Follow motion with delay and collisions.

Hi, Just started learning Unity and I'd like to create snake-like movements with collisions.
I'd appreciate any tips on how to solve that, for now, I managed to create follow movement, but I have issues with keeping the initial distance and activating collisions.
Adding just a rigid body to the cubes does not work very smoothly.

Important for me is to keep the length of a snake as procedural as possible.

Here's a preview of what I have:
https://www.dropbox.com/s/m0s5eok3l2gihzj/unity.mp4?dl=0

Didn't find any good answer about that, maybe I should ray-cast test the collisions? or generate some kind of joint hierarchy instead of separate objects?

and some code.

Code (CSharp):

1. using System.Collections;
2. using System.Collections.Generic;
3. using UnityEngine;
4.  
5. public class BodyGenerator : MonoBehaviour
6. {
7.     public float bodyParts = 1;
8.     public Vector3 bodyPartSize;
9.     public int Gap = 10;
10.     public GameObject petMain;
11.     public PlayerController pc;
12.  
13.     // Lists
14.     private List<GameObject> BodyParts = new List<GameObject>();
15.     private List<Vector3> PositionsHistory = new List<Vector3>();
16.  
17.     void Start() {
18.         CreateBody();
19.     }
20.  
21.  
22.     void Update()
23.     {
24.         // if (pc.isMoving == true) {
25.         PositionsHistory.Insert(0, gameObject.transform.position);
26.  
27.         int index = 0;
28.         foreach (var body in BodyParts) {
29.             Vector3 point = PositionsHistory[Mathf.Clamp(index * Gap, 0, PositionsHistory.Count -1)];
30.             Vector3 moveDirection = point - body.transform.position;
31.             body.transform.position += moveDirection * 5 * Time.deltaTime;
32.             body.transform.LookAt(point);
33.             index++;
34.         }
35.  
36.         if (PositionsHistory.Count > 200) {
37.             PositionsHistory.RemoveAt(PositionsHistory.Count - 1);
38.         }
39.         // }
40.  
41.  
42.        
43.     }
44.  
45.     private void CreateBody() {
46.         GameObject body = new GameObject("Body_grp");
47.         body.transform.parent = petMain.transform;
48.  
49.         Vector3 position = new Vector3(0, 0, 0);
50.         GameObject parent = body;
51.  
52.         for (int i=0; i <= bodyParts; i++) {
53.             GameObject bodyCube = CreateCube(bodyPartSize, position, parent);
54.             position = position - new Vector3(0,0,bodyPartSize.z);
55.             // parent = bodyCube;
56.             BodyParts.Add(bodyCube);
57.         }
58.  
59.     }
60.  
61.     private GameObject CreateCube(Vector3 scale, Vector3 postition, GameObject parent)  {
62.         GameObject cube = GameObject.CreatePrimitive(PrimitiveType.Cube);
63.         cube.transform.localScale = scale;
64.         cube.transform.position = postition;
65.         cube.transform.parent = parent.transform;
66.  
67.         return cube;
68.     }
69. }
70.  

Thanks in advance.