can't insert data in php poo

To avoid sql injection you should use prepared statements. These come with PDO and are pretty simple to use. Have a look at the following example.

$sql = "
    INSERT INTO 
        usuarios 
        (nombre, apellidos, email, password,role) 
    VALUES
        (:nombre, :apellidos, :email, 'user')
";

$stmt = $this->db->prepare($sql);
$result = $stmt->execute([
    'nombre' => $this->getNombre(),
    'apellidos' => $this->getApellidos(),
    'email' => $this->getEmail()
]);

return $result;

Further more you can wrap the execution of your sql query via PDO in a try/catch block. So if any exception occurs, you can catch it and see, what exactly went wrong.

try {
    // execute your logic here
} catch (PDOException $e) {
    var_dump($e, $this->db->errorInfo());
}

Hope this helps.

Beside that your SQL Syntax got an error. The last comma after rol. Further the error message says, that an entry () for the key uq_email already exists. This kind of exeptions you can catch with the above shown try/catch block.