2D character script causing player to go off screen?

I am very new to C#, so the errors might be obvious. I’m trying to make a 2D character controller and the script I have runs, but when I hit play the player goes off the screen to the right and I am unable to control it, if that makes sense? Does anyone see the error in the script?

using UnityEngine;
using System.Collections;


public class RobotControllerScript : MonoBehaviour
{
	public float maxSpeed = 10f;
	bool facingRight = true;

	Animator anim;

	bool grounded = false;
	public Transform groundCheck;
	float groundRadius = 0.2f;
	public LayerMask whatIsGround;
	public float jumpForce = 700f;

	bool doubleJump = false;

	void Start ()
	{
		anim = GetComponent<Animator> ();
	}
	void FixedUpdate ()
	{
		grounded = Physics2D.OverlapCircle (groundCheck.position, groundRadius, whatIsGround);
		anim.SetBool ("Ground", grounded);

		if (grounded)
			doubleJump = false;
		anim.SetFloat ("vSpeed", rigidbody2D.velocity.y);

		if(!grounded) return;

		float move = Input.GetAxis ("Horizontal");

		anim.SetFloat ("Speed", Mathf.Abs (move));
		rigidbody2D.velocity = new Vector2(move + maxSpeed, rigidbody2D.velocity.y);

		if (move > 0 && !facingRight)
			Flip ();
		else if (move < 0 && facingRight)
			Flip ();
	}
	void Update ()
	{
		if ((grounded || !doubleJump) && Input.GetKeyDown (KeyCode.Space)) 
		{
			anim.SetBool("Ground", false);
			rigidbody2D.AddForce(new Vector2(0, jumpForce));
			if(!doubleJump && !grounded)
				doubleJump = true;
		}
	}
	void Flip()
	{
		facingRight = !facingRight;
		Vector3 theScale = transform.localScale;
		theScale.x *= -1;
		transform.localScale = theScale;
	}
}

rigidbody2D.velocity = new Vector2(move + maxSpeed, rigidbody2D.velocity.y);

your character will move in the X direction by 10 units every update since your maxspeed is being added to move.

Even with no input, the script reads…

rigidbody2D.velocity = new Vector2(0 + 10.0f, rigidbody2D.velocity.y);

you want to multiply it

rigidbody2D.velocity = new Vector2(move * maxSpeed, rigidbody2D.velocity.y);

If input is 0 your X velocity will be 0.
If input is 1 your X velocity will be 10.
if input is -1 your X velocity will be -10.