Try in the URL doing:

?startDate={!URLENCODE(TEXT(object.Start_date__c))}

in the controller user

Date startDate = Date.valueOf( EncodingUtil.urlDecode( ApexPages.currentPage().getParameters().get('startDate'), 'UTF-8') );

Set this in the URL:

?startDate={!URLENCODE(TEXT(object.Start_date__c))}

and in the controller try this code:

Date startDate =  Date.valueOf( EncodingUtil.urlDecode( ApexPages.currentPage().getParameters().get('startDate'), 'UTF-8') );