 2

I assume what you want is your object moving with a constant speed to the first position. Once it reaches it, move to the next one.
I would do it in a simple Coroutine which is better to understand and maintain than doing stuff in Update:
private void Start()
{
// todo assign positions
StartCoroutine(RunPositions());
}
private IEnumerator RunPositions()
{
foreach(var position in positions)
{
while(!Mathf.Approximately(Vector3.Distance(transform.position, position), 0))
{
var maxDistance = speed_* Time.deltaTime;
transform.position = Vector3.MoveTowards(transform.position, positions[counter], maxDistance);
// render and continue in the next frame
yield return null;
}
}
}
If you are fine with a precision of 0.00001 you can also simply use
while(transform.position != position)
instead.