Mongodb string to date conversion

Below is my sample mongodb collection

{
    "_id" : ObjectId("57ed32f4070577ec56a56b9f"),
    "log_id" : "180308",
    "issue_id" : "108850",
    "author_key" : "priyadarshinim_contus",
    "timespent" : NumberLong(18000),
    "comment" : "Added charts in the dashboard page of the application.",
    "created_on" : "2017-08-16T18:22:04.816+0530",
    "updated_on" : "2017-08-16T18:22:04.816+0530",
    "started_on" : "2017-08-16T18:21:39.000+0530",
    "started_date" : "2017-08-02",
    "updated_date" : "2017-08-02",
    "role" : "PHP",
    "updated_at" : ISODate("2017-09-29T15:27:48.069Z"),
    "created_at" : ISODate("2017-09-29T15:27:48.069Z"),
    "status" : 1.0
}

I need to get record with help of started date , by default I will give two date in that i will check $gt and $lt of started date .

        $current_date =  '2017-08-31';
        $sixmonthfromcurrent ='2017-08-01';

     $worklogs = Worklog::raw ( function ($collection) use ($issue_jira_id, $current_date, $sixmonthfromcurrent) {
     return $collection->aggregate ( [ 
              ['$match' => ['issue_id' => ['$in' => $issue_jira_id],
                          'started_date' => ['$lte' => $current_date,'$gte' => $sixmonthfromcurrent] 
                    ] 
              ],

              ['$group' => ['issue_id' => ['$push' => '$issue_id'],
                          '_id' => ['year' => ['$year' => '$started_date'],
                          'week' => ['$week' => '$started_date'],'resource_key' => '$author_key'],
                          'sum' => array ('$sum' => '$timespent')] 
              ],
              [ '$sort' => ['_id' => 1] 
              ] 
        ] );
     } );

if i run this query am getting this type of error can't convert from BSON type string to Date ,how to rectify this error, Thanks in advance..

via Chebli Mohamed