Recreating object movement with single touch (or mouse)

Hello,

I am trying to recreate character movement, where player moves forward all the time, you just change direction (rotation) of object with a single finger (touch) on screen (or mouse in editor).

Reference game: Crowd city from Voodoo
Video:

My current code:

Code (CSharp):

1. using UnityEngine;
2.  
3. public class PlayerManager : MonoBehaviour {
4.  
5.     [SerializeField]
6.     private float speed = 5f;
7.  
8.     private Rigidbody rb;
9.  
10.     // center where mouse is first clicked on the screen
11.     private Vector2 mouseStartPosition = new Vector2(-1, -1);
12.  
13.     private void Awake()
14.     {
15.         rb = GetComponent<Rigidbody>();
16.     }
17.  
18.  
19.     void FixedUpdate ()
20.     {
21.         // if mouse is clicked
22.         if (Input.GetMouseButton(0))
23.         {
24.             // if mouse center is not set ...
25.             if (mouseStartPosition == new Vector2(-1, -1))
26.             {
27.                 mouseStartPosition = Input.mousePosition; // ... set mouse center and return function
28.                 return;
29.             }
30.  
31.             Vector2 mousePosition = Input.mousePosition;
32.  
33.             // calculate angle between mouseStartPosition and current position of the mouse
34.             Vector2 v2 = (mousePosition - mouseStartPosition).normalized;
35.  
36.             /* took that part of code from web */
37.             float angle = Mathf.Atan2(v2.y, v2.x) * Mathf.Rad2Deg;
38.             if (angle < 0)
39.             {
40.                 angle = 360 + angle;
41.             }
42.             angle = 360 - angle;
43.             angle -= 270f; // to set correct angle specific for my camera
44.  
45.  
46.             // current y rotation of rigidbody
47.             float yRotation = rb.rotation.eulerAngles.y;
48.  
49.             // smoothly rotate current rotation towards new angle
50.             yRotation = Mathf.MoveTowardsAngle(yRotation, angle, 5f);
51.  
52.             // apply new rotation
53.             rb.rotation = Quaternion.Euler(0f, yRotation, 0f);
54.  
55.         }
56.         else
57.         {
58.             // if mouse released, delete center (first mouse position)
59.             mouseStartPosition = new Vector2(-1, -1);
60.         }
61.  
62.  
63.         // player always drives forward with certain speed
64.         rb.velocity = transform.forward * speed;
65.  
66.     }
67.  
68. }
69.  

My current concept is:
- When I press/touch on the screen for the first time, point of press is set as center
- While press/touch remains on screen, I calculate angle between center and current press/touch position
- I smoothly move rigidbodys y-angle towards calculated angle
- When press/touch is released, I delete center
- Repeat

My concept works OK, but not as good/smooth as referenced game. When my current press/touch position is far away from center, angle changes are smaller. Referenced game seems like it updates center all the time.

Maybe any tips to implement this kind of movement/rotation ?

Best Regards, L