Problem with collision detection in an animated object

I’m trying to create a simple fighting game scene.
I have an animated model that contains an animation of different strokes.

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To move, I use the following code

transform.Translate(new Vector3(0,0, 0.5f * Time.deltaTime));

and now I have the problem of collision detection. Character passes through a wall, if you make it a solid object falls through the floor and it is impossible to move it.

I tried to apply colliders as child objects, tried to make a solid, tried to use Mesh Collider. None of this helped me.

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That is, I need to adequately move the object and get its collision. How to create a mesh that will wrap around the entire body of the object?

http://docs.unity3d.com/Documentation/Manual/Physics.html