I guess you would need to have your own method in your controller to fire up the indexing tool. From what it looks like, you need a few things to get going:

- The classname of the tool i.e `AssetIndex`
- An array of asset sources or `*` for them all
- An indexing session id
- An array of parameters to send to the tool

So I managed to get something working with the following code (this would go in your plugin controller)

    public function actionUpdateIndex()
    {
      // Get the AssetIndex tool
      $tool = craft()->components->getComponentByTypeAndClass(ComponentType::Tool, 'AssetIndex');

      // Generate an AssetIndex session id for us to use
      $sessionId = craft()->assetIndexing->getIndexingSessionId();

      // Set up some params
      $params = array(
        'start' => '1', // Tells the tool this is the initial request
        'sources' => '*', // All of them or [1,2,3] just ids1
      );
      
      // Get an initial response from the tool, will contain an array containing the assets to index
      $response = $tool->performAction($params);

      // See [1]
      foreach($response['batches'] as $key => $value)
      {
        foreach($value as $key => $batch)
        {
           // All the needed params are set in the array to do the index
           $tool->performAction($batch['params']);
        }
      }
      
    }

Each time you call `$tool->performAction($batch['params']);` you will an array back, something like:

    Array
    (
     [success] => 1
    )


--- 

**[1]** Because this is the initial request craft will return an array with a `batches` index, which we then have to do a few loops through, it looks something like this:

    Array
    (
     [batches] => Array
      (
       [0] => Array
        (
         [0] => Array
          (
           [params] => Array
            (
             [sessionId] => 6d08c5ba-169f-4b99-a7bd-cdc26c9428c7
             [sourceId] => 1
             [total] => 12
             [offset] => 0
             [process] => 1
            )

           )

          )

        )

     [total] => 0
    )

Not sure if this is the absolute best way to do it, I was learning as I was going, but this worked for me so hopefully it'll work for you too :)