I think you can avoid manipulating the datepicker manually and instead set the date either by just sending the keys with a today’s date value:
var picker = element(by.model("invoice.fromdate"));
// get today's date
var today = new Date();
var dd = today.getDate();
var mm = today.getMonth()+1; //January is 0!
var yyyy = today.getFullYear();
if(dd<10) {
dd='0'+dd
}
if(mm<10) {
mm='0'+mm
}
today = mm+"https://stackoverflow.com/"+dd+"https://stackoverflow.com/"+yyyy;
picker.clear();
picker.sendKeys(today);
Or, by setting the associated model’s value directly:
picker.evaluate("invoice.fromdate="" + today + """);