Need help interfacing motors to motor shield

Currently I'm doing a project which needs me to control the direction of a wheelchair with buttons. I'm using an Arduino Uno with this shield My code is

// set pin numbers:
const int buttonPin1 = 0; //front
const int buttonPin2 = 1; //back
const int buttonPin3 = 2; //left
const int buttonPin4 = 3;
int E1 = 5;  
int M1 = 4; 
int E2 = 6;                      
int M2 = 7; 

// variables for reading button
int buttonState1 = 0;
int buttonState2 = 0;
int buttonState3 = 0;
int buttonState4 = 0;

void setup() {
  pinMode(M1, OUTPUT);   
  pinMode(M2, OUTPUT);
  pinMode(buttonPin1, INPUT);
  pinMode(buttonPin2, INPUT);
  pinMode(buttonPin3, INPUT);
  pinMode(buttonPin4, INPUT);


void loop(){
  // read the state of the pushbutton value:
  buttonState1 = digitalRead(buttonPin1);
  buttonState2 = digitalRead(buttonPin2);
  buttonState3 = digitalRead(buttonPin3);
  buttonState4 = digitalRead(buttonPin4);
  if (buttonState1 == LOW) {     
    analogWrite(E1, 255);   
    analogWrite(E2, 255);

 else if (buttonState2 == LOW) {     
    digitalWrite(M2, LOW);       
    analogWrite(E1, 255);   
    analogWrite(E2, 255);   
 else if (buttonState3 == LOW) {     
 else if (buttonState4 == LOW) {     
  else if (buttonState1 == HIGH &&buttonState2 ==HIGH && buttonState3==HIGH && buttonState4 ==HIGH) {

So basically the motors will be attached to the 2 back wheels of the wheelchair, forward movement will be the 2 motors moving at the same time while left movement will be the right motor moving and vice versa. I tested my code with 6V DC motors and it worked.

The problem now is finding the suitable motor to power a wheelchair, my research has concluded with 24V DC motors that draws 20A from the board. But if I'm not wrong the motor shield only allows up to 2A. My question is : Is there anyway to interface 24V DC motors to my motor shield with the same function as my code and how?

You need motor controllers that can handle the high amperage. Your existing shield will either burn up or shutdown to protect itself. Fortunately many designers have this need and hi amp controllers are readily available from many vendors.

Search 'wheelchair' in this forum and get many hits.

You need dual 20A+ motor controllers - not going to be in shield form! Some of the larger robotics controllers are probably appropriate, as would be a wheelchair controller (unsurprisingly).